[{"Name":"Elementary Properties","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Basic Definitions","Duration":"3m 6s","ChapterTopicVideoID":16865,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16865.jpeg","UploadDate":"2019-02-19T05:31:44.0200000","DurationForVideoObject":"PT3M6S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.740 ","End":"00:03.960","Text":"Hi, today we\u0027re going to talk about"},{"Start":"00:03.960 ","End":"00:07.965","Text":"some basic concepts that we need to start our study of chemistry."},{"Start":"00:07.965 ","End":"00:10.080","Text":"The first one is matter."},{"Start":"00:10.080 ","End":"00:13.500","Text":"Matter is anything that occupies space."},{"Start":"00:13.500 ","End":"00:18.465","Text":"You yourself are composed of matter and everything around you is composed of matter,"},{"Start":"00:18.465 ","End":"00:25.560","Text":"from your cell phone to the foods you eat even the air you breathe is composed of matter."},{"Start":"00:25.560 ","End":"00:29.730","Text":"Although, the particles in it are too small for you to see."},{"Start":"00:29.730 ","End":"00:35.465","Text":"Now, every object consists of matter and has a mass."},{"Start":"00:35.465 ","End":"00:39.305","Text":"The mass tells us how much matter there is in an object."},{"Start":"00:39.305 ","End":"00:41.825","Text":"If there are 2 balls of the same material,"},{"Start":"00:41.825 ","End":"00:44.375","Text":"a small one, and a larger one,"},{"Start":"00:44.375 ","End":"00:49.940","Text":"the larger one will have a greater mass than the smaller one provided,"},{"Start":"00:49.940 ","End":"00:53.645","Text":"of course, they are composed of precisely the same material."},{"Start":"00:53.645 ","End":"00:55.880","Text":"Now, how do we measure mass?"},{"Start":"00:55.880 ","End":"01:05.795","Text":"The way we measure mass is in kilograms and we can write that for short kg."},{"Start":"01:05.795 ","End":"01:08.300","Text":"Now there\u0027s another concept."},{"Start":"01:08.300 ","End":"01:14.389","Text":"This is very often confused with mass and that is weight."},{"Start":"01:14.389 ","End":"01:17.105","Text":"Weight and mass are not the same,"},{"Start":"01:17.105 ","End":"01:20.285","Text":"although very often people assume that they are."},{"Start":"01:20.285 ","End":"01:24.665","Text":"Now the mass of an object is the same wherever it is."},{"Start":"01:24.665 ","End":"01:26.540","Text":"A man will have the same mass,"},{"Start":"01:26.540 ","End":"01:32.270","Text":"whether he is on the Earth or on the moon."},{"Start":"01:32.270 ","End":"01:36.080","Text":"However, he will not have the same weight."},{"Start":"01:36.080 ","End":"01:43.325","Text":"Weight is a force acting on an object due to gravity so the stronger the gravity,"},{"Start":"01:43.325 ","End":"01:45.905","Text":"the greater the weight."},{"Start":"01:45.905 ","End":"01:50.585","Text":"The gravity on the moon is smaller than that on the Earth."},{"Start":"01:50.585 ","End":"01:53.465","Text":"When astronauts go into space,"},{"Start":"01:53.465 ","End":"01:55.655","Text":"they still have the same mass,"},{"Start":"01:55.655 ","End":"02:00.460","Text":"but their weight is only 16 percent of that on Earth."},{"Start":"02:00.460 ","End":"02:05.630","Text":"That\u0027s why the look as if they\u0027re floating because gravity is"},{"Start":"02:05.630 ","End":"02:10.820","Text":"not sufficiently great to stick their feet onto the moon."},{"Start":"02:10.820 ","End":"02:12.815","Text":"Unlike us, when we hop,"},{"Start":"02:12.815 ","End":"02:16.285","Text":"all have our feet solidly on the ground."},{"Start":"02:16.285 ","End":"02:24.335","Text":"Now, every object composed of matter has a particular composition."},{"Start":"02:24.335 ","End":"02:30.575","Text":"The composition of a sample of mater is the quantity of each component in the sample."},{"Start":"02:30.575 ","End":"02:32.450","Text":"Let\u0027s take an example."},{"Start":"02:32.450 ","End":"02:34.640","Text":"Let\u0027s take the example of water."},{"Start":"02:34.640 ","End":"02:41.460","Text":"Water is 89 percent oxygen and 11 percent hydrogen."},{"Start":"02:41.460 ","End":"02:44.180","Text":"It doesn\u0027t matter where the water is,"},{"Start":"02:44.180 ","End":"02:46.235","Text":"whether it\u0027s in a glass,"},{"Start":"02:46.235 ","End":"02:47.780","Text":"or on the moon,"},{"Start":"02:47.780 ","End":"02:49.100","Text":"or on the Earth,"},{"Start":"02:49.100 ","End":"02:54.979","Text":"it will always consist of 89 percent oxygen and 11 percent of hydrogen."},{"Start":"02:54.979 ","End":"03:00.485","Text":"In this video, we\u0027ve talked about matter and about its composition."},{"Start":"03:00.485 ","End":"03:01.790","Text":"In the next video,"},{"Start":"03:01.790 ","End":"03:06.990","Text":"we\u0027ll talk about the physical and chemical properties of matter."}],"ID":17612},{"Watched":false,"Name":"Physical and Chemical Properties","Duration":"3m 50s","ChapterTopicVideoID":16867,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16867.jpeg","UploadDate":"2019-02-19T05:32:18.8030000","DurationForVideoObject":"PT3M50S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.440 ","End":"00:06.375","Text":"In this video, we\u0027re going to discuss how we can distinguish 1 substance from another."},{"Start":"00:06.375 ","End":"00:08.895","Text":"There are 2 properties that can help us to"},{"Start":"00:08.895 ","End":"00:11.595","Text":"tell the difference between different substances,"},{"Start":"00:11.595 ","End":"00:14.595","Text":"physical properties, and chemical properties."},{"Start":"00:14.595 ","End":"00:17.445","Text":"Let\u0027s first consider physical properties."},{"Start":"00:17.445 ","End":"00:20.550","Text":"These are properties such as color, taste,"},{"Start":"00:20.550 ","End":"00:25.125","Text":"and smell, which are not associated with a change in composition."},{"Start":"00:25.125 ","End":"00:27.135","Text":"Let\u0027s take an example."},{"Start":"00:27.135 ","End":"00:28.890","Text":"The example I\u0027ve chosen,"},{"Start":"00:28.890 ","End":"00:31.470","Text":"is orange juice and tomato juice."},{"Start":"00:31.470 ","End":"00:35.280","Text":"Here\u0027s a bottle of orange juice and the bottle of tomato juice."},{"Start":"00:35.280 ","End":"00:41.025","Text":"Of course, we can tell the difference very easily by 2 different colors,"},{"Start":"00:41.025 ","End":"00:44.810","Text":"and of course, they have different tastes and different smells."},{"Start":"00:44.810 ","End":"00:47.135","Text":"What are physical changes?"},{"Start":"00:47.135 ","End":"00:51.860","Text":"Physical changes are changes in the physical properties of a substance,"},{"Start":"00:51.860 ","End":"00:54.260","Text":"without changing its composition."},{"Start":"00:54.260 ","End":"00:55.775","Text":"Let\u0027s take an example."},{"Start":"00:55.775 ","End":"00:57.830","Text":"A very good example of this,"},{"Start":"00:57.830 ","End":"01:00.695","Text":"is a freezing or boiling of water."},{"Start":"01:00.695 ","End":"01:04.340","Text":"Let\u0027s consider the 3 states of water."},{"Start":"01:04.340 ","End":"01:08.780","Text":"We can have ice that\u0027s shown here."},{"Start":"01:08.780 ","End":"01:11.820","Text":"We can have liquid water that\u0027s shown here."},{"Start":"01:11.820 ","End":"01:14.240","Text":"We can have steam that\u0027s shown here."},{"Start":"01:14.240 ","End":"01:17.420","Text":"Now, these are all physical properties of the water."},{"Start":"01:17.420 ","End":"01:23.230","Text":"Now we can change ice into liquid water or liquid water into steam."},{"Start":"01:23.230 ","End":"01:25.590","Text":"For example, freezing,"},{"Start":"01:25.590 ","End":"01:29.000","Text":"we can take liquid water and freeze it,"},{"Start":"01:29.000 ","End":"01:31.556","Text":"get ice, that\u0027s called freezing,"},{"Start":"01:31.556 ","End":"01:35.630","Text":"or we can take liquid water and turn it into steam."},{"Start":"01:35.630 ","End":"01:39.845","Text":"That\u0027s called boiling or evaporation."},{"Start":"01:39.845 ","End":"01:41.735","Text":"We can also do the opposite."},{"Start":"01:41.735 ","End":"01:44.405","Text":"All these processes are reversible."},{"Start":"01:44.405 ","End":"01:47.480","Text":"Instead of turning liquid water into ice,"},{"Start":"01:47.480 ","End":"01:51.845","Text":"we can turn ice into liquid water. That\u0027s melting."},{"Start":"01:51.845 ","End":"01:58.730","Text":"We can turn steam back into liquid water, That\u0027s called condensation."},{"Start":"01:58.730 ","End":"02:03.095","Text":"Sometimes we can turn ice directly into steam,"},{"Start":"02:03.095 ","End":"02:05.970","Text":"and that\u0027s called sublimation."},{"Start":"02:05.970 ","End":"02:10.400","Text":"All these processes are called physical changes."},{"Start":"02:10.400 ","End":"02:15.485","Text":"Freezing, boiling, melting, condensation, sublimation."},{"Start":"02:15.485 ","End":"02:19.495","Text":"Now, let\u0027s consider chemical changes."},{"Start":"02:19.495 ","End":"02:22.286","Text":"This is a little bit more complicated."},{"Start":"02:22.286 ","End":"02:28.385","Text":"We\u0027re going to consider chemical properties and chemical changes at the same time."},{"Start":"02:28.385 ","End":"02:33.035","Text":"Chemical properties are associated with a chemical change."},{"Start":"02:33.035 ","End":"02:34.985","Text":"When we see a chemical change,"},{"Start":"02:34.985 ","End":"02:37.670","Text":"we can talk about a chemical property."},{"Start":"02:37.670 ","End":"02:39.635","Text":"Let\u0027s take an example."},{"Start":"02:39.635 ","End":"02:45.905","Text":"The example I\u0027ve chosen is gold in water and sodium in water."},{"Start":"02:45.905 ","End":"02:51.350","Text":"Here we see gold in water and sodium in water."},{"Start":"02:51.350 ","End":"02:53.525","Text":"What\u0027s the difference between them?"},{"Start":"02:53.525 ","End":"02:56.855","Text":"We can see that the gold does not react with water."},{"Start":"02:56.855 ","End":"02:58.585","Text":"Nothing is happening here."},{"Start":"02:58.585 ","End":"03:00.290","Text":"On the other hand,"},{"Start":"03:00.290 ","End":"03:02.960","Text":"the sodium is reacting with the water,"},{"Start":"03:02.960 ","End":"03:07.070","Text":"producing sodium hydroxide and hydrogen gas."},{"Start":"03:07.070 ","End":"03:10.310","Text":"Sodium usually reacts rather violently with water,"},{"Start":"03:10.310 ","End":"03:15.350","Text":"which is why it\u0027s kept in an oil and not just outside on the shelf."},{"Start":"03:15.350 ","End":"03:17.375","Text":"Now, what can we say about this?"},{"Start":"03:17.375 ","End":"03:22.565","Text":"We can say that the sodium has undergone a chemical change."},{"Start":"03:22.565 ","End":"03:26.510","Text":"The chemical property of sodium is it reacts with water."},{"Start":"03:26.510 ","End":"03:28.160","Text":"On the other hand,"},{"Start":"03:28.160 ","End":"03:33.245","Text":"gold has a chemical property that it does not react with water."},{"Start":"03:33.245 ","End":"03:36.485","Text":"It has not undergone a chemical change,"},{"Start":"03:36.485 ","End":"03:40.655","Text":"so its chemical property does not react with water."},{"Start":"03:40.655 ","End":"03:43.490","Text":"In this video, we have shown that we can distinguish"},{"Start":"03:43.490 ","End":"03:49.860","Text":"1 substance by other\u0027s physical or its chemical properties."}],"ID":17613},{"Watched":false,"Name":"Exercise 1","Duration":"1m 35s","ChapterTopicVideoID":16870,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16870.jpeg","UploadDate":"2019-02-19T05:34:00.0800000","DurationForVideoObject":"PT1M35S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.760","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.760 ","End":"00:06.795","Text":"State whether the following properties are physical or chemical: A,"},{"Start":"00:06.795 ","End":"00:09.225","Text":"liquid water freezes into ice; B,"},{"Start":"00:09.225 ","End":"00:12.120","Text":"zinc reacts with hydrochloric acid solution to produce"},{"Start":"00:12.120 ","End":"00:15.120","Text":"hydrogen gas into a solution of zinc chloride and water;"},{"Start":"00:15.120 ","End":"00:17.280","Text":"C, copper is reddish-brown;"},{"Start":"00:17.280 ","End":"00:20.420","Text":"and D, a bronze statue develops a green coating."},{"Start":"00:20.420 ","End":"00:23.570","Text":"First, we will look at A, liquid water freezes into ice."},{"Start":"00:23.570 ","End":"00:25.370","Text":"When liquid water freezes into ice,"},{"Start":"00:25.370 ","End":"00:26.720","Text":"there is no chemical change."},{"Start":"00:26.720 ","End":"00:30.860","Text":"The water is H2O and the ice stays H2O."},{"Start":"00:30.860 ","End":"00:34.525","Text":"Therefore A is a physical property."},{"Start":"00:34.525 ","End":"00:39.050","Text":"B, zinc reacts with hydrochloric acid solution to produce"},{"Start":"00:39.050 ","End":"00:42.890","Text":"hydrogen gas and a solution of zinc chloride in water."},{"Start":"00:42.890 ","End":"00:45.475","Text":"In the beginning we have zinc, this is B."},{"Start":"00:45.475 ","End":"00:46.850","Text":"In the beginning, we have zinc,"},{"Start":"00:46.850 ","End":"00:47.945","Text":"which is a solid,"},{"Start":"00:47.945 ","End":"00:50.950","Text":"and we have hydrochloric acid,"},{"Start":"00:50.950 ","End":"00:53.415","Text":"which is a solution."},{"Start":"00:53.415 ","End":"00:55.350","Text":"At the end, we get hydrogen,"},{"Start":"00:55.350 ","End":"00:58.130","Text":"which is a gas, and zinc chloride in water,"},{"Start":"00:58.130 ","End":"01:00.180","Text":"which is a solution."},{"Start":"01:03.200 ","End":"01:06.545","Text":"Here you can see a chemical change happened."},{"Start":"01:06.545 ","End":"01:09.810","Text":"Therefore, this is a chemical property."},{"Start":"01:10.010 ","End":"01:14.740","Text":"Now we\u0027re going to solve C. Copper is reddish-brown,"},{"Start":"01:14.740 ","End":"01:17.550","Text":"color is a physical property."},{"Start":"01:18.740 ","End":"01:23.565","Text":"Now we will solve D. A bronze statue develops a green coating."},{"Start":"01:23.565 ","End":"01:26.050","Text":"When a bronze statue develops a green coating,"},{"Start":"01:26.050 ","End":"01:27.830","Text":"this is because of a chemical change,"},{"Start":"01:27.830 ","End":"01:30.440","Text":"for example, oxidation, and therefore,"},{"Start":"01:30.440 ","End":"01:32.590","Text":"this is a chemical property."},{"Start":"01:32.590 ","End":"01:35.650","Text":"Thank you very much for watching."}],"ID":17614},{"Watched":false,"Name":"Exercise 2","Duration":"3m 9s","ChapterTopicVideoID":22829,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22829.jpeg","UploadDate":"2020-12-10T04:05:48.8000000","DurationForVideoObject":"PT3M9S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.465","Text":"Hi, we are going to solve the following exercise."},{"Start":"00:03.465 ","End":"00:07.120","Text":"Express each of the following in decimal form."},{"Start":"00:07.550 ","End":"00:12.970","Text":"We have here a couple of numbers that we have to express in decimal form."},{"Start":"00:13.940 ","End":"00:16.050","Text":"We\u0027re going to begin with a,"},{"Start":"00:16.050 ","End":"00:18.660","Text":"2.78 times 10^negative 3 and"},{"Start":"00:18.660 ","End":"00:26.775","Text":"we need to express this in decimal form."},{"Start":"00:26.775 ","End":"00:29.865","Text":"What we need to do is we need to move the decimal point."},{"Start":"00:29.865 ","End":"00:33.540","Text":"The number of places indicated by the power of 10."},{"Start":"00:33.540 ","End":"00:35.415","Text":"You see here that we have minus 3."},{"Start":"00:35.415 ","End":"00:38.025","Text":"Minus means we can move it to the left,"},{"Start":"00:38.025 ","End":"00:39.360","Text":"and 3 is 3 places."},{"Start":"00:39.360 ","End":"00:40.590","Text":"Meaning, we take the decimal point,"},{"Start":"00:40.590 ","End":"00:42.885","Text":"we move it 1, 2, 3."},{"Start":"00:42.885 ","End":"00:45.895","Text":"The decimal point moves to here."},{"Start":"00:45.895 ","End":"00:49.929","Text":"We fill in with the zeros in places where we don\u0027t have digits,"},{"Start":"00:49.929 ","End":"00:54.090","Text":"so 2.78 times 10^negative 3 equals,"},{"Start":"00:54.090 ","End":"00:56.233","Text":"we can put a 0 in the beginning, we don\u0027t have to."},{"Start":"00:56.233 ","End":"00:58.490","Text":"You see the decimal point comes here."},{"Start":"00:58.490 ","End":"01:01.340","Text":"Now we have 2 places without digits,"},{"Start":"01:01.340 ","End":"01:07.020","Text":"so they will be 0,0 and then 278."},{"Start":"01:07.020 ","End":"01:11.445","Text":"Our answer for a is 0.00278."},{"Start":"01:11.445 ","End":"01:13.080","Text":"Now we\u0027re going to go onto b."},{"Start":"01:13.080 ","End":"01:18.910","Text":"B we have 3,245.9 times 10^negative 5."},{"Start":"01:18.920 ","End":"01:26.730","Text":"Again, 3,245.9 times 10^negative 5."},{"Start":"01:26.730 ","End":"01:29.900","Text":"Again, the minus means we move it to"},{"Start":"01:29.900 ","End":"01:33.770","Text":"the left and the 5 is the number of places that we move the decimal point,"},{"Start":"01:33.770 ","End":"01:36.170","Text":"so 1, 2,"},{"Start":"01:36.170 ","End":"01:38.850","Text":"3, 4, 5."},{"Start":"01:38.850 ","End":"01:40.875","Text":"The decimal point moves here."},{"Start":"01:40.875 ","End":"01:43.200","Text":"Again, this equals 0 point,"},{"Start":"01:43.200 ","End":"01:46.340","Text":"we have one 0 because there are no digits here,"},{"Start":"01:46.340 ","End":"01:53.650","Text":"032459, and that\u0027s our answer for b."},{"Start":"01:53.650 ","End":"02:00.340","Text":"Now, we\u0027re going to go onto c. In c we have 21.4 times 10^negative 2."},{"Start":"02:00.340 ","End":"02:03.584","Text":"Again, we move the decimal point 2 places to the left,"},{"Start":"02:03.584 ","End":"02:10.025","Text":"1,2, so it equals 0.214."},{"Start":"02:10.025 ","End":"02:13.039","Text":"That\u0027s our answer for c. Next,"},{"Start":"02:13.039 ","End":"02:16.550","Text":"we\u0027re going to go onto d. In d,"},{"Start":"02:16.550 ","End":"02:23.135","Text":"we have 5.678 times 10^2."},{"Start":"02:23.135 ","End":"02:26.270","Text":"This time the power is positive, therefore,"},{"Start":"02:26.270 ","End":"02:30.555","Text":"the decimal point will move to the right, not to the left."},{"Start":"02:30.555 ","End":"02:33.170","Text":"We need to move it 2 places, so 1,"},{"Start":"02:33.170 ","End":"02:38.360","Text":"2, this comes to 567.8."},{"Start":"02:38.360 ","End":"02:41.767","Text":"That is our answer for d. Now in e,"},{"Start":"02:41.767 ","End":"02:49.110","Text":"we have 8.2 times 10^third power, 8.2 times 10^3."},{"Start":"02:49.110 ","End":"02:52.730","Text":"Again, we move the decimal point to the right and we move it 3 places,"},{"Start":"02:52.730 ","End":"02:55.070","Text":"1, 2, 3."},{"Start":"02:55.070 ","End":"02:57.860","Text":"We put zeros where we don\u0027t have digits,"},{"Start":"02:57.860 ","End":"03:06.815","Text":"so this comes to 8,200 and that is our answer for e. Those are our final answers."},{"Start":"03:06.815 ","End":"03:09.510","Text":"Thank you very much for watching."}],"ID":23640},{"Watched":false,"Name":"Exercise 3","Duration":"3m 5s","ChapterTopicVideoID":22830,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22830.jpeg","UploadDate":"2020-12-10T04:05:58.8070000","DurationForVideoObject":"PT3M5S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.015","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:03.015 ","End":"00:06.060","Text":"Express each of the following in exponential form."},{"Start":"00:06.060 ","End":"00:09.760","Text":"We\u0027re going to start with a, 4,300."},{"Start":"00:11.900 ","End":"00:16.815","Text":"In order to express a number in exponential form,"},{"Start":"00:16.815 ","End":"00:19.680","Text":"we first need to move the decimal point"},{"Start":"00:19.680 ","End":"00:22.920","Text":"to obtain a coefficient with a value between 1 and 10."},{"Start":"00:22.920 ","End":"00:28.070","Text":"We can do this by placing a decimal point right after the first non-zero digit."},{"Start":"00:28.070 ","End":"00:29.630","Text":"Let\u0027s take an example."},{"Start":"00:29.630 ","End":"00:30.823","Text":"We have 4,300,"},{"Start":"00:30.823 ","End":"00:32.900","Text":"our first non-zero digit is 4."},{"Start":"00:32.900 ","End":"00:34.865","Text":"We\u0027re going to take our decimal point,"},{"Start":"00:34.865 ","End":"00:36.850","Text":"which is here after the second 0,"},{"Start":"00:36.850 ","End":"00:43.115","Text":"and we\u0027re going to move it right after the 4, we get 4.300."},{"Start":"00:43.115 ","End":"00:48.380","Text":"Now it\u0027s .300 since our decimal point before was after the second zero."},{"Start":"00:48.380 ","End":"00:49.568","Text":"We\u0027re going to keep our zeros."},{"Start":"00:49.568 ","End":"00:52.055","Text":"It\u0027s 4.300 times 10,"},{"Start":"00:52.055 ","End":"00:55.460","Text":"now in order to know the power of 10, we can look."},{"Start":"00:55.460 ","End":"00:57.530","Text":"We have our decimal point here before the 3,"},{"Start":"00:57.530 ","End":"00:59.990","Text":"and we want a decimal point to reach after the 0,"},{"Start":"00:59.990 ","End":"01:01.550","Text":"meaning we need to move it to the right,"},{"Start":"01:01.550 ","End":"01:03.725","Text":"3 places, 1, 2, 3."},{"Start":"01:03.725 ","End":"01:05.480","Text":"Therefore, 10 is going to be cubed."},{"Start":"01:05.480 ","End":"01:08.135","Text":"That\u0027s our answer for a."},{"Start":"01:08.135 ","End":"01:14.720","Text":"Now we\u0027re going to go on to b. I b we have 0.00976."},{"Start":"01:14.720 ","End":"01:18.260","Text":"Now again, our first non-zero digit is our 9."},{"Start":"01:18.260 ","End":"01:20.090","Text":"We\u0027re going to put the decimal point after the 9,"},{"Start":"01:20.090 ","End":"01:22.760","Text":"so it\u0027s going to be 9.76,"},{"Start":"01:22.760 ","End":"01:24.815","Text":"everything we have after the 9."},{"Start":"01:24.815 ","End":"01:26.570","Text":"Again, we multiply by 10,"},{"Start":"01:26.570 ","End":"01:29.300","Text":"and to know the power of the 10,"},{"Start":"01:29.300 ","End":"01:30.680","Text":"we look at our decimal point."},{"Start":"01:30.680 ","End":"01:33.650","Text":"We have here the decimal point right after the 9,"},{"Start":"01:33.650 ","End":"01:35.000","Text":"and in our answer,"},{"Start":"01:35.000 ","End":"01:39.920","Text":"we need the decimal point to be 3 places to the left of the 9,"},{"Start":"01:39.920 ","End":"01:43.985","Text":"meaning we\u0027re going to multiply it by 10^-3."},{"Start":"01:43.985 ","End":"01:47.680","Text":"Negative, since we moved the decimal point to the left."},{"Start":"01:47.680 ","End":"01:49.940","Text":"That is our answer for b."},{"Start":"01:49.940 ","End":"01:57.810","Text":"Now we\u0027re going to go on to c. In c we have 56,322."},{"Start":"01:58.990 ","End":"02:01.190","Text":"Again, same as before,"},{"Start":"02:01.190 ","End":"02:03.530","Text":"we\u0027re going to put our decimal point right after our 5."},{"Start":"02:03.530 ","End":"02:07.795","Text":"We have 5.6322,"},{"Start":"02:07.795 ","End":"02:09.570","Text":"and we\u0027re going to multiply this by 10,"},{"Start":"02:09.570 ","End":"02:10.770","Text":"and to know the power of the 10,"},{"Start":"02:10.770 ","End":"02:12.020","Text":"again, we\u0027re going to look at our answer."},{"Start":"02:12.020 ","End":"02:14.960","Text":"We need to move our decimal point 4 places to the right,"},{"Start":"02:14.960 ","End":"02:17.060","Text":"1, 2, 3, 4."},{"Start":"02:17.060 ","End":"02:20.350","Text":"Therefore, it\u0027s going to be 10^4."},{"Start":"02:20.350 ","End":"02:29.350","Text":"That is our answer for c. Now we\u0027re going to look at d. In d we have 724.8."},{"Start":"02:32.860 ","End":"02:39.050","Text":"Again we move our decimal point after the 7, so it\u0027s 7.248."},{"Start":"02:39.050 ","End":"02:43.385","Text":"We\u0027re going to multiply it by 10^2."},{"Start":"02:43.385 ","End":"02:46.970","Text":"Since in our case we need to reach 724.8,"},{"Start":"02:46.970 ","End":"02:51.080","Text":"the decimal point which is after the 7 needs to move to be after the 4."},{"Start":"02:51.080 ","End":"02:53.010","Text":"It\u0027s 1, 2,"},{"Start":"02:53.010 ","End":"03:00.750","Text":"so 2 places to the right, so it\u0027s 10^2."},{"Start":"03:00.750 ","End":"03:02.220","Text":"That\u0027s our answer for d,"},{"Start":"03:02.220 ","End":"03:03.920","Text":"and those are all our answers."},{"Start":"03:03.920 ","End":"03:06.450","Text":"Thank you very much for watching."}],"ID":23641},{"Watched":false,"Name":"Exercise 4","Duration":"5m 23s","ChapterTopicVideoID":22826,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22826.jpeg","UploadDate":"2020-12-10T04:05:09.8670000","DurationForVideoObject":"PT5M23S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.090","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:03.090 ","End":"00:05.865","Text":"How many significant figures are shown in the following?"},{"Start":"00:05.865 ","End":"00:07.980","Text":"Explain. Let\u0027s begin with a."},{"Start":"00:07.980 ","End":"00:11.230","Text":"In a we have 0.0617."},{"Start":"00:14.870 ","End":"00:18.480","Text":"Now we know that non-zero digits are significant,"},{"Start":"00:18.480 ","End":"00:22.395","Text":"and now we have to look at the zeros if they are significant or not."},{"Start":"00:22.395 ","End":"00:27.705","Text":"Here the zeros come to the left of the first non-zero digit,"},{"Start":"00:27.705 ","End":"00:32.510","Text":"and zeros which come to the left of the first non-zero digit are non significant."},{"Start":"00:32.510 ","End":"00:34.700","Text":"Therefore, these zeros are not significant,"},{"Start":"00:34.700 ","End":"00:37.580","Text":"and therefore 6, 1 and 7 are significant."},{"Start":"00:37.580 ","End":"00:46.385","Text":"We have 3 significant numbers so it equals 3 significant numbers since, the reason is,"},{"Start":"00:46.385 ","End":"00:52.719","Text":"that the zeros to the left"},{"Start":"00:55.840 ","End":"00:59.670","Text":"of the first non-zero digits"},{"Start":"01:07.400 ","End":"01:10.690","Text":"are not significant."},{"Start":"01:15.010 ","End":"01:20.440","Text":"Our answer for a is 3 significant figures since the zeros to"},{"Start":"01:20.440 ","End":"01:25.915","Text":"the left of the first non-zero digit are not significant."},{"Start":"01:25.915 ","End":"01:27.850","Text":"Here our first non-zero digit is"},{"Start":"01:27.850 ","End":"01:31.960","Text":"6 and the zeros to the left of the 6 are not significant."},{"Start":"01:31.960 ","End":"01:34.195","Text":"Therefore, we have 3 significant figures."},{"Start":"01:34.195 ","End":"01:39.470","Text":"In b we have a very similar case, we have 0.0089."},{"Start":"01:40.260 ","End":"01:44.935","Text":"Again, we have zeros to the left of the first non-zero digit."},{"Start":"01:44.935 ","End":"01:47.530","Text":"Therefore these zeros are non-significant,"},{"Start":"01:47.530 ","End":"01:51.980","Text":"and therefore we have only 2 significant figures."},{"Start":"01:59.480 ","End":"02:01.930","Text":"In b for the same reason as a,"},{"Start":"02:01.930 ","End":"02:04.475","Text":"we have 2 significant figures."},{"Start":"02:04.475 ","End":"02:09.070","Text":"In c we have 429.52,"},{"Start":"02:11.530 ","End":"02:15.810","Text":"and here we have 5 significant figures."},{"Start":"02:23.340 ","End":"02:26.185","Text":"The reason here is because"},{"Start":"02:26.185 ","End":"02:29.995","Text":"all the non-zero digits are significant and here they are all non-zero digits."},{"Start":"02:29.995 ","End":"02:40.570","Text":"Again, all non-zero digits are significant."},{"Start":"02:44.930 ","End":"02:47.780","Text":"Again our answer for c is 5,"},{"Start":"02:47.780 ","End":"02:51.440","Text":"since all non-zero digits are significant."},{"Start":"02:54.320 ","End":"03:03.480","Text":"Now, we\u0027re going to take a look at d. In d we have 9.035 and,"},{"Start":"03:03.480 ","End":"03:05.970","Text":"in d we have 4 significant figures."},{"Start":"03:05.970 ","End":"03:10.630","Text":"The reason is when we have a 0 which is bound between 2 non-zero digits,"},{"Start":"03:10.630 ","End":"03:12.400","Text":"the 0 is significant,"},{"Start":"03:12.400 ","End":"03:15.775","Text":"so we have 4 significant figures."},{"Start":"03:15.775 ","End":"03:19.960","Text":"Again, for the reason that bound zeros,"},{"Start":"03:19.960 ","End":"03:26.950","Text":"meaning bound between 2 non-zero digits, are significant."},{"Start":"03:31.400 ","End":"03:33.886","Text":"That\u0027s our answer for d, 4,"},{"Start":"03:33.886 ","End":"03:37.405","Text":"since bound zeros are significant."},{"Start":"03:37.405 ","End":"03:40.460","Text":"Now we\u0027re going on to e,"},{"Start":"03:40.460 ","End":"03:43.290","Text":"in e we have 62,000."},{"Start":"03:43.290 ","End":"03:46.850","Text":"Now, in e we don\u0027t know how many significant figures there are"},{"Start":"03:46.850 ","End":"03:49.815","Text":"since we don\u0027t have a decimal point in our number."},{"Start":"03:49.815 ","End":"03:51.615","Text":"Therefore we could have between 2,"},{"Start":"03:51.615 ","End":"03:53.910","Text":"which is the 6 and the 2, two significant figures,"},{"Start":"03:53.910 ","End":"03:56.570","Text":"to 5 because if all of the zeros are significant,"},{"Start":"03:56.570 ","End":"03:58.865","Text":"we would have 5 significant numbers."},{"Start":"03:58.865 ","End":"04:04.625","Text":"Here it\u0027s between 2-5 and we don\u0027t know how many significant figures there are."},{"Start":"04:04.625 ","End":"04:08.730","Text":"Now in f, we have 567.70."},{"Start":"04:10.490 ","End":"04:14.500","Text":"Here we have 5 significant figures."},{"Start":"04:20.380 ","End":"04:23.630","Text":"Because if we look at the 0 at the end of the number,"},{"Start":"04:23.630 ","End":"04:27.980","Text":"when we have a 0 at the end of the number to the right of the decimal point like here,"},{"Start":"04:27.980 ","End":"04:29.690","Text":"0 is significant, therefore,"},{"Start":"04:29.690 ","End":"04:34.540","Text":"we have 5 significant figures."},{"Start":"04:34.800 ","End":"04:43.790","Text":"Zeros at the end of a number"},{"Start":"04:45.900 ","End":"04:52.060","Text":"to the right of"},{"Start":"04:52.060 ","End":"04:59.960","Text":"a decimal place are significant."},{"Start":"05:04.760 ","End":"05:10.230","Text":"These are answers for e and"},{"Start":"05:10.230 ","End":"05:11.710","Text":"f."},{"Start":"05:19.700 ","End":"05:21.810","Text":"Those are our final answers"},{"Start":"05:21.810 ","End":"05:24.370","Text":"thank you very much for watching."}],"ID":23637},{"Watched":false,"Name":"Exercise 5","Duration":"3m 16s","ChapterTopicVideoID":22827,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22827.jpeg","UploadDate":"2020-12-10T04:05:19.1370000","DurationForVideoObject":"PT3M16S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.150","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:03.150 ","End":"00:06.765","Text":"Express each of the following numbers to three significant figures."},{"Start":"00:06.765 ","End":"00:10.570","Text":"We\u0027re going to start with a. In a we have 27,000."},{"Start":"00:11.240 ","End":"00:16.365","Text":"In order to express this number to three significant figures,"},{"Start":"00:16.365 ","End":"00:19.795","Text":"we\u0027re going to write the exponential form of the number."},{"Start":"00:19.795 ","End":"00:23.580","Text":"In the coefficient we\u0027re going to have three significant numbers,"},{"Start":"00:23.580 ","End":"00:27.690","Text":"meaning 2.70 times 10."},{"Start":"00:27.690 ","End":"00:31.245","Text":"Now we need to get to 27,000."},{"Start":"00:31.245 ","End":"00:34.970","Text":"We\u0027re going to multiply it by 10^4."},{"Start":"00:34.970 ","End":"00:38.540","Text":"The coefficient contains three significant numbers and we"},{"Start":"00:38.540 ","End":"00:43.220","Text":"multiply it by 10^4 we\u0027ll get the number, 27,000."},{"Start":"00:43.220 ","End":"00:47.520","Text":"Now in b we have, 276.3."},{"Start":"00:50.210 ","End":"00:53.690","Text":"Again, we have to round this to three significant numbers,"},{"Start":"00:53.690 ","End":"00:56.945","Text":"meaning the 3 first numbers which are 276."},{"Start":"00:56.945 ","End":"01:01.580","Text":"In order to know if to round the 6 off to 5 or 7."},{"Start":"01:01.580 ","End":"01:04.700","Text":"We look at the number that\u0027s after the decimal point."},{"Start":"01:04.700 ","End":"01:08.805","Text":"We have a 3, 3 is smaller than 5, therefore,"},{"Start":"01:08.805 ","End":"01:10.470","Text":"we round downwards,"},{"Start":"01:10.470 ","End":"01:15.235","Text":"so 276.3 is going to equal 276."},{"Start":"01:15.235 ","End":"01:17.505","Text":"Again, because the 3 is smaller than 5."},{"Start":"01:17.505 ","End":"01:19.970","Text":"If 3 was 5 or higher,"},{"Start":"01:19.970 ","End":"01:23.060","Text":"we would round up and the number would be 277."},{"Start":"01:23.060 ","End":"01:26.880","Text":"Now in C we have 53.07."},{"Start":"01:29.320 ","End":"01:32.330","Text":"Again, we want to round this off to three numbers,"},{"Start":"01:32.330 ","End":"01:35.855","Text":"so 53 are two numbers point."},{"Start":"01:35.855 ","End":"01:39.305","Text":"Now we\u0027re going to have one number after the point,"},{"Start":"01:39.305 ","End":"01:41.300","Text":"and this number is going to be 1, since again,"},{"Start":"01:41.300 ","End":"01:44.350","Text":"7 is greater than 5 so we round upwards."},{"Start":"01:44.350 ","End":"01:48.090","Text":"The zero is rounded off to 1."},{"Start":"01:48.090 ","End":"01:51.780","Text":"The .07 is rounded off to .1."},{"Start":"01:51.780 ","End":"02:02.680","Text":"In d we have 8.977 times 10^4."},{"Start":"02:02.680 ","End":"02:05.665","Text":"Since we want to round this off to three significant numbers,"},{"Start":"02:05.665 ","End":"02:07.150","Text":"we\u0027re going to take our coefficient,"},{"Start":"02:07.150 ","End":"02:14.235","Text":"which is 8.9777 and round it off to three significant figures, so it\u0027s 8.98."},{"Start":"02:14.235 ","End":"02:17.685","Text":"Again, since the 7 is greater than 5,"},{"Start":"02:17.685 ","End":"02:22.510","Text":"we round upwards, times 10^4."},{"Start":"02:24.170 ","End":"02:27.310","Text":"Now in e we have,"},{"Start":"02:29.510 ","End":"02:32.945","Text":"0.05467, and again,"},{"Start":"02:32.945 ","End":"02:36.625","Text":"we need to round this off to three significant figures."},{"Start":"02:36.625 ","End":"02:41.780","Text":"The zeros to the left of the 5 are not significant."},{"Start":"02:41.780 ","End":"02:48.030","Text":"We don\u0027t count them in, so it\u0027s 0.0 and 3 significant figures are 5 4."},{"Start":"02:49.190 ","End":"02:52.140","Text":"Again, since the 7 is greater than 5,"},{"Start":"02:52.140 ","End":"02:55.005","Text":"we round upwards, so 0.0547."},{"Start":"02:55.005 ","End":"02:58.695","Text":"Our answer for a is 2.70 times 10^4,"},{"Start":"02:58.695 ","End":"03:01.680","Text":"our answer for b is 276,"},{"Start":"03:01.680 ","End":"03:04.395","Text":"our answer for c is 53.1,"},{"Start":"03:04.395 ","End":"03:07.710","Text":"our answer for d is 8.98 times 10^4,"},{"Start":"03:07.710 ","End":"03:12.250","Text":"and our answer for e is 0.0547."},{"Start":"03:12.250 ","End":"03:16.320","Text":"Those are our answers. Thank you very much for watching."}],"ID":23638},{"Watched":false,"Name":"Exercise 6","Duration":"7m 8s","ChapterTopicVideoID":22828,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/22828.jpeg","UploadDate":"2020-12-10T04:05:39.5330000","DurationForVideoObject":"PT7M8S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.580","Text":"Hi, we\u0027re going to solve the following exercise."},{"Start":"00:02.580 ","End":"00:04.800","Text":"Calculate each of the following and express"},{"Start":"00:04.800 ","End":"00:08.220","Text":"the answers with the appropriate number of significant numbers."},{"Start":"00:08.220 ","End":"00:10.035","Text":"Let\u0027s take a look at A."},{"Start":"00:10.035 ","End":"00:14.550","Text":"We have 0.7382 times 0.0035."},{"Start":"00:14.550 ","End":"00:17.340","Text":"Here we have a multiplication."},{"Start":"00:17.340 ","End":"00:21.825","Text":"Now I just want to remind you that when we have a multiplication or division,"},{"Start":"00:21.825 ","End":"00:25.725","Text":"the result of the multiplication or the division may contain"},{"Start":"00:25.725 ","End":"00:27.810","Text":"only as many significant figures as"},{"Start":"00:27.810 ","End":"00:30.735","Text":"the least precisely known quantity in the calculation."},{"Start":"00:30.735 ","End":"00:32.520","Text":"If we look at our first number,"},{"Start":"00:32.520 ","End":"00:34.350","Text":"we have 0.7382,"},{"Start":"00:34.350 ","End":"00:37.005","Text":"this contains 4 significant figures."},{"Start":"00:37.005 ","End":"00:42.090","Text":"In our second number, 0.0035 contains only 2 significant figures."},{"Start":"00:42.090 ","End":"00:48.650","Text":"Since remember the zeros that come before the first non-zero digit are not significant,"},{"Start":"00:48.650 ","End":"00:50.630","Text":"so here we have only 2 significant figures,"},{"Start":"00:50.630 ","End":"00:52.580","Text":"meaning that the result of"},{"Start":"00:52.580 ","End":"00:57.000","Text":"our multiplication is going to contain only 2 significant figures."},{"Start":"00:57.000 ","End":"01:07.450","Text":"After multiplying, the result in the calculator gives us 2.5837 times 10^-3,"},{"Start":"01:07.450 ","End":"01:09.515","Text":"that\u0027s the result in our calculator."},{"Start":"01:09.515 ","End":"01:14.360","Text":"Since we said that we have to have 2 significant figures in our result,"},{"Start":"01:14.360 ","End":"01:16.340","Text":"we\u0027re going to take the 2 first digits,"},{"Start":"01:16.340 ","End":"01:19.785","Text":"so it\u0027s 2., here we\u0027re going to round off to 6,"},{"Start":"01:19.785 ","End":"01:24.720","Text":"since the 8 is greater than a 5 times 10^-3."},{"Start":"01:24.720 ","End":"01:27.620","Text":"That\u0027s the result of our multiplication."},{"Start":"01:27.620 ","End":"01:31.925","Text":"That\u0027s our answer for a 2.6 times 10^-3."},{"Start":"01:31.925 ","End":"01:34.980","Text":"We\u0027re going to go onto B."},{"Start":"01:35.510 ","End":"01:39.045","Text":"In B we have addition and subtraction."},{"Start":"01:39.045 ","End":"01:40.680","Text":"In addition and subtraction,"},{"Start":"01:40.680 ","End":"01:41.990","Text":"we have a different case."},{"Start":"01:41.990 ","End":"01:45.740","Text":"In this case, the result must be expressed with the same number of digits"},{"Start":"01:45.740 ","End":"01:50.405","Text":"beyond the decimal point as the quantity carrying the smallest number of such digits."},{"Start":"01:50.405 ","End":"01:52.310","Text":"Meaning if we look at our numbers,"},{"Start":"01:52.310 ","End":"01:56.645","Text":"we can see that in 0.23 we have 2 digits after the decimal point."},{"Start":"01:56.645 ","End":"02:01.070","Text":"In 12.692 we have 3 digits after the decimal point and"},{"Start":"02:01.070 ","End":"02:05.930","Text":"in 0.075 we also have 3 digits after the decimal point."},{"Start":"02:05.930 ","End":"02:09.710","Text":"We can see the number with the smallest number of digits is 0.23,"},{"Start":"02:09.710 ","End":"02:12.230","Text":"meaning after the decimal point in our results,"},{"Start":"02:12.230 ","End":"02:15.175","Text":"we\u0027re going to have 2 numbers."},{"Start":"02:15.175 ","End":"02:16.970","Text":"Again from the calculator,"},{"Start":"02:16.970 ","End":"02:21.365","Text":"the results that I received is 12.847."},{"Start":"02:21.365 ","End":"02:24.304","Text":"But as we said, since we have here addition and subtraction,"},{"Start":"02:24.304 ","End":"02:28.355","Text":"we\u0027re going to have to have 2 digits after the decimal point,"},{"Start":"02:28.355 ","End":"02:31.095","Text":"meaning we need to round this off."},{"Start":"02:31.095 ","End":"02:32.400","Text":"This is going to be rounded off to"},{"Start":"02:32.400 ","End":"02:41.355","Text":"12.85 and the 4 is rounded off to a 5 since the 7 is greater than a 5."},{"Start":"02:41.355 ","End":"02:44.800","Text":"Our answer for B is 12.85."},{"Start":"02:45.380 ","End":"02:47.960","Text":"Now we\u0027re going on to C. In C again,"},{"Start":"02:47.960 ","End":"02:50.180","Text":"we have multiplication and division."},{"Start":"02:50.180 ","End":"02:53.720","Text":"First of all, we\u0027re going to calculate this on"},{"Start":"02:53.720 ","End":"03:04.610","Text":"our calculator and the result that I got with the calculator is 32,623.84."},{"Start":"03:04.610 ","End":"03:06.890","Text":"That\u0027s the results I got with a calculator."},{"Start":"03:06.890 ","End":"03:08.990","Text":"However, if we look at our significant figures,"},{"Start":"03:08.990 ","End":"03:11.210","Text":"since we have multiplication and division here,"},{"Start":"03:11.210 ","End":"03:15.955","Text":"our first number 45.82 contains 4 significant figures."},{"Start":"03:15.955 ","End":"03:20.625","Text":"Our second number, 35.6 contains 3 significant numbers."},{"Start":"03:20.625 ","End":"03:25.350","Text":"The third number 0.050 contains only 2 significant numbers,"},{"Start":"03:25.350 ","End":"03:30.485","Text":"meaning our result needs to contain 2 significant figures."},{"Start":"03:30.485 ","End":"03:33.410","Text":"We\u0027re going to change this to exponential form."},{"Start":"03:33.410 ","End":"03:41.375","Text":"We\u0027re going to keep a 3.3 since we need 2 significant figures times 10 to the,"},{"Start":"03:41.375 ","End":"03:44.855","Text":"let\u0027s see how much we need to move our decimal point by 1,"},{"Start":"03:44.855 ","End":"03:46.745","Text":"2, 3, 4."},{"Start":"03:46.745 ","End":"03:50.330","Text":"It\u0027s times 10^4."},{"Start":"03:50.330 ","End":"03:56.330","Text":"3.3 times 10^4 is our answer for C. Now,"},{"Start":"03:56.330 ","End":"03:59.440","Text":"we\u0027re going on to D. In D,"},{"Start":"03:59.440 ","End":"04:05.220","Text":"we also have addition and subtraction and we also have division."},{"Start":"04:05.220 ","End":"04:09.289","Text":"First of all, we\u0027re going to calculate this in our calculator."},{"Start":"04:09.289 ","End":"04:18.590","Text":"The answer from our calculator the result is 0.274283872."},{"Start":"04:18.590 ","End":"04:20.494","Text":"That\u0027s the result in our calculator."},{"Start":"04:20.494 ","End":"04:23.060","Text":"Now if we look at our equation,"},{"Start":"04:23.060 ","End":"04:26.030","Text":"we can see that in the numerator and the denominator,"},{"Start":"04:26.030 ","End":"04:27.544","Text":"we\u0027ve got addition and subtraction,"},{"Start":"04:27.544 ","End":"04:29.225","Text":"and between them we have division."},{"Start":"04:29.225 ","End":"04:31.370","Text":"Now, if we look at our numerator,"},{"Start":"04:31.370 ","End":"04:34.295","Text":"we have 2.345 plus 0.6329."},{"Start":"04:34.295 ","End":"04:40.385","Text":"Just going to write this here, 2.9779."},{"Start":"04:40.385 ","End":"04:43.910","Text":"However, in addition, and subtraction,"},{"Start":"04:43.910 ","End":"04:48.020","Text":"the number of digits after the decimal point are what counts."},{"Start":"04:48.020 ","End":"04:49.910","Text":"Since we have, in our first number,"},{"Start":"04:49.910 ","End":"04:52.505","Text":"3 numbers after the decimal point."},{"Start":"04:52.505 ","End":"04:56.555","Text":"In our second number, we have 4 numbers after the decimal point."},{"Start":"04:56.555 ","End":"05:00.260","Text":"We have to keep the least number of numbers after the decimal point,"},{"Start":"05:00.260 ","End":"05:03.460","Text":"meaning 3 numbers after the decimal point,"},{"Start":"05:03.460 ","End":"05:11.205","Text":"2.9779 is going to become 2.978 when you round it off."},{"Start":"05:11.205 ","End":"05:17.480","Text":"This way we have 3 digits after the decimal point, just like in our first number."},{"Start":"05:17.480 ","End":"05:20.870","Text":"Now, this is going to be divided by the denominator,"},{"Start":"05:20.870 ","End":"05:24.910","Text":"and the denominator just to know how many significant figures we have to keep."},{"Start":"05:24.910 ","End":"05:30.875","Text":"The result in the calculator equals 10.857."},{"Start":"05:30.875 ","End":"05:35.235","Text":"However, again, we\u0027re doing addition subtraction"},{"Start":"05:35.235 ","End":"05:42.500","Text":"and the number of digits after the decimal point will need to be 1 number,"},{"Start":"05:42.500 ","End":"05:45.425","Text":"so its going to be 10.9."},{"Start":"05:45.425 ","End":"05:47.525","Text":"Since again, we have 3 numbers,"},{"Start":"05:47.525 ","End":"05:51.110","Text":"and the first one we have 1 digit after the decimal point."},{"Start":"05:51.110 ","End":"05:53.450","Text":"In the second one, we have 2 digits after the decimal point."},{"Start":"05:53.450 ","End":"05:55.730","Text":"In the third, we have 3 digits after the decimal point,"},{"Start":"05:55.730 ","End":"05:59.090","Text":"and we need the least number of digits after the decimal point, so it\u0027s going to be 1."},{"Start":"05:59.090 ","End":"06:02.975","Text":"Now, if we look here, we can see that in the numerator we have 4 significant figures."},{"Start":"06:02.975 ","End":"06:06.545","Text":"In the denominator, we have 3 significant figures."},{"Start":"06:06.545 ","End":"06:08.720","Text":"In division and multiplication,"},{"Start":"06:08.720 ","End":"06:11.090","Text":"we need to keep the least number of significant figures."},{"Start":"06:11.090 ","End":"06:14.510","Text":"We need 3 significant figures in our results."},{"Start":"06:14.510 ","End":"06:22.420","Text":"The result that we got into the calculator is going to be rounded off to 0.274."},{"Start":"06:22.420 ","End":"06:24.660","Text":"That\u0027s going to be our answer."},{"Start":"06:24.660 ","End":"06:27.585","Text":"Now I want to go over this again."},{"Start":"06:27.585 ","End":"06:33.470","Text":"In D, we have an equation which contains also addition and subtraction,"},{"Start":"06:33.470 ","End":"06:35.495","Text":"and also contains division."},{"Start":"06:35.495 ","End":"06:37.700","Text":"The first thing we do is calculate this in"},{"Start":"06:37.700 ","End":"06:40.850","Text":"our calculator and achieve the results and write it down."},{"Start":"06:40.850 ","End":"06:43.340","Text":"The second thing we do is to decide"},{"Start":"06:43.340 ","End":"06:46.295","Text":"how many significant figures we need to keep in our result."},{"Start":"06:46.295 ","End":"06:52.805","Text":"For this case, we calculated the addition and subtraction individually."},{"Start":"06:52.805 ","End":"06:57.170","Text":"Then we round it off to the number of significant figures, what we needed to."},{"Start":"06:57.170 ","End":"07:04.355","Text":"In this way, we decided how many significant figures are needed in our result."},{"Start":"07:04.355 ","End":"07:06.320","Text":"These are our final answers."},{"Start":"07:06.320 ","End":"07:09.030","Text":"Thank you very much for listening."}],"ID":23639},{"Watched":false,"Name":"Elements and Compounds","Duration":"2m 55s","ChapterTopicVideoID":16866,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16866.jpeg","UploadDate":"2019-02-19T05:31:58.3830000","DurationForVideoObject":"PT2M55S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.650 ","End":"00:06.015","Text":"In this video, we\u0027re going to talk about elements and compounds."},{"Start":"00:06.015 ","End":"00:08.325","Text":"Let\u0027s first consider elements."},{"Start":"00:08.325 ","End":"00:12.329","Text":"An element consists of a collection of identical atoms."},{"Start":"00:12.329 ","End":"00:16.530","Text":"For example, all the atoms in iron are identical"},{"Start":"00:16.530 ","End":"00:20.915","Text":"to each other and all the atoms in gold are identical to each other."},{"Start":"00:20.915 ","End":"00:24.515","Text":"But the atoms of iron are quite different from those of gold."},{"Start":"00:24.515 ","End":"00:25.640","Text":"Later in the course,"},{"Start":"00:25.640 ","End":"00:27.124","Text":"we\u0027ll talk about the difference,"},{"Start":"00:27.124 ","End":"00:30.875","Text":"precise difference between the atoms of different elements."},{"Start":"00:30.875 ","End":"00:35.955","Text":"Now let\u0027s consider compounds, chemical compounds."},{"Start":"00:35.955 ","End":"00:40.310","Text":"A chemical compound consists of at least 2 elements."},{"Start":"00:40.310 ","End":"00:43.880","Text":"For example, let\u0027s take the example of water."},{"Start":"00:43.880 ","End":"00:46.955","Text":"Water consists of 2 elements,"},{"Start":"00:46.955 ","End":"00:50.870","Text":"hydrogen, hydrogen, and oxygen."},{"Start":"00:50.870 ","End":"00:55.505","Text":"The basic unit in a compound is called a molecule."},{"Start":"00:55.505 ","End":"00:58.430","Text":"Molecules consists of atoms."},{"Start":"00:58.430 ","End":"01:02.780","Text":"For example, each molecule of water"},{"Start":"01:02.780 ","End":"01:09.455","Text":"consists of 2 atoms of hydrogen and 1 atom of oxygen,"},{"Start":"01:09.455 ","End":"01:11.960","Text":"and we can write that as H_2_O."},{"Start":"01:11.960 ","End":"01:14.210","Text":"There are other ways of writing this."},{"Start":"01:14.210 ","End":"01:18.410","Text":"For example, we can use this picture where we have"},{"Start":"01:18.410 ","End":"01:24.995","Text":"a central oxygen indicated by the letter O and 2 hydrogens,"},{"Start":"01:24.995 ","End":"01:26.300","Text":"1 in each side,"},{"Start":"01:26.300 ","End":"01:32.570","Text":"indicated by the letter H. The central oxygen is bonded to the hydrogen,"},{"Start":"01:32.570 ","End":"01:34.565","Text":"bonded to another hydrogen,"},{"Start":"01:34.565 ","End":"01:36.500","Text":"and there\u0027s an angle between them."},{"Start":"01:36.500 ","End":"01:39.830","Text":"We can also consider another way of looking at it."},{"Start":"01:39.830 ","End":"01:42.770","Text":"It is called a space-filling model,"},{"Start":"01:42.770 ","End":"01:49.190","Text":"in which we see that the central oxygen is"},{"Start":"01:49.190 ","End":"01:56.660","Text":"represented by big red ball and the hydrogens by 2 small white balls."},{"Start":"01:56.660 ","End":"01:59.600","Text":"This just shows us that oxygen is much,"},{"Start":"01:59.600 ","End":"02:04.955","Text":"much bigger than hydrogen and that the 2 are attached to each other."},{"Start":"02:04.955 ","End":"02:07.415","Text":"Now, these are very simple molecules."},{"Start":"02:07.415 ","End":"02:11.105","Text":"Sometimes we have much more complicated models."},{"Start":"02:11.105 ","End":"02:15.440","Text":"For example, biological molecules."},{"Start":"02:15.440 ","End":"02:18.755","Text":"Biological molecules are very large."},{"Start":"02:18.755 ","End":"02:20.495","Text":"Here\u0027s an example of 1."},{"Start":"02:20.495 ","End":"02:24.410","Text":"Each of these tiny little balls is an atom."},{"Start":"02:24.410 ","End":"02:27.890","Text":"We see this enormous number of balls."},{"Start":"02:27.890 ","End":"02:33.830","Text":"Biological molecule can consist of tens of thousands of atoms."},{"Start":"02:33.830 ","End":"02:35.430","Text":"Now in this video,"},{"Start":"02:35.430 ","End":"02:40.535","Text":"we\u0027ve shown that an element consists of just 1 sort of atom,"},{"Start":"02:40.535 ","End":"02:44.410","Text":"whereas a molecule consists of more than 1 sort of atom."},{"Start":"02:44.410 ","End":"02:45.860","Text":"So in this video,"},{"Start":"02:45.860 ","End":"02:49.685","Text":"we have shown that an element consists of 1 sort of atom,"},{"Start":"02:49.685 ","End":"02:55.110","Text":"whereas a compound consist of more than 1 sort of atom."}],"ID":17615},{"Watched":false,"Name":"Separation of Matter","Duration":"6m 46s","ChapterTopicVideoID":16868,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16868.jpeg","UploadDate":"2019-02-19T05:33:07.8100000","DurationForVideoObject":"PT6M46S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.140 ","End":"00:04.560","Text":"Today we\u0027re going to talk about the separation of matter."},{"Start":"00:04.560 ","End":"00:09.900","Text":"The first question we\u0027re going to ask is the sample we have a substance,"},{"Start":"00:09.900 ","End":"00:11.880","Text":"a single pure substance,"},{"Start":"00:11.880 ","End":"00:14.010","Text":"or a mixture of substances."},{"Start":"00:14.010 ","End":"00:16.470","Text":"Here we have it in the diagram."},{"Start":"00:16.470 ","End":"00:22.920","Text":"Here\u0027s matter, if we can separate it into more than 1 substance,"},{"Start":"00:22.920 ","End":"00:24.480","Text":"then its a mixture."},{"Start":"00:24.480 ","End":"00:28.260","Text":"If we can\u0027t separate it into more than 1 substance,"},{"Start":"00:28.260 ","End":"00:30.600","Text":"then it is a pure substance."},{"Start":"00:30.600 ","End":"00:32.250","Text":"The question we ask is,"},{"Start":"00:32.250 ","End":"00:34.665","Text":"can it be separated physically?"},{"Start":"00:34.665 ","End":"00:41.925","Text":"Let\u0027s take an example and the example we\u0027re going to consider is pure water,"},{"Start":"00:41.925 ","End":"00:44.010","Text":"which is a pure substance,"},{"Start":"00:44.010 ","End":"00:48.125","Text":"and salty water, which is a mixture of salt and water."},{"Start":"00:48.125 ","End":"00:51.755","Text":"Let\u0027s consider these 2 substances."},{"Start":"00:51.755 ","End":"00:55.460","Text":"In 1 case we have water,"},{"Start":"00:55.460 ","End":"00:59.000","Text":"the other case we have salty water."},{"Start":"00:59.000 ","End":"01:01.205","Text":"Now they both look the same."},{"Start":"01:01.205 ","End":"01:06.485","Text":"You can\u0027t tell by looking at them whether it\u0027s pure water or salty water."},{"Start":"01:06.485 ","End":"01:08.450","Text":"How could we tell the difference?"},{"Start":"01:08.450 ","End":"01:10.465","Text":"Well, if we were to heat them,"},{"Start":"01:10.465 ","End":"01:12.730","Text":"here\u0027s a Bunsen burner,"},{"Start":"01:12.730 ","End":"01:16.550","Text":"not commonly used in many labs nowadays."},{"Start":"01:16.550 ","End":"01:17.920","Text":"If we heat them,"},{"Start":"01:17.920 ","End":"01:25.230","Text":"all the water here will evaporate and what will be left with is just an empty container."},{"Start":"01:25.230 ","End":"01:27.110","Text":"Whereas in this case,"},{"Start":"01:27.110 ","End":"01:33.020","Text":"the water will evaporate and we\u0027ll be left with a residue of salt on the bottom."},{"Start":"01:33.020 ","End":"01:40.980","Text":"Then we can say we physically separated the salt from the water."},{"Start":"01:41.110 ","End":"01:48.005","Text":"Now let\u0027s consider 2 examples of separation methods."},{"Start":"01:48.005 ","End":"01:52.655","Text":"Here we\u0027re having examples of physical separation methods."},{"Start":"01:52.655 ","End":"01:55.955","Text":"Later we\u0027ll talk about chemical separation methods."},{"Start":"01:55.955 ","End":"01:59.785","Text":"The first 1 we\u0027re going to consider is filtration."},{"Start":"01:59.785 ","End":"02:04.610","Text":"I\u0027m going to consider the filtration of sand and water."},{"Start":"02:04.610 ","End":"02:14.330","Text":"Here we have it. We have a filter in a filter funnel with special filter paper inside."},{"Start":"02:14.330 ","End":"02:19.280","Text":"We put into the funnel our mixture of sand and water."},{"Start":"02:19.280 ","End":"02:27.275","Text":"The water drips down through the paper into the container and the sand is left behind."},{"Start":"02:27.275 ","End":"02:32.810","Text":"We\u0027ve effectively separated sand and water."},{"Start":"02:32.810 ","End":"02:35.405","Text":"That process is called filtration."},{"Start":"02:35.405 ","End":"02:41.830","Text":"Another possibility, another separation method is distillation."},{"Start":"02:41.830 ","End":"02:46.265","Text":"Here we\u0027re going to consider distillation of water and alcohol."},{"Start":"02:46.265 ","End":"02:48.770","Text":"Here\u0027s our distillation apparatus."},{"Start":"02:48.770 ","End":"02:51.300","Text":"In this bowl here,"},{"Start":"02:51.310 ","End":"02:56.255","Text":"we have alcohol and water mixture."},{"Start":"02:56.255 ","End":"02:57.810","Text":"Now we\u0027re heating it,"},{"Start":"02:57.810 ","End":"02:59.570","Text":"this is a heating element."},{"Start":"02:59.570 ","End":"03:03.725","Text":"The alcohol boils at a lower temperature than the water,"},{"Start":"03:03.725 ","End":"03:10.075","Text":"so it evaporates first and goes up as a gas up into this tube."},{"Start":"03:10.075 ","End":"03:16.685","Text":"Then it\u0027s forced down this tube and as we circulate cold water round about it,"},{"Start":"03:16.685 ","End":"03:18.935","Text":"it turns into liquid water,"},{"Start":"03:18.935 ","End":"03:22.125","Text":"which drips into the container."},{"Start":"03:22.125 ","End":"03:27.560","Text":"Effectively, we\u0027ve separated our alcohol and water."},{"Start":"03:27.560 ","End":"03:29.570","Text":"If you go to a distillery,"},{"Start":"03:29.570 ","End":"03:32.420","Text":"you\u0027ll see that they do this social process many,"},{"Start":"03:32.420 ","End":"03:35.970","Text":"many times until they get almost pure alcohol."},{"Start":"03:35.970 ","End":"03:37.995","Text":"The next question we\u0027re going to ask,"},{"Start":"03:37.995 ","End":"03:42.320","Text":"is a pure substance a compound or an element?"},{"Start":"03:42.320 ","End":"03:44.285","Text":"In a previous video,"},{"Start":"03:44.285 ","End":"03:48.230","Text":"we discussed the difference between a compound and an element."},{"Start":"03:48.230 ","End":"03:50.224","Text":"An element you\u0027ll remember,"},{"Start":"03:50.224 ","End":"03:52.805","Text":"consists only 1 atom,"},{"Start":"03:52.805 ","End":"03:57.755","Text":"whereas the compound consists of more than 1 element."},{"Start":"03:57.755 ","End":"03:59.985","Text":"Here we have a diagram."},{"Start":"03:59.985 ","End":"04:02.235","Text":"Here\u0027s our substance."},{"Start":"04:02.235 ","End":"04:06.695","Text":"The question is it a compound or is it an element?"},{"Start":"04:06.695 ","End":"04:12.800","Text":"The way we can separate them is by decomposing them chemically."},{"Start":"04:12.800 ","End":"04:15.280","Text":"If they can be decomposed,"},{"Start":"04:15.280 ","End":"04:16.530","Text":"then we have a compound,"},{"Start":"04:16.530 ","End":"04:18.410","Text":"we have more than 1 element."},{"Start":"04:18.410 ","End":"04:20.750","Text":"If it cannot be decomposed,"},{"Start":"04:20.750 ","End":"04:22.625","Text":"then it\u0027s a single element."},{"Start":"04:22.625 ","End":"04:29.835","Text":"The next question we\u0027re going to consider is the mixture homogeneous or heterogeneous?"},{"Start":"04:29.835 ","End":"04:32.175","Text":"We have a mixture,"},{"Start":"04:32.175 ","End":"04:36.455","Text":"we want to know whether it\u0027s homogeneous or heterogeneous."},{"Start":"04:36.455 ","End":"04:40.970","Text":"First of all, we have to know what the differences between homogeneous and heterogeneous."},{"Start":"04:40.970 ","End":"04:44.030","Text":"The differences is homogeneous looks the same"},{"Start":"04:44.030 ","End":"04:49.130","Text":"throughout and heterogeneous has different areas look different."},{"Start":"04:49.130 ","End":"04:53.000","Text":"We\u0027re considering whether we have something that is uniform."},{"Start":"04:53.000 ","End":"04:54.949","Text":"Is the mixture uniform?"},{"Start":"04:54.949 ","End":"04:57.440","Text":"If it is, it\u0027s homogeneous,"},{"Start":"04:57.440 ","End":"04:59.660","Text":"if it isn\u0027t, it\u0027s heterogeneous."},{"Start":"04:59.660 ","End":"05:01.895","Text":"Let\u0027s take some examples."},{"Start":"05:01.895 ","End":"05:05.470","Text":"Let\u0027s first consider a homogeneous mixture."},{"Start":"05:05.470 ","End":"05:09.590","Text":"The example we\u0027re going to take is once again,"},{"Start":"05:09.590 ","End":"05:11.780","Text":"salt dissolved in water."},{"Start":"05:11.780 ","End":"05:15.605","Text":"Now if you have a container with salt in water,"},{"Start":"05:15.605 ","End":"05:18.935","Text":"it looks just the same regardless of where you look."},{"Start":"05:18.935 ","End":"05:20.500","Text":"If I look at this area,"},{"Start":"05:20.500 ","End":"05:23.380","Text":"or this area, it will be just the same,"},{"Start":"05:23.380 ","End":"05:25.045","Text":"it just looks like water."},{"Start":"05:25.045 ","End":"05:28.035","Text":"This is a homogeneous mixture."},{"Start":"05:28.035 ","End":"05:31.085","Text":"Now let\u0027s consider a heterogeneous mixture."},{"Start":"05:31.085 ","End":"05:35.100","Text":"The example we\u0027re going to consider, this milk."},{"Start":"05:35.620 ","End":"05:39.905","Text":"Now you may not have thought of milk has a heterogeneous mixture."},{"Start":"05:39.905 ","End":"05:41.930","Text":"Let\u0027s see how it is."},{"Start":"05:41.930 ","End":"05:44.530","Text":"Here we have milk,"},{"Start":"05:44.530 ","End":"05:49.145","Text":"if I take a sample of this milk under a microscope,"},{"Start":"05:49.145 ","End":"05:55.295","Text":"what we will see is that it\u0027s not just not uniform like water,"},{"Start":"05:55.295 ","End":"06:04.155","Text":"has little globules of fat moving around and so it\u0027s really heterogeneous."},{"Start":"06:04.155 ","End":"06:07.530","Text":"Nowadays, most milk is homogenized,"},{"Start":"06:07.530 ","End":"06:11.060","Text":"you\u0027ll see that on the carton that it\u0027s homogenized."},{"Start":"06:11.060 ","End":"06:20.030","Text":"All that means is the little globules of fat have been broken up into even smaller ones."},{"Start":"06:20.030 ","End":"06:22.880","Text":"It looks as if with the naked eye,"},{"Start":"06:22.880 ","End":"06:24.920","Text":"as if it\u0027s uniform,"},{"Start":"06:24.920 ","End":"06:26.480","Text":"but in fact it isn\u0027t."},{"Start":"06:26.480 ","End":"06:30.110","Text":"If we look at a microscope we\u0027ll see that it isn\u0027t at all"},{"Start":"06:30.110 ","End":"06:35.525","Text":"uniform and there are tiny of globules of fat floating around."},{"Start":"06:35.525 ","End":"06:37.850","Text":"In this video, we\u0027ve talked about"},{"Start":"06:37.850 ","End":"06:40.400","Text":"the difference between a pure substance and a mixture of"},{"Start":"06:40.400 ","End":"06:46.260","Text":"substances and how to separate a mixture into its components.tt11"}],"ID":17616},{"Watched":false,"Name":"States of Matter","Duration":"1m 12s","ChapterTopicVideoID":16869,"CourseChapterTopicPlaylistID":99000,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16869.jpeg","UploadDate":"2019-02-19T05:33:16.2400000","DurationForVideoObject":"PT1M12S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:04.320","Text":"In this video, we\u0027re going to talk about 3 states of matter,"},{"Start":"00:04.320 ","End":"00:07.620","Text":"solid, liquid, and gas."},{"Start":"00:07.620 ","End":"00:09.885","Text":"There are 3 common states of matter,"},{"Start":"00:09.885 ","End":"00:11.880","Text":"solid, liquid and gas."},{"Start":"00:11.880 ","End":"00:18.450","Text":"The important thing is that each change in state is called a phase change."},{"Start":"00:18.450 ","End":"00:20.250","Text":"Let\u0027s take an example."},{"Start":"00:20.250 ","End":"00:22.860","Text":"Example we consider is water."},{"Start":"00:22.860 ","End":"00:25.570","Text":"We have considered this before."},{"Start":"00:25.640 ","End":"00:29.310","Text":"Here are the 3 states of matter of water."},{"Start":"00:29.310 ","End":"00:32.325","Text":"We have ice, which is solid,"},{"Start":"00:32.325 ","End":"00:33.960","Text":"we have liquid water,"},{"Start":"00:33.960 ","End":"00:35.310","Text":"which is liquid,"},{"Start":"00:35.310 ","End":"00:38.045","Text":"and we have steam, which is a gas."},{"Start":"00:38.045 ","End":"00:41.840","Text":"Now each change in state is called a phase change."},{"Start":"00:41.840 ","End":"00:44.570","Text":"We go from a solid to a gas,"},{"Start":"00:44.570 ","End":"00:47.885","Text":"or backwards from a gas to a solid,"},{"Start":"00:47.885 ","End":"00:49.415","Text":"that\u0027s a phase change."},{"Start":"00:49.415 ","End":"00:53.000","Text":"If we go from a gas to liquid or liquid to a gas,"},{"Start":"00:53.000 ","End":"00:54.635","Text":"it\u0027s also phase change,"},{"Start":"00:54.635 ","End":"00:59.550","Text":"and if we go from a liquid to a solid or vice versa,"},{"Start":"00:59.550 ","End":"01:01.530","Text":"that\u0027s also phase change."},{"Start":"01:01.530 ","End":"01:03.469","Text":"Is a very important concept,"},{"Start":"01:03.469 ","End":"01:06.425","Text":"which we\u0027ll see later on in the course."},{"Start":"01:06.425 ","End":"01:12.180","Text":"In this video, we\u0027ve talked about phase changes and the 3 states of matter."}],"ID":17617}],"Thumbnail":null,"ID":99000},{"Name":"Basic Tools For Calculations","TopicPlaylistFirstVideoID":0,"Duration":null,"Videos":[{"Watched":false,"Name":"Basic Units in Chemistry","Duration":"10m 50s","ChapterTopicVideoID":16871,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16871.jpeg","UploadDate":"2019-02-19T05:33:39.0170000","DurationForVideoObject":"PT10M50S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.320 ","End":"00:03.930","Text":"Hello. Today we\u0027re going to talk about"},{"Start":"00:03.930 ","End":"00:08.430","Text":"chemistry and how the units commonly used in chemistry."},{"Start":"00:08.430 ","End":"00:11.310","Text":"What system to chemists use?"},{"Start":"00:11.310 ","End":"00:14.280","Text":"Chemists typically use the metric system."},{"Start":"00:14.280 ","End":"00:19.250","Text":"Metric system is used throughout the world and it\u0027s based on powers of 10,"},{"Start":"00:19.250 ","End":"00:22.080","Text":"based on 10 is the basic unit."},{"Start":"00:22.080 ","End":"00:27.270","Text":"The system that chemists use is Systeme Internationale."},{"Start":"00:27.270 ","End":"00:32.910","Text":"That is French for international system and abbreviated as SI."},{"Start":"00:32.910 ","End":"00:37.254","Text":"We talk about SI units."},{"Start":"00:37.254 ","End":"00:39.890","Text":"Now, there are quite a number of these units."},{"Start":"00:39.890 ","End":"00:42.770","Text":"But today we\u0027re only going to discuss a few of them,"},{"Start":"00:42.770 ","End":"00:45.170","Text":"those commonly used by chemists."},{"Start":"00:45.170 ","End":"00:48.695","Text":"The first one we\u0027re going to talk about is the length."},{"Start":"00:48.695 ","End":"00:51.235","Text":"The length is a physical property."},{"Start":"00:51.235 ","End":"00:55.350","Text":"It\u0027s basic unit is meter."},{"Start":"00:55.350 ","End":"01:01.845","Text":"The symbol use to write meter is m. As well as length,"},{"Start":"01:01.845 ","End":"01:04.250","Text":"we might want to talk about mass."},{"Start":"01:04.250 ","End":"01:06.110","Text":"Here\u0027s the mass."},{"Start":"01:06.110 ","End":"01:10.045","Text":"The basic unit of mass is kilograms."},{"Start":"01:10.045 ","End":"01:11.925","Text":"How do we write that?"},{"Start":"01:11.925 ","End":"01:15.790","Text":"In short we use the user symbol kg."},{"Start":"01:16.490 ","End":"01:19.970","Text":"You\u0027re all familiar with that."},{"Start":"01:19.970 ","End":"01:21.955","Text":"Now, in addition to length and mass,"},{"Start":"01:21.955 ","End":"01:26.945","Text":"other common physical property that we like to talk about is time."},{"Start":"01:26.945 ","End":"01:29.190","Text":"Here we have time."},{"Start":"01:29.190 ","End":"01:32.485","Text":"Now, what units might we use to express time?"},{"Start":"01:32.485 ","End":"01:35.680","Text":"The units we usually use are seconds."},{"Start":"01:35.680 ","End":"01:38.080","Text":"Of course, we can talk about minutes and hours,"},{"Start":"01:38.080 ","End":"01:40.704","Text":"but they\u0027re all related easily to seconds."},{"Start":"01:40.704 ","End":"01:44.485","Text":"Then we write second as s,"},{"Start":"01:44.485 ","End":"01:47.652","Text":"not sec, just s. Now,"},{"Start":"01:47.652 ","End":"01:52.915","Text":"another two units which are less familiar to you,"},{"Start":"01:52.915 ","End":"01:56.035","Text":"but which are very useful are"},{"Start":"01:56.035 ","End":"02:00.435","Text":"the unit used to measure temperature and that\u0027s called Kelvin."},{"Start":"02:00.435 ","End":"02:02.033","Text":"In the SI system,"},{"Start":"02:02.033 ","End":"02:04.820","Text":"the unit of temperature is Kelvin."},{"Start":"02:04.820 ","End":"02:07.055","Text":"You\u0027re probably not familiar with it."},{"Start":"02:07.055 ","End":"02:10.790","Text":"We\u0027ll show later that it\u0027s similar to degrees Celsius."},{"Start":"02:10.790 ","End":"02:13.580","Text":"It\u0027s related closely to degrees Celsius."},{"Start":"02:13.580 ","End":"02:16.970","Text":"The way we write it is K,"},{"Start":"02:16.970 ","End":"02:24.455","Text":"not degrees K, just K. We\u0027ll talk about this in great detail when we talk about gases."},{"Start":"02:24.455 ","End":"02:28.475","Text":"Now, another unit which you\u0027re probably even less familiar"},{"Start":"02:28.475 ","End":"02:34.235","Text":"with is the one used for the amount of substance and that\u0027s called a mole,"},{"Start":"02:34.235 ","End":"02:36.455","Text":"just like the furry animal."},{"Start":"02:36.455 ","End":"02:39.195","Text":"It\u0027s written mol. Now,"},{"Start":"02:39.195 ","End":"02:42.720","Text":"we\u0027ll talk about that in great detail later in"},{"Start":"02:42.720 ","End":"02:46.823","Text":"the course and you\u0027ll have to be very familiar with it."},{"Start":"02:46.823 ","End":"02:48.990","Text":"We\u0027ve used the units, meter,"},{"Start":"02:48.990 ","End":"02:52.275","Text":"kilogram, second, Kelvin, mol."},{"Start":"02:52.275 ","End":"02:57.410","Text":"Now, meters, kilograms and seconds are written MKS."},{"Start":"02:57.410 ","End":"03:03.390","Text":"We can write that as m for meter,"},{"Start":"03:03.390 ","End":"03:08.830","Text":"k for kilogram and s for second,"},{"Start":"03:08.830 ","End":"03:14.220","Text":"called the MKS system or units."},{"Start":"03:14.220 ","End":"03:18.210","Text":"Now, sometimes we want a whole lot of"},{"Start":"03:18.210 ","End":"03:23.180","Text":"meters or we want a whole lot of kilograms or a whole lot of seconds."},{"Start":"03:23.180 ","End":"03:26.300","Text":"We sometimes have very large numbers"},{"Start":"03:26.300 ","End":"03:29.810","Text":"and we want a very convenient way of expressing them."},{"Start":"03:29.810 ","End":"03:33.955","Text":"Let\u0027s take a very large number like a million."},{"Start":"03:33.955 ","End":"03:38.220","Text":"You all know that we can write that as 10^6."},{"Start":"03:38.650 ","End":"03:43.130","Text":"A million is written as 10^6."},{"Start":"03:43.130 ","End":"03:48.710","Text":"We\u0027re going to see that there is a nice prefix that we can attach to the meter,"},{"Start":"03:48.710 ","End":"03:51.725","Text":"for example, that will express this."},{"Start":"03:51.725 ","End":"03:55.384","Text":"We\u0027ll see that 10^6 is called mega."},{"Start":"03:55.384 ","End":"03:58.670","Text":"Mega if it\u0027s a meter is 10^6 meters."},{"Start":"03:58.670 ","End":"04:00.827","Text":"We\u0027ll write it as megameter."},{"Start":"04:00.827 ","End":"04:05.675","Text":"Now, sometimes we have very small numbers,"},{"Start":"04:05.675 ","End":"04:08.479","Text":"like a millionth of something."},{"Start":"04:08.479 ","End":"04:11.590","Text":"That\u0027s 10^-6."},{"Start":"04:11.590 ","End":"04:20.190","Text":"I hope you remember that 10^-6 is just 1 divided by 10^6."},{"Start":"04:20.190 ","End":"04:26.310","Text":"Sometimes we have these very small numbers and we need some prefix,"},{"Start":"04:26.310 ","End":"04:33.280","Text":"some name that we can use to express this very small number, 10^-6."},{"Start":"04:33.280 ","End":"04:36.110","Text":"We\u0027ll see in a few minutes that the way we call"},{"Start":"04:36.110 ","End":"04:44.756","Text":"that micrometer and we write it Mu m. The Greek letter, Mu."},{"Start":"04:44.756 ","End":"04:46.595","Text":"Here we call this mega,"},{"Start":"04:46.595 ","End":"04:50.312","Text":"M, m for meter."},{"Start":"04:50.312 ","End":"04:55.595","Text":"What are these prefixes that we can use?"},{"Start":"04:55.595 ","End":"04:58.055","Text":"Now, there are many of them,"},{"Start":"04:58.055 ","End":"05:00.970","Text":"but we\u0027re not going to write all of them,"},{"Start":"05:00.970 ","End":"05:04.055","Text":"just the ones that we\u0027re going to use in this course."},{"Start":"05:04.055 ","End":"05:07.388","Text":"For example, something that\u0027s very large,"},{"Start":"05:07.388 ","End":"05:12.450","Text":"10^9 that\u0027s 1000 times 1,000,000."},{"Start":"05:12.450 ","End":"05:17.605","Text":"If you had money like that,"},{"Start":"05:17.605 ","End":"05:23.360","Text":"if you would have so much money you\u0027d be called a billionaire."},{"Start":"05:23.360 ","End":"05:26.360","Text":"But in chemistry we call it giga."},{"Start":"05:26.360 ","End":"05:31.265","Text":"You could have giga dollars that will make you a billionaire."},{"Start":"05:31.265 ","End":"05:35.570","Text":"We call it giga and we abbreviate it by this"},{"Start":"05:35.570 ","End":"05:43.050","Text":"G. Then the next one you might be familiar with this from gigabytes."},{"Start":"05:43.050 ","End":"05:45.720","Text":"In computers we talk about gigabytes."},{"Start":"05:45.720 ","End":"05:47.795","Text":"You\u0027re probably familiar with that."},{"Start":"05:47.795 ","End":"05:52.661","Text":"The next one we\u0027re going to talk about is 10^6."},{"Start":"05:52.661 ","End":"05:54.630","Text":"That\u0027s 1,000,000."},{"Start":"05:54.630 ","End":"05:57.394","Text":"That we write as mega."},{"Start":"05:57.394 ","End":"06:06.230","Text":"We call that mega and abbreviate it as a M. Where might you be familiar with this?"},{"Start":"06:06.230 ","End":"06:08.300","Text":"You might be familiar with this from computers."},{"Start":"06:08.300 ","End":"06:12.433","Text":"We talked about megabytes."},{"Start":"06:12.433 ","End":"06:17.435","Text":"The next one is kilo,"},{"Start":"06:17.435 ","End":"06:19.160","Text":"10^3, that\u0027s 1,000."},{"Start":"06:19.160 ","End":"06:26.730","Text":"A thousand kilos is a kilo and we express it as small k. We might"},{"Start":"06:26.730 ","End":"06:36.705","Text":"have 1,000 grams and 1,000 grams is a kilogram."},{"Start":"06:36.705 ","End":"06:42.580","Text":"A thousand meters is a kilometer."},{"Start":"06:45.590 ","End":"06:49.705","Text":"Centi, we get to very small numbers."},{"Start":"06:49.705 ","End":"06:53.247","Text":"Here they were all powers much bigger than one."},{"Start":"06:53.247 ","End":"06:55.840","Text":"Now, we\u0027re getting a part of one."},{"Start":"06:55.840 ","End":"06:58.670","Text":"The first one we\u0027re going to meet is called centi."},{"Start":"06:58.670 ","End":"07:01.580","Text":"That\u0027s 10^-2."},{"Start":"07:01.790 ","End":"07:10.773","Text":"This is not strictly an SI unit because SI units generally go in the powers of 3,"},{"Start":"07:10.773 ","End":"07:16.870","Text":"like 10^9, 10^6,"},{"Start":"07:16.870 ","End":"07:21.385","Text":"10^3, 10^-3, 10^-6,10^-9,10^-12 This is a bit of an odd man out, but very useful."},{"Start":"07:21.385 ","End":"07:23.365","Text":"It\u0027s called centi."},{"Start":"07:23.365 ","End":"07:25.090","Text":"10^-2 is called centi."},{"Start":"07:25.090 ","End":"07:32.120","Text":"We\u0027ll write it as c. You\u0027re all very familiar with the centimeter."},{"Start":"07:32.120 ","End":"07:39.360","Text":"We know that the centimeter is 0.01 of a meter."},{"Start":"07:39.360 ","End":"07:41.250","Text":"Now, even smaller than that,"},{"Start":"07:41.250 ","End":"07:47.795","Text":"and again a proper SI unit is 10^-3, that\u0027s milli."},{"Start":"07:47.795 ","End":"07:54.950","Text":"We\u0027ll call that milli and write it as m. Then you\u0027re pretty familiar with millimeters."},{"Start":"07:54.950 ","End":"07:56.240","Text":"What\u0027s a millimeter?"},{"Start":"07:56.240 ","End":"07:59.955","Text":"0.001 of a meter."},{"Start":"07:59.955 ","End":"08:02.730","Text":"That\u0027s quite a common unit."},{"Start":"08:02.730 ","End":"08:04.475","Text":"You\u0027ve all heard of it."},{"Start":"08:04.475 ","End":"08:09.993","Text":"But even smaller than that by a factor of 1,000 is 10^-6."},{"Start":"08:09.993 ","End":"08:14.955","Text":"10^-6 is smaller by a factor of 1,000 than 10^-3."},{"Start":"08:14.955 ","End":"08:22.260","Text":"It\u0027s called micro and written with the Greek letter, Mu."},{"Start":"08:22.260 ","End":"08:24.080","Text":"How might we write that?"},{"Start":"08:24.080 ","End":"08:26.360","Text":"We write it for its meters,"},{"Start":"08:26.360 ","End":"08:30.120","Text":"micrometers or micrograms."},{"Start":"08:30.120 ","End":"08:34.310","Text":"That is 10^-6."},{"Start":"08:34.310 ","End":"08:38.086","Text":"It\u0027s 0.000001."},{"Start":"08:38.086 ","End":"08:41.870","Text":"These are all units you\u0027re familiar with."},{"Start":"08:41.870 ","End":"08:46.910","Text":"Then we can get to something even smaller, 10^-9."},{"Start":"08:46.910 ","End":"08:50.855","Text":"That\u0027s 1,000 times smaller than 10^-6."},{"Start":"08:50.855 ","End":"08:52.280","Text":"It\u0027s called nano."},{"Start":"08:52.280 ","End":"08:55.340","Text":"We\u0027ve all heard of nanotechnology,"},{"Start":"08:55.340 ","End":"08:58.115","Text":"nano science, and so on."},{"Start":"08:58.115 ","End":"09:02.735","Text":"In the university where I work as in many other universities,"},{"Start":"09:02.735 ","End":"09:08.135","Text":"people dealing with nanoscience occupy the largest, tallest building."},{"Start":"09:08.135 ","End":"09:12.365","Text":"Nanoscientists can often be in large buildings."},{"Start":"09:12.365 ","End":"09:15.290","Text":"Nano, nanometer here."},{"Start":"09:15.290 ","End":"09:18.020","Text":"Now, can we write how many zeros that is?"},{"Start":"09:18.020 ","End":"09:27.005","Text":"That\u0027s an awful lot of zeros, 0.000000007."},{"Start":"09:27.005 ","End":"09:30.640","Text":"It\u0027s very small."},{"Start":"09:30.640 ","End":"09:37.200","Text":"But even smaller by a power of 1000 is this 10^-12."},{"Start":"09:37.200 ","End":"09:39.915","Text":"10^-12 is a 1,000 of 10^-9."},{"Start":"09:39.915 ","End":"09:43.110","Text":"It\u0027s called pico, which is the Italian for something"},{"Start":"09:43.110 ","End":"09:47.895","Text":"small and abbreviated p. When might we use this?"},{"Start":"09:47.895 ","End":"09:49.725","Text":"We\u0027ll use this later on the course,"},{"Start":"09:49.725 ","End":"09:55.550","Text":"picometers we\u0027ll use when we\u0027re trying to talk about the lengths of chemical bonds."},{"Start":"09:55.550 ","End":"09:58.610","Text":"We might say that the length of a particular chemical bond is,"},{"Start":"09:58.610 ","End":"10:02.570","Text":"for example, 123 picometers."},{"Start":"10:02.570 ","End":"10:09.432","Text":"We could just say it is 0.123 nanometers,"},{"Start":"10:09.432 ","End":"10:14.630","Text":"but many people prefer to use numbers without the decimal point."},{"Start":"10:14.630 ","End":"10:17.555","Text":"They call it 123 picometers,"},{"Start":"10:17.555 ","End":"10:22.035","Text":"which is just the same as 0.123 nanometers."},{"Start":"10:22.035 ","End":"10:25.604","Text":"That\u0027s all we\u0027re going to say at the moment about these units."},{"Start":"10:25.604 ","End":"10:28.595","Text":"We\u0027ll meet other units later on."},{"Start":"10:28.595 ","End":"10:34.475","Text":"What we will do in another movie is show how to convert one to the other."},{"Start":"10:34.475 ","End":"10:41.180","Text":"For example, how would one convert picometers to gigameters or some such thing?"},{"Start":"10:41.180 ","End":"10:43.175","Text":"How do we do conversions?"},{"Start":"10:43.175 ","End":"10:49.890","Text":"That is very important chemistry and we\u0027ll meet that in the next movie. Bye."}],"ID":17618},{"Watched":false,"Name":"Conversion Factors","Duration":"9m 24s","ChapterTopicVideoID":16872,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16872.jpeg","UploadDate":"2019-02-19T05:34:28.0000000","DurationForVideoObject":"PT9M24S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.680 ","End":"00:03.375","Text":"Hi, in this movie,"},{"Start":"00:03.375 ","End":"00:06.315","Text":"we\u0027re going to talk about conversion factors."},{"Start":"00:06.315 ","End":"00:10.650","Text":"This help us to solve problems and get the correct units."},{"Start":"00:10.650 ","End":"00:13.020","Text":"Why do we need the correct units?"},{"Start":"00:13.020 ","End":"00:16.140","Text":"For example, we can solve a problem,"},{"Start":"00:16.140 ","End":"00:18.255","Text":"and get the answer 10."},{"Start":"00:18.255 ","End":"00:20.520","Text":"Now, if it\u0027s a distance,"},{"Start":"00:20.520 ","End":"00:29.025","Text":"it\u0027s important whether it\u0027s 10 meters or 10 kilometers."},{"Start":"00:29.025 ","End":"00:31.210","Text":"First, you should run 10."},{"Start":"00:31.210 ","End":"00:37.115","Text":"You\u0027ll be concerned to know whether it\u0027s 10 meters or 10 kilometers."},{"Start":"00:37.115 ","End":"00:39.830","Text":"Now, here\u0027s our example."},{"Start":"00:39.830 ","End":"00:46.205","Text":"Supposing we want to convert 7 kilometers to meters."},{"Start":"00:46.205 ","End":"00:47.810","Text":"Now, you\u0027ll all say,"},{"Start":"00:47.810 ","End":"00:51.340","Text":"\"Well that\u0027s very easy,\" as indeed it is."},{"Start":"00:51.340 ","End":"00:57.730","Text":"You\u0027ll recall that 1 kilometer is indeed 1,000 meters."},{"Start":"00:57.730 ","End":"01:08.265","Text":"Then, it\u0027s very easy to write that 7 kilometers is equal to 7 times 1,000 meters,"},{"Start":"01:08.265 ","End":"01:13.370","Text":"which is equal to 7,000 meters."},{"Start":"01:13.370 ","End":"01:15.115","Text":"Very simple."},{"Start":"01:15.115 ","End":"01:18.640","Text":"But often things are not quite so simple,"},{"Start":"01:18.640 ","End":"01:21.905","Text":"and it\u0027s not quite so obvious what to do."},{"Start":"01:21.905 ","End":"01:25.765","Text":"In order to help us when it\u0027s not really very obvious,"},{"Start":"01:25.765 ","End":"01:28.704","Text":"we\u0027re going to use conversion factors."},{"Start":"01:28.704 ","End":"01:30.745","Text":"What\u0027s a conversion factor?"},{"Start":"01:30.745 ","End":"01:32.620","Text":"Here we have an example,"},{"Start":"01:32.620 ","End":"01:36.880","Text":"1,000 meters is exactly the same as 1 kilometer."},{"Start":"01:36.880 ","End":"01:40.840","Text":"We write it as a ratio, as a factor,"},{"Start":"01:40.840 ","End":"01:44.530","Text":"1,000 meters divided by 1 kilometer equal to 1,"},{"Start":"01:44.530 ","End":"01:48.475","Text":"or 1 kilometer divided by 1,000 meters is equals to1."},{"Start":"01:48.475 ","End":"01:53.350","Text":"Sometimes you need this way up and sometimes you need upside down."},{"Start":"01:53.350 ","End":"01:55.765","Text":"But these are always equal to 1."},{"Start":"01:55.765 ","End":"01:57.460","Text":"Anything, like 1,000,"},{"Start":"01:57.460 ","End":"01:58.720","Text":"and we multiply it by 1,"},{"Start":"01:58.720 ","End":"02:00.040","Text":"it stays a 1,000."},{"Start":"02:00.040 ","End":"02:01.480","Text":"If I divide by 1,"},{"Start":"02:01.480 ","End":"02:03.280","Text":"it also stays 1,000."},{"Start":"02:03.280 ","End":"02:06.265","Text":"We can introduce 1 anywhere we want,"},{"Start":"02:06.265 ","End":"02:08.275","Text":"anywhere where it\u0027s convenient."},{"Start":"02:08.275 ","End":"02:13.525","Text":"Now how will we convert 7 kilometers to meters?"},{"Start":"02:13.525 ","End":"02:16.960","Text":"We\u0027ll do it using our conversion factor,"},{"Start":"02:16.960 ","End":"02:19.087","Text":"using these factors here."},{"Start":"02:19.087 ","End":"02:20.395","Text":"What will we do?"},{"Start":"02:20.395 ","End":"02:25.125","Text":"We\u0027ll write 7 kilometers equal to 7 kilometers."},{"Start":"02:25.125 ","End":"02:27.190","Text":"That\u0027s pretty obvious."},{"Start":"02:27.190 ","End":"02:29.905","Text":"Then we\u0027ll introduce our conversion factor."},{"Start":"02:29.905 ","End":"02:33.495","Text":"Here it is, we\u0027re taking this conversion factor, putting it here."},{"Start":"02:33.495 ","End":"02:36.050","Text":"Now, why are we putting it this way?"},{"Start":"02:36.050 ","End":"02:39.214","Text":"Because we want to get rid of the kilometers,"},{"Start":"02:39.214 ","End":"02:41.675","Text":"and to have only meters left."},{"Start":"02:41.675 ","End":"02:44.270","Text":"If we write it this way,"},{"Start":"02:44.270 ","End":"02:46.350","Text":"we have 7 times 1,000,"},{"Start":"02:46.350 ","End":"02:49.520","Text":"that\u0027s 7,000, but what about the units?"},{"Start":"02:49.520 ","End":"02:54.020","Text":"We have kilometers in the numerator and kilometers in the denominator."},{"Start":"02:54.020 ","End":"02:56.210","Text":"So we can score those out."},{"Start":"02:56.210 ","End":"02:59.300","Text":"The only units we\u0027re left with is meters."},{"Start":"02:59.300 ","End":"03:03.190","Text":"We have 7 times 1,000 equals 7,000 meters."},{"Start":"03:03.190 ","End":"03:04.940","Text":"This is very simple."},{"Start":"03:04.940 ","End":"03:10.235","Text":"But supposing we want to do something more complicated."},{"Start":"03:10.235 ","End":"03:12.785","Text":"Supposing, as often happens,"},{"Start":"03:12.785 ","End":"03:15.520","Text":"we have more than 1 conversion factor."},{"Start":"03:15.520 ","End":"03:20.180","Text":"Sometimes we have to change the units more than once in a problem."},{"Start":"03:20.180 ","End":"03:26.315","Text":"Then it\u0027s a good idea to have more than 1 unit to see how to do it."},{"Start":"03:26.315 ","End":"03:27.830","Text":"In order to do this,"},{"Start":"03:27.830 ","End":"03:32.120","Text":"we\u0027re going to take a unit that we haven\u0027t introduced before."},{"Start":"03:32.120 ","End":"03:36.615","Text":"It\u0027s not an SI unit, non-SI unit,"},{"Start":"03:36.615 ","End":"03:39.285","Text":"an it\u0027s the one you know very well,"},{"Start":"03:39.285 ","End":"03:40.965","Text":"a unit that you know very well,"},{"Start":"03:40.965 ","End":"03:44.040","Text":"called a liter, 1 liter."},{"Start":"03:44.040 ","End":"03:45.660","Text":"1 liter of milk,"},{"Start":"03:45.660 ","End":"03:47.690","Text":"1 liter of Coca-Cola."},{"Start":"03:47.690 ","End":"03:52.315","Text":"We can buy things in bottles that contain 1 liter."},{"Start":"03:52.315 ","End":"03:57.035","Text":"Now, 1 liter, it\u0027s official definition is that"},{"Start":"03:57.035 ","End":"04:01.700","Text":"1 liter is equal to 1,000 centimeters cubed."},{"Start":"04:01.700 ","End":"04:05.074","Text":"In a moment, we\u0027ll discuss what\u0027s a centimeter cube."},{"Start":"04:05.074 ","End":"04:07.070","Text":"Bear with me at the moment,"},{"Start":"04:07.070 ","End":"04:09.290","Text":"it\u0027s 1,000 centimeter cubed."},{"Start":"04:09.290 ","End":"04:12.875","Text":"Of course, it\u0027s 1,000 milliliters as well."},{"Start":"04:12.875 ","End":"04:15.710","Text":"How do you know this is 1,000 milliliters?"},{"Start":"04:15.710 ","End":"04:19.515","Text":"Because you know that 1 milliliter"},{"Start":"04:19.515 ","End":"04:26.366","Text":"is 1/1,000 of a liter."},{"Start":"04:26.366 ","End":"04:33.420","Text":"Obviously, 1,000 milliliters is equal to 1 liter."},{"Start":"04:33.580 ","End":"04:36.095","Text":"Here we have, again,"},{"Start":"04:36.095 ","End":"04:39.845","Text":"1 liter, we write it as capital L,"},{"Start":"04:39.845 ","End":"04:42.440","Text":"is equal to 1,000 milliliter,"},{"Start":"04:42.440 ","End":"04:46.385","Text":"and that\u0027s equal to 1,000 centimeters cubed."},{"Start":"04:46.385 ","End":"04:48.860","Text":"Now, what\u0027s a centimeter cubed?"},{"Start":"04:48.860 ","End":"04:53.330","Text":"A centimeter cube is just a little cube where"},{"Start":"04:53.330 ","End":"05:00.050","Text":"every side of it has the unit of 1 centimeter."},{"Start":"05:00.050 ","End":"05:03.935","Text":"Every cube, has 1 centimeter on each side,"},{"Start":"05:03.935 ","End":"05:08.220","Text":"so that its volume is 1 centimeter cubed."},{"Start":"05:09.380 ","End":"05:13.230","Text":"We can say that,"},{"Start":"05:13.230 ","End":"05:14.700","Text":"go back here,"},{"Start":"05:14.700 ","End":"05:18.575","Text":"if 1 liter is 1,000 centimeters cubed,"},{"Start":"05:18.575 ","End":"05:21.935","Text":"and 1,000 milliliters is 1,000 centimeters cubed,"},{"Start":"05:21.935 ","End":"05:27.860","Text":"we can write that 1 centimeter cubed is just 1 milliliter."},{"Start":"05:27.860 ","End":"05:30.290","Text":"We\u0027ll often use this conversion."},{"Start":"05:30.290 ","End":"05:34.715","Text":"Sometimes we\u0027ll state the volume in milliliters,"},{"Start":"05:34.715 ","End":"05:37.760","Text":"and sometimes we\u0027ll have the volume in centimeters cubed."},{"Start":"05:37.760 ","End":"05:40.059","Text":"They\u0027re both identical. Now,"},{"Start":"05:40.059 ","End":"05:42.935","Text":"supposing, we want to do a problem."},{"Start":"05:42.935 ","End":"05:45.020","Text":"Now here\u0027s the problem."},{"Start":"05:45.020 ","End":"05:51.440","Text":"Supposing we want to convert 1 liter to meters cubed,"},{"Start":"05:51.440 ","End":"05:54.200","Text":"not centimeters cubed, meters cubed."},{"Start":"05:54.200 ","End":"05:57.155","Text":"Now what conversion factors do we use?"},{"Start":"05:57.155 ","End":"05:59.615","Text":"We need two conversion factors."},{"Start":"05:59.615 ","End":"06:04.908","Text":"We need the one that takes us from 1 liter to centimeters cubed,"},{"Start":"06:04.908 ","End":"06:06.300","Text":"that we already know,"},{"Start":"06:06.300 ","End":"06:08.660","Text":"and then from centimeters cubed,"},{"Start":"06:08.660 ","End":"06:10.475","Text":"we need to go to meters cubed."},{"Start":"06:10.475 ","End":"06:13.220","Text":"So we really need two conversion factors."},{"Start":"06:13.220 ","End":"06:17.725","Text":"From 1,000 centimeter cubed divided by 1 liter is equal to 1."},{"Start":"06:17.725 ","End":"06:21.950","Text":"That\u0027s true because 1 liter is 1,000 centimeters cubed."},{"Start":"06:21.950 ","End":"06:26.345","Text":"We need another one that takes us from centimeter to meter."},{"Start":"06:26.345 ","End":"06:32.255","Text":"We know that 1 centimeter is the same as 10^-2 meters."},{"Start":"06:32.255 ","End":"06:34.940","Text":"We had that in a previous video,"},{"Start":"06:34.940 ","End":"06:37.415","Text":"and that is equal to 1 too."},{"Start":"06:37.415 ","End":"06:41.000","Text":"Now, how are we going to do this conversion?"},{"Start":"06:41.000 ","End":"06:44.510","Text":"We can do it in more or less one step."},{"Start":"06:44.510 ","End":"06:46.340","Text":"We have 1 liter,"},{"Start":"06:46.340 ","End":"06:50.975","Text":"and we want to get rid of the liter and get to centimeters cubed."},{"Start":"06:50.975 ","End":"06:54.500","Text":"We turn the conversion factor this way round."},{"Start":"06:54.500 ","End":"06:56.210","Text":"If we do it that way,"},{"Start":"06:56.210 ","End":"06:58.573","Text":"then we can cancel the liter,"},{"Start":"06:58.573 ","End":"07:01.295","Text":"and we\u0027re left just with the centimeter cubed."},{"Start":"07:01.295 ","End":"07:05.930","Text":"Now we want to get rid of the centimeter cubed and get to meters cubed,"},{"Start":"07:05.930 ","End":"07:08.240","Text":"because that\u0027s what it says in the question."},{"Start":"07:08.240 ","End":"07:10.370","Text":"We have centimeters cubed here."},{"Start":"07:10.370 ","End":"07:13.340","Text":"Now what we know is,"},{"Start":"07:13.340 ","End":"07:16.765","Text":"we know 1 centimeter is 10^-2 meters,"},{"Start":"07:16.765 ","End":"07:19.160","Text":"but we want centimeter cubed,"},{"Start":"07:19.160 ","End":"07:22.985","Text":"so we just take 10^-2/1 centimeter,"},{"Start":"07:22.985 ","End":"07:26.105","Text":"10^-2 meters is the same as 1 centimeter."},{"Start":"07:26.105 ","End":"07:28.885","Text":"Because here we have centimeters cubed,"},{"Start":"07:28.885 ","End":"07:30.620","Text":"we cube the whole thing."},{"Start":"07:30.620 ","End":"07:32.420","Text":"We\u0027re putting all this,"},{"Start":"07:32.420 ","End":"07:35.021","Text":"what\u0027s over in brackets to the power of 3."},{"Start":"07:35.021 ","End":"07:37.295","Text":"Let\u0027s do another step."},{"Start":"07:37.295 ","End":"07:39.915","Text":"We have 1 liter, again,"},{"Start":"07:39.915 ","End":"07:43.190","Text":"we have 1,000 centimeters cubed, and this time,"},{"Start":"07:43.190 ","End":"07:47.366","Text":"to simplify matters, I\u0027ve written it as 10^3."},{"Start":"07:47.366 ","End":"07:49.850","Text":"I\u0027ve written it in scientific notation,"},{"Start":"07:49.850 ","End":"07:53.490","Text":"centimeters cubed divided by 1 liter."},{"Start":"07:53.490 ","End":"07:57.435","Text":"Now, I cube all this,"},{"Start":"07:57.435 ","End":"08:00.825","Text":"10^-2 cubed is 10^-6,"},{"Start":"08:00.825 ","End":"08:05.239","Text":"1 centimeter is 1 centimeter cubed,"},{"Start":"08:05.239 ","End":"08:07.790","Text":"meter is meter cubed."},{"Start":"08:07.790 ","End":"08:10.130","Text":"Now I have it all together."},{"Start":"08:10.130 ","End":"08:14.675","Text":"What can I do? I can get rid of the centimeter cubed."},{"Start":"08:14.675 ","End":"08:17.420","Text":"I can get rid of the liters as before,"},{"Start":"08:17.420 ","End":"08:20.615","Text":"the only units I\u0027m left with are meter cubed."},{"Start":"08:20.615 ","End":"08:22.610","Text":"Now, what about the numerical parts?"},{"Start":"08:22.610 ","End":"08:30.765","Text":"I have 10^3 times 10^6 which is 10^-3."},{"Start":"08:30.765 ","End":"08:40.090","Text":"I\u0027ve discovered that 1 liter is equal to10^-3 meters cubed."},{"Start":"08:41.380 ","End":"08:44.930","Text":"What we\u0027ve done here, is to convert 1 liter"},{"Start":"08:44.930 ","End":"08:50.000","Text":"to 10^-3 meter cubed using two conversion factors."},{"Start":"08:50.000 ","End":"08:53.000","Text":"Sometimes we have to go through a chain of"},{"Start":"08:53.000 ","End":"08:57.785","Text":"3 or even 4 conversion factors in order to get to the right units."},{"Start":"08:57.785 ","End":"09:01.280","Text":"But now we\u0027re totally convinced that we\u0027ve done it all the"},{"Start":"09:01.280 ","End":"09:05.735","Text":"right way by canceling the units."},{"Start":"09:05.735 ","End":"09:08.420","Text":"This is a technique we\u0027ll use throughout,"},{"Start":"09:08.420 ","End":"09:12.500","Text":"and you\u0027ll see it also in solving the many problems,"},{"Start":"09:12.500 ","End":"09:16.135","Text":"the many exercises in this course."},{"Start":"09:16.135 ","End":"09:19.205","Text":"Next time when you see this,"},{"Start":"09:19.205 ","End":"09:21.905","Text":"when you have to convert units,"},{"Start":"09:21.905 ","End":"09:24.990","Text":"you\u0027ll see this is really very easy."}],"ID":17619},{"Watched":false,"Name":"Exercise 1","Duration":"4m 52s","ChapterTopicVideoID":16874,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16874.jpeg","UploadDate":"2019-02-19T05:37:54.2170000","DurationForVideoObject":"PT4M52S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.120","Text":"Hi. We are going to perform the following conversions."},{"Start":"00:03.120 ","End":"00:04.950","Text":"So in (a),"},{"Start":"00:04.950 ","End":"00:08.595","Text":"0.145 liters equals how many milliliters?"},{"Start":"00:08.595 ","End":"00:11.520","Text":"In order to convert 1 unit to the other,"},{"Start":"00:11.520 ","End":"00:13.605","Text":"we are going to use conversion factors."},{"Start":"00:13.605 ","End":"00:18.820","Text":"Recall that 1 liter equals 1,000 milliliters."},{"Start":"00:19.160 ","End":"00:24.460","Text":"Therefore, 1 liter divided by 1,000 ml equals 1,"},{"Start":"00:24.980 ","End":"00:32.305","Text":"and 1,000 ml divided by 1 liter equals 1."},{"Start":"00:32.305 ","End":"00:34.745","Text":"These 2 are conversion factors."},{"Start":"00:34.745 ","End":"00:37.850","Text":"Now, in order to decide which conversion factor we are going to use,"},{"Start":"00:37.850 ","End":"00:40.639","Text":"we need to look at our units."},{"Start":"00:40.639 ","End":"00:42.920","Text":"So we have units of liters,"},{"Start":"00:42.920 ","End":"00:45.095","Text":"and we want to change them into milliliters."},{"Start":"00:45.095 ","End":"00:50.015","Text":"Therefore, we will use the conversion factor that the liters is in the denominator."},{"Start":"00:50.015 ","End":"00:52.100","Text":"That way, the liters will cancel out,"},{"Start":"00:52.100 ","End":"00:53.870","Text":"and we will be left with milliliters,"},{"Start":"00:53.870 ","End":"00:56.000","Text":"which is in our numerator. So let\u0027s see."},{"Start":"00:56.000 ","End":"00:57.795","Text":"So in (a),"},{"Start":"00:57.795 ","End":"01:01.255","Text":"we have 0.145 liters."},{"Start":"01:01.255 ","End":"01:04.370","Text":"We multiply this by our conversion factor that"},{"Start":"01:04.370 ","End":"01:07.115","Text":"we said that the liters is in the denominator."},{"Start":"01:07.115 ","End":"01:11.900","Text":"So we multiply this by 1,000 ml divided by 1 liter."},{"Start":"01:11.900 ","End":"01:14.610","Text":"The liters cancels out."},{"Start":"01:14.840 ","End":"01:19.890","Text":"We\u0027re left with milliliters 145 ml."},{"Start":"01:23.030 ","End":"01:29.089","Text":"So 0.145 liters equals 145 milliliters."},{"Start":"01:29.089 ","End":"01:31.720","Text":"That is our answer for (a)."},{"Start":"01:31.720 ","End":"01:34.290","Text":"Now we will look at (b)."},{"Start":"01:34.290 ","End":"01:39.900","Text":"In (b), we have to convert 18.2 milliliters to liters. So 18.2 milliliters."},{"Start":"01:42.290 ","End":"01:46.050","Text":"This time, we will multiply"},{"Start":"01:46.050 ","End":"01:50.275","Text":"the conversion factor where the milliliters is in the denominator,"},{"Start":"01:50.275 ","End":"01:54.250","Text":"1 liter divided by 1,000 ml."},{"Start":"01:54.470 ","End":"01:57.590","Text":"This way, our milliliters cancels out."},{"Start":"01:57.590 ","End":"01:59.840","Text":"We are left with liters."},{"Start":"01:59.840 ","End":"02:06.090","Text":"So this equals 0.0182 liters."},{"Start":"02:06.530 ","End":"02:09.210","Text":"That is our final answer for (b),"},{"Start":"02:09.210 ","End":"02:14.400","Text":"18.2 ml equals 0.0182 liters."},{"Start":"02:14.400 ","End":"02:16.335","Text":"Now we look at (c)."},{"Start":"02:16.335 ","End":"02:21.407","Text":"In (c), we have 671 centimeters cubed,"},{"Start":"02:21.407 ","End":"02:23.975","Text":"and we have to convert the centimeters cubed to liters."},{"Start":"02:23.975 ","End":"02:30.570","Text":"Again, recall that 1 liter equals 1,000 centimeters cubed."},{"Start":"02:31.060 ","End":"02:36.715","Text":"Recall that 1 centimeter cubed equals 1 ml."},{"Start":"02:36.715 ","End":"02:43.620","Text":"Therefore, 1 liter divided by 1,000 centimeters cubed equals 1,"},{"Start":"02:43.620 ","End":"02:50.150","Text":"and 1,000 centimeters cubed divided by 1 liter also equals 1."},{"Start":"02:50.150 ","End":"02:53.510","Text":"Here again, we have centimeters cubed."},{"Start":"02:53.510 ","End":"02:56.110","Text":"We want to convert it into liters."},{"Start":"02:56.110 ","End":"02:58.620","Text":"For this reason, we will use"},{"Start":"02:58.620 ","End":"03:01.910","Text":"the conversion factor that the centimeters cubed is in the denominator,"},{"Start":"03:01.910 ","End":"03:07.933","Text":"so times 1 liter divided by 1,000 centimeters cubed."},{"Start":"03:07.933 ","End":"03:12.340","Text":"This way the centimeters cubed cancels out,"},{"Start":"03:12.340 ","End":"03:18.040","Text":"and we get an answer of 0.671 liters."},{"Start":"03:18.040 ","End":"03:20.400","Text":"That is our final answer for (c),"},{"Start":"03:20.400 ","End":"03:25.130","Text":"671 centimeters cubed equals 0.671 liters."},{"Start":"03:25.130 ","End":"03:26.930","Text":"Now we will go on to (d)."},{"Start":"03:26.930 ","End":"03:30.260","Text":"In (d), we begin with 3.64 meters cubed,"},{"Start":"03:30.260 ","End":"03:32.540","Text":"and we have to change it into centimeters cubed,"},{"Start":"03:32.540 ","End":"03:37.140","Text":"so 3.64 meters cubed."},{"Start":"03:37.340 ","End":"03:43.515","Text":"Now, recall that 1 meter equals 100 centimeters."},{"Start":"03:43.515 ","End":"03:53.580","Text":"Therefore, 1 meter cubed equals 100^3 centimeters cubed,and therefore,"},{"Start":"03:53.580 ","End":"03:57.700","Text":"1 meter cubed equals 10^6 centimeters cubed."},{"Start":"04:00.290 ","End":"04:07.170","Text":"So 1 meter cubed divided by 10^6 centimeters cubed equals 1,"},{"Start":"04:07.170 ","End":"04:15.000","Text":"and 10^6 centimeters cubed divided by 1 meter cubed also equals 1."},{"Start":"04:15.000 ","End":"04:18.231","Text":"Again, we\u0027re going to look at the units here, we have meters cubed."},{"Start":"04:18.231 ","End":"04:20.210","Text":"Therefore, we will use the conversion factor"},{"Start":"04:20.210 ","End":"04:22.685","Text":"which centimeters cubed is in the denominator."},{"Start":"04:22.685 ","End":"04:31.160","Text":"We multiply by 10^6 centimeters cubed divided by 1 meter cubed."},{"Start":"04:31.160 ","End":"04:41.250","Text":"Meter cubed cancels out, and we\u0027re left with 3.64 times 10^6 centimeters cubed."},{"Start":"04:41.250 ","End":"04:49.000","Text":"So 3.64 meters cubed comes out to 3.64 times 10^6 centimeters cubed."},{"Start":"04:49.000 ","End":"04:51.095","Text":"That is our final answer."},{"Start":"04:51.095 ","End":"04:53.640","Text":"Thank you very much for listening."}],"ID":17620},{"Watched":false,"Name":"Exercise 2","Duration":"4m 40s","ChapterTopicVideoID":16875,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16875.jpeg","UploadDate":"2019-02-19T05:38:27.2870000","DurationForVideoObject":"PT4M40S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:04.065","Text":"Hi, we are going to perform the following conversions."},{"Start":"00:04.065 ","End":"00:08.385","Text":"In a, we need to convert 1.67 kilograms to grams."},{"Start":"00:08.385 ","End":"00:14.230","Text":"Recall that 1 kilogram equals 1,000 grams."},{"Start":"00:14.900 ","End":"00:20.440","Text":"Therefore, 1 kilogram divided by 1,000 grams equals 1,"},{"Start":"00:20.600 ","End":"00:25.545","Text":"and 1,000 grams divided by 1 kilogram also equals 1."},{"Start":"00:25.545 ","End":"00:31.005","Text":"In a, we\u0027re asked to convert 1.67kilograms to grams."},{"Start":"00:31.005 ","End":"00:33.625","Text":"These are conversion factors."},{"Start":"00:33.625 ","End":"00:35.840","Text":"In order to know which one we\u0027re going to use,"},{"Start":"00:35.840 ","End":"00:37.445","Text":"we will look at our units."},{"Start":"00:37.445 ","End":"00:40.250","Text":"Here we have kilograms, we want to convert them to grams."},{"Start":"00:40.250 ","End":"00:42.650","Text":"Therefore, we will use the conversion factor."},{"Start":"00:42.650 ","End":"00:46.534","Text":"Where\u0027s the kilogram is in the denominator and the gram is in the numerator."},{"Start":"00:46.534 ","End":"00:51.630","Text":"This way, the kilograms will cancel out here,"},{"Start":"00:51.630 ","End":"00:54.570","Text":"and we will be left with grams."},{"Start":"00:54.570 ","End":"00:57.460","Text":"We are left with 1,670 grams."},{"Start":"00:59.030 ","End":"01:02.100","Text":"That is our final answer for a."},{"Start":"01:02.100 ","End":"01:10.470","Text":"In b, we\u0027re asked to convert 711 grams to kilograms, 711 grams."},{"Start":"01:10.470 ","End":"01:13.370","Text":"This way, we will multiply by the conversion factor,"},{"Start":"01:13.370 ","End":"01:15.990","Text":"which the gram is in the denominator,"},{"Start":"01:15.990 ","End":"01:20.145","Text":"times 1 kilogram divided by 1,000 grams."},{"Start":"01:20.145 ","End":"01:23.435","Text":"This way, the grams will cancel out,"},{"Start":"01:23.435 ","End":"01:25.565","Text":"and our answer will be in kilograms."},{"Start":"01:25.565 ","End":"01:28.585","Text":"It equals 0.711 kilograms,"},{"Start":"01:28.585 ","End":"01:32.550","Text":"and that is our final answer for b."},{"Start":"01:32.550 ","End":"01:42.645","Text":"In c, we\u0027re asked to convert 3,896 millimeters to centimeters, so 3,896 millimeters."},{"Start":"01:42.645 ","End":"01:48.550","Text":"Now recall that 1 centimeter equals 10 millimeters."},{"Start":"01:48.800 ","End":"01:53.475","Text":"Therefore, 1 centimeters divided by 10 millimeters equals 1,"},{"Start":"01:53.475 ","End":"01:59.520","Text":"and 10 millimeters divided by 1 centimeter also equals 1."},{"Start":"01:59.520 ","End":"02:01.384","Text":"Here we\u0027ll use a conversion factor,"},{"Start":"02:01.384 ","End":"02:03.540","Text":"which is the millimeters is in the denominator."},{"Start":"02:03.540 ","End":"02:07.065","Text":"It\u0027s times 1 centimeter divided by 10 millimeters."},{"Start":"02:07.065 ","End":"02:15.870","Text":"The millimeters cancel out and we get 389.6 centimeters."},{"Start":"02:15.870 ","End":"02:18.840","Text":"That is our final answer for c. In d,"},{"Start":"02:18.840 ","End":"02:25.760","Text":"we\u0027re asked to convert 0.211 centimeters to millimeters, so 0.211 centimeters."},{"Start":"02:25.760 ","End":"02:28.235","Text":"This time we will multiply by the conversion factor,"},{"Start":"02:28.235 ","End":"02:30.410","Text":"which is centimeters is in the denominator."},{"Start":"02:30.410 ","End":"02:34.925","Text":"It\u0027s times 10 millimeters divided by 1 centimeter."},{"Start":"02:34.925 ","End":"02:37.505","Text":"Centimeters cancel out,"},{"Start":"02:37.505 ","End":"02:42.780","Text":"and we get 2.11 millimeters."},{"Start":"02:42.780 ","End":"02:45.150","Text":"That is our final answer for d. In e,"},{"Start":"02:45.150 ","End":"02:48.365","Text":"we\u0027re asked to convert 1 meters squared to kilometers squared."},{"Start":"02:48.365 ","End":"02:52.400","Text":"Recall that 1 kilometer equals 1,000 meters."},{"Start":"02:52.400 ","End":"02:57.975","Text":"1 kilometer squared equals 1,000 squared, meters squared."},{"Start":"02:57.975 ","End":"03:04.145","Text":"1 kilometer squared equals 10^6 meters squared."},{"Start":"03:04.145 ","End":"03:10.625","Text":"1 kilometer squared, divided by 10^6 meters squared equals 1,"},{"Start":"03:10.625 ","End":"03:13.025","Text":"and 10^6 meter squared,"},{"Start":"03:13.025 ","End":"03:16.780","Text":"divided by 1 kilometer squared also equals 1."},{"Start":"03:16.780 ","End":"03:18.665","Text":"Here we\u0027ll use the conversion factor,"},{"Start":"03:18.665 ","End":"03:20.930","Text":"which the meter squared is in the denominator."},{"Start":"03:20.930 ","End":"03:27.660","Text":"It\u0027s times 1 kilometer squared divided by 10^6 meter squared."},{"Start":"03:27.660 ","End":"03:29.010","Text":"Meter squared cancel out,"},{"Start":"03:29.010 ","End":"03:34.560","Text":"and we get 1 times 10^-6 kilometer squared."},{"Start":"03:34.560 ","End":"03:37.680","Text":"That is our final answer for e. Now in f,"},{"Start":"03:37.680 ","End":"03:42.550","Text":"we\u0027re asked to convert 1 meters cubed to centimeters cubed. 1 meters cubed."},{"Start":"03:43.610 ","End":"03:46.140","Text":"1 meters equals 100 centimeter."},{"Start":"03:46.140 ","End":"03:52.830","Text":"Therefore, 1 meter cubed equals 100 cubed, centimeters cubed."},{"Start":"03:52.830 ","End":"03:58.965","Text":"1 meter cubed equals 10^6 centimeters cubed."},{"Start":"03:58.965 ","End":"04:06.520","Text":"1 meter cubed divided by 10^6 centimeters cubed equals 1,"},{"Start":"04:06.530 ","End":"04:13.270","Text":"and 10^6 centimeters cubed divided by 1 meter cubed also equals 1."},{"Start":"04:13.270 ","End":"04:18.140","Text":"Here we\u0027ll use the conversion factor which the meters cubed is in the denominator."},{"Start":"04:18.140 ","End":"04:26.825","Text":"It\u0027s times 10^6 centimeters cubed divided by 1 meters cubed."},{"Start":"04:26.825 ","End":"04:28.925","Text":"Meters cubed will cancel out,"},{"Start":"04:28.925 ","End":"04:33.725","Text":"and we\u0027re left with 1 times 10^6 centimeters cubed."},{"Start":"04:33.725 ","End":"04:36.560","Text":"That is our final answer for f. Thank you very"},{"Start":"04:36.560 ","End":"04:40.290","Text":"much for listening and we\u0027ll look forward to seeing you again."}],"ID":17621},{"Watched":false,"Name":"Exercise 3","Duration":"2m 8s","ChapterTopicVideoID":16876,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16876.jpeg","UploadDate":"2019-02-19T05:38:40.5100000","DurationForVideoObject":"PT2M8S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.745","Text":"Hi, we are going to solve the following exercise."},{"Start":"00:02.745 ","End":"00:04.260","Text":"Here we have unit conversions."},{"Start":"00:04.260 ","End":"00:08.010","Text":"In A, 65.2 inches equals how many centimeters?"},{"Start":"00:08.010 ","End":"00:11.100","Text":"In B, 87 feet equals how many meters?"},{"Start":"00:11.100 ","End":"00:14.490","Text":"In C, 1.36 pounds equals how many grams?"},{"Start":"00:14.490 ","End":"00:17.655","Text":"In D, 252 pounds equals how many kilograms?"},{"Start":"00:17.655 ","End":"00:20.970","Text":"In E, 1.79 gallons equals how many liters?"},{"Start":"00:20.970 ","End":"00:22.410","Text":"We will start with A."},{"Start":"00:22.410 ","End":"00:25.485","Text":"We begin with inches, 65.2 inches."},{"Start":"00:25.485 ","End":"00:27.765","Text":"You have to convert them to centimeters."},{"Start":"00:27.765 ","End":"00:29.280","Text":"Whenever you\u0027re 1 inch,"},{"Start":"00:29.280 ","End":"00:32.085","Text":"we have 2.54 centimeters."},{"Start":"00:32.085 ","End":"00:34.485","Text":"This is our conversion factor."},{"Start":"00:34.485 ","End":"00:36.570","Text":"When we multiply this,"},{"Start":"00:36.570 ","End":"00:44.750","Text":"we see that the inches cancels out and we\u0027re left with 165.61 centimeters,"},{"Start":"00:44.750 ","End":"00:49.205","Text":"so 65.2 inches equals 165.61 centimeters."},{"Start":"00:49.205 ","End":"00:51.200","Text":"Now, we will look at B. In B,"},{"Start":"00:51.200 ","End":"00:53.255","Text":"we begin with 87 feet."},{"Start":"00:53.255 ","End":"00:55.850","Text":"We need to convert the feet into meters."},{"Start":"00:55.850 ","End":"01:02.840","Text":"The conversion factor we will use is that every 1 foot contains 0.3048 meters times this,"},{"Start":"01:02.840 ","End":"01:09.735","Text":"the feet cancel out and this equals 26.52 meters."},{"Start":"01:09.735 ","End":"01:12.575","Text":"In C, we begin with 1.36 pounds,"},{"Start":"01:12.575 ","End":"01:15.410","Text":"and we need to convert this into grams."},{"Start":"01:15.410 ","End":"01:17.525","Text":"We\u0027ll use a conversion factor."},{"Start":"01:17.525 ","End":"01:19.105","Text":"For every 1 pound,"},{"Start":"01:19.105 ","End":"01:23.800","Text":"we have 453.6 grams."},{"Start":"01:23.800 ","End":"01:30.530","Text":"The pounds cancel out and our answer equals 616.9 grams."},{"Start":"01:30.530 ","End":"01:35.030","Text":"In D, we\u0027re asked to convert 252 pounds to kilograms."},{"Start":"01:35.030 ","End":"01:36.845","Text":"Again, we will use a conversion factor."},{"Start":"01:36.845 ","End":"01:41.659","Text":"In every 1 pound we have 0.454 kilograms."},{"Start":"01:41.659 ","End":"01:47.885","Text":"The pounds cancel out and our answer equals 114.41 kilograms."},{"Start":"01:47.885 ","End":"01:52.210","Text":"In E, we were asked to convert 1.79 gallons to liters."},{"Start":"01:52.210 ","End":"01:54.410","Text":"Again, we will use a conversion factor."},{"Start":"01:54.410 ","End":"01:56.150","Text":"In every 1 gallon,"},{"Start":"01:56.150 ","End":"01:58.415","Text":"we have 3.79 liters."},{"Start":"01:58.415 ","End":"02:04.905","Text":"The gallons cancel out and our answer equals 6.78 liters."},{"Start":"02:04.905 ","End":"02:06.420","Text":"These are our answers."},{"Start":"02:06.420 ","End":"02:09.100","Text":"Thank you very much for watching."}],"ID":17622},{"Watched":false,"Name":"Exercise 4","Duration":"3m 32s","ChapterTopicVideoID":16877,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16877.jpeg","UploadDate":"2019-02-19T05:39:01.6900000","DurationForVideoObject":"PT3M32S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.210","Text":"Hi. We\u0027re going to answer the following question."},{"Start":"00:03.210 ","End":"00:04.935","Text":"Which is the greater mass,"},{"Start":"00:04.935 ","End":"00:11.565","Text":"3,378 micrograms or 0.0618 milligrams?"},{"Start":"00:11.565 ","End":"00:14.985","Text":"In order to do this, we\u0027re going to bring both of them,"},{"Start":"00:14.985 ","End":"00:16.590","Text":"both of these numbers,"},{"Start":"00:16.590 ","End":"00:18.090","Text":"2 units of grams,"},{"Start":"00:18.090 ","End":"00:19.680","Text":"and then we could compare between them."},{"Start":"00:19.680 ","End":"00:25.095","Text":"We\u0027ll take the first number, 3,378 micrograms."},{"Start":"00:25.095 ","End":"00:27.360","Text":"In order to bring it to a grams units,"},{"Start":"00:27.360 ","End":"00:28.830","Text":"we need a conversion factor,"},{"Start":"00:28.830 ","End":"00:33.225","Text":"so 1 micrograms equals 10^-6 grams,"},{"Start":"00:33.225 ","End":"00:35.835","Text":"because micro is 10^-6."},{"Start":"00:35.835 ","End":"00:40.725","Text":"Therefore, 1 microgram divided by 10^-6"},{"Start":"00:40.725 ","End":"00:48.435","Text":"grams equals 1 and 10^-6 grams divided by 1 microgram will also equals 1."},{"Start":"00:48.435 ","End":"00:51.740","Text":"Now, the conversion factor we need is the conversion factor where we"},{"Start":"00:51.740 ","End":"00:55.145","Text":"have the grams in the numerator and the micrograms in the denominator."},{"Start":"00:55.145 ","End":"00:59.990","Text":"Therefore, the micrograms will cancel out and our answer will be in grams."},{"Start":"00:59.990 ","End":"01:08.559","Text":"We will multiply a number by the conversion factor 10^-6 grams divided by 1 microgram."},{"Start":"01:08.559 ","End":"01:17.930","Text":"Micrograms cancel out and we get an answer of 3.38 times 10^-3 grams."},{"Start":"01:17.960 ","End":"01:22.005","Text":"We have our first number in grams units."},{"Start":"01:22.005 ","End":"01:24.110","Text":"Now, we will take our second number."},{"Start":"01:24.110 ","End":"01:26.495","Text":"Let\u0027s call this 1."},{"Start":"01:26.495 ","End":"01:28.160","Text":"Now, we will start with Number 2."},{"Start":"01:28.160 ","End":"01:33.330","Text":"Our number is 0.00618 milligrams."},{"Start":"01:33.330 ","End":"01:35.840","Text":"Now, in order to bring the milligrams to grams,"},{"Start":"01:35.840 ","End":"01:37.940","Text":"we will also use a conversion factor."},{"Start":"01:37.940 ","End":"01:41.820","Text":"1 milligram equals 10^-3 grams."},{"Start":"01:41.820 ","End":"01:47.430","Text":"Therefore, 1 milligram divided by 10^-3 grams equals"},{"Start":"01:47.430 ","End":"01:54.615","Text":"1 and 10^-3 grams divided by 1 milligram also equals 1."},{"Start":"01:54.615 ","End":"01:58.670","Text":"Again, the conversion factor we want to use is a conversion factor,"},{"Start":"01:58.670 ","End":"01:59.939","Text":"which the grams is in the numerator,"},{"Start":"01:59.939 ","End":"02:02.745","Text":"and the milligrams is in the denominator."},{"Start":"02:02.745 ","End":"02:06.190","Text":"That way the milligrams will cancel out and we will get our answer in grams."},{"Start":"02:06.190 ","End":"02:13.250","Text":"We will multiply our second number by 10^-3 grams divided by 1 milligram."},{"Start":"02:13.250 ","End":"02:15.395","Text":"Milligrams cancel out."},{"Start":"02:15.395 ","End":"02:24.675","Text":"The answer that we get is 6.18 times 10^-6 grams."},{"Start":"02:24.675 ","End":"02:26.840","Text":"Now, we will look at both of the answers we got."},{"Start":"02:26.840 ","End":"02:33.565","Text":"The first one is 3.38 times 10^-3 grams."},{"Start":"02:33.565 ","End":"02:39.785","Text":"The second number that we were saved is 6.18 times 10^-6 grams."},{"Start":"02:39.785 ","End":"02:44.930","Text":"Now, first of all, the number that we multiply by here is 3.38 and here\u0027s 6.18."},{"Start":"02:44.930 ","End":"02:49.895","Text":"Here the number that we multiply by 6.18 is greater than 3.38."},{"Start":"02:49.895 ","End":"02:53.055","Text":"However, the important number is our 10."},{"Start":"02:53.055 ","End":"02:54.990","Text":"Here we have 10^-3,"},{"Start":"02:54.990 ","End":"02:57.405","Text":"and here we have 10^-6."},{"Start":"02:57.405 ","End":"03:03.590","Text":"So 10^-3 is the number of orders of magnitude greater than 10^-6,"},{"Start":"03:03.590 ","End":"03:06.760","Text":"and therefore the first number is greater."},{"Start":"03:06.760 ","End":"03:09.135","Text":"Our final answer is,"},{"Start":"03:09.135 ","End":"03:12.300","Text":"this was our first number, it\u0027s 3,378,"},{"Start":"03:12.300 ","End":"03:20.205","Text":"so 3,378 micrograms is greater than,"},{"Start":"03:20.205 ","End":"03:28.605","Text":"this was our second number here, 0.00618 milligrams."},{"Start":"03:28.605 ","End":"03:30.375","Text":"That is our final answer,"},{"Start":"03:30.375 ","End":"03:33.220","Text":"and thank you very much for listening."}],"ID":17623},{"Watched":false,"Name":"Exercise 5","Duration":"3m 13s","ChapterTopicVideoID":16878,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16878.jpeg","UploadDate":"2019-02-19T05:39:21.1230000","DurationForVideoObject":"PT3M13S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.000","Text":"Hi. We\u0027re going to answer the following question."},{"Start":"00:03.000 ","End":"00:04.260","Text":"Which is the greater mass,"},{"Start":"00:04.260 ","End":"00:11.930","Text":"3,456 milligrams or 0.000584 kilograms?"},{"Start":"00:11.930 ","End":"00:14.280","Text":"In the first number, we have milligrams as our units,"},{"Start":"00:14.280 ","End":"00:17.085","Text":"and in the second number, we have kilograms as our units."},{"Start":"00:17.085 ","End":"00:19.905","Text":"We\u0027re going to bring both to the grams units,"},{"Start":"00:19.905 ","End":"00:21.375","Text":"and then we will compare them."},{"Start":"00:21.375 ","End":"00:25.879","Text":"We\u0027ll take our first number, 3,456 milligrams."},{"Start":"00:25.879 ","End":"00:29.790","Text":"In order to bring it to a grams unit,"},{"Start":"00:29.790 ","End":"00:31.845","Text":"we will use a conversion factor."},{"Start":"00:31.845 ","End":"00:38.831","Text":"1 milligram equals 10 to the minus 3 grams because milli is 10 to the minus 3."},{"Start":"00:38.831 ","End":"00:42.960","Text":"Therefore, 1 milligram divided by 10 to the minus 3 grams equals"},{"Start":"00:42.960 ","End":"00:50.453","Text":"1 and 10t to the minus 3 grams divided by 1 milligram equals 1."},{"Start":"00:50.453 ","End":"00:55.070","Text":"To choose a conversion factor,"},{"Start":"00:55.070 ","End":"00:58.220","Text":"the first one or the second one, we will look at our units."},{"Start":"00:58.220 ","End":"01:01.670","Text":"Our units are milligrams and therefore we need a conversion factor in which"},{"Start":"01:01.670 ","End":"01:05.390","Text":"the grams is in the numerator and the milligrams is in the denominator."},{"Start":"01:05.390 ","End":"01:07.325","Text":"That way, the milligrams will cancel out."},{"Start":"01:07.325 ","End":"01:14.695","Text":"We will multiply our number by 10 to the minus 3 grams divided by 1 milligram."},{"Start":"01:14.695 ","End":"01:18.068","Text":"The milligrams cancels out."},{"Start":"01:18.068 ","End":"01:23.240","Text":"The answer that we receive is 3.46 grams."},{"Start":"01:23.240 ","End":"01:27.245","Text":"That is our first number in grams units."},{"Start":"01:27.245 ","End":"01:29.465","Text":"Our second number is"},{"Start":"01:29.465 ","End":"01:37.415","Text":"0.000584 kilograms and we want to change our kilograms to grams units."},{"Start":"01:37.415 ","End":"01:40.115","Text":"We will also use a conversion factor for this."},{"Start":"01:40.115 ","End":"01:44.720","Text":"Now, 1 kilogram equals 10^3 gram,"},{"Start":"01:44.720 ","End":"01:46.569","Text":"because kilo is 10^3."},{"Start":"01:46.569 ","End":"01:51.175","Text":"Therefore, 1 kilogram divided by 10^3 grams equals"},{"Start":"01:51.175 ","End":"02:00.025","Text":"1 and 10^3 grams divided by 1 kilogram also equals 1."},{"Start":"02:00.025 ","End":"02:02.390","Text":"Again, to decide which conversion factor we will use,"},{"Start":"02:02.390 ","End":"02:03.770","Text":"the first or the second,"},{"Start":"02:03.770 ","End":"02:05.180","Text":"we\u0027ll look at our units."},{"Start":"02:05.180 ","End":"02:07.910","Text":"We have our units in kilogram and we want to reach grams,"},{"Start":"02:07.910 ","End":"02:10.340","Text":"therefore we will use the conversion factor,"},{"Start":"02:10.340 ","End":"02:14.465","Text":"in which the grams is in the numerator and the kilograms is in the denominator."},{"Start":"02:14.465 ","End":"02:20.830","Text":"We\u0027ll multiply our number by 10^3 grams divided by 1 kilogram."},{"Start":"02:20.830 ","End":"02:25.395","Text":"Kilogram cancels out."},{"Start":"02:25.395 ","End":"02:32.680","Text":"The answer that we get is 0.584 grams."},{"Start":"02:34.480 ","End":"02:36.960","Text":"Now, we can compare both numbers."},{"Start":"02:36.960 ","End":"02:44.675","Text":"Our first number is 3.46 grams and our second number is 0.584 grams."},{"Start":"02:44.675 ","End":"02:50.290","Text":"We can also round it off so it\u0027s 0.58 grams."},{"Start":"02:50.290 ","End":"02:51.500","Text":"We compare 1 to the other,"},{"Start":"02:51.500 ","End":"02:55.070","Text":"we see that 3.46 is greater than 0.58."},{"Start":"02:55.070 ","End":"02:58.470","Text":"Therefore, our first number,"},{"Start":"03:04.690 ","End":"03:08.480","Text":"3,456 milligrams is greater than 0.000584 kilograms."},{"Start":"03:08.480 ","End":"03:10.640","Text":"That is our final answer."},{"Start":"03:10.640 ","End":"03:13.260","Text":"Thank you very much for listening."}],"ID":17624},{"Watched":false,"Name":"Exercise 6","Duration":"2m ","ChapterTopicVideoID":16879,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16879.jpeg","UploadDate":"2019-02-19T05:39:34.1170000","DurationForVideoObject":"PT2M","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.020 ","End":"00:03.690","Text":"Hi. We\u0027re going to answer the following question."},{"Start":"00:03.690 ","End":"00:06.960","Text":"On a thermometer, the lowest temperature mark is at minus"},{"Start":"00:06.960 ","End":"00:10.815","Text":"10 degrees Celsius and the highest mark is 65 degrees Celsius."},{"Start":"00:10.815 ","End":"00:13.245","Text":"What are the equivalent Fahrenheit temperatures?"},{"Start":"00:13.245 ","End":"00:17.955","Text":"First, we\u0027re going to look at the relationship between Fahrenheit and Celsius."},{"Start":"00:17.955 ","End":"00:26.850","Text":"The temperature in degrees Fahrenheit equals the temperature in degrees"},{"Start":"00:26.850 ","End":"00:36.285","Text":"Celsius times 1.8 plus 32 degrees."},{"Start":"00:36.285 ","End":"00:39.180","Text":"Our first temperature that we want to change from"},{"Start":"00:39.180 ","End":"00:42.345","Text":"Celsius to Fahrenheit is minus 10 degrees Celsius."},{"Start":"00:42.345 ","End":"00:45.820","Text":"Therefore, our temperature in degrees"},{"Start":"00:45.820 ","End":"00:49.270","Text":"Fahrenheit will equal the temperature in degrees Celsius,"},{"Start":"00:49.270 ","End":"00:59.290","Text":"which is minus 10 times 1.8 plus 32,"},{"Start":"00:59.290 ","End":"01:06.665","Text":"which is minus 18 plus 32, which equals 14."},{"Start":"01:06.665 ","End":"01:10.380","Text":"Our answer is 14 degrees in Fahrenheit."},{"Start":"01:10.380 ","End":"01:13.260","Text":"That\u0027s from minus 10 degrees Celsius."},{"Start":"01:13.260 ","End":"01:17.145","Text":"Now we will look at our second temperature."},{"Start":"01:17.145 ","End":"01:19.935","Text":"Our second temperature is 65 degrees Celsius."},{"Start":"01:19.935 ","End":"01:22.020","Text":"Again, we will do the same thing."},{"Start":"01:22.020 ","End":"01:26.960","Text":"Our temperature in degrees Fahrenheit equals"},{"Start":"01:26.960 ","End":"01:34.280","Text":"65 times 1.8 plus 32,"},{"Start":"01:34.280 ","End":"01:40.515","Text":"which equals 149 degrees Fahrenheit."},{"Start":"01:40.515 ","End":"01:45.380","Text":"Our minus 10 degrees Celsius equals 14 degrees Fahrenheit and our"},{"Start":"01:45.380 ","End":"01:50.385","Text":"65 degrees Celsius equals 149 degrees Fahrenheit."},{"Start":"01:50.385 ","End":"01:56.900","Text":"So 14 degrees in Fahrenheit and 149 degrees Fahrenheit, our final answers."},{"Start":"01:56.900 ","End":"01:59.790","Text":"Thank you very much for listening."}],"ID":17625},{"Watched":false,"Name":"Exercise 7","Duration":"1m 31s","ChapterTopicVideoID":16880,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16880.jpeg","UploadDate":"2019-02-19T05:39:44.6330000","DurationForVideoObject":"PT1M31S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.315","Text":"Hi, we\u0027re going to answer the following question."},{"Start":"00:03.315 ","End":"00:05.610","Text":"In San Bernardino, California,"},{"Start":"00:05.610 ","End":"00:10.395","Text":"the lowest and highest temperatures are 20 degrees Fahrenheit and 120 degrees Fahrenheit."},{"Start":"00:10.395 ","End":"00:13.215","Text":"What are the equivalent Celsius temperatures?"},{"Start":"00:13.215 ","End":"00:15.480","Text":"First of all, we\u0027re going to look at the relationship"},{"Start":"00:15.480 ","End":"00:19.559","Text":"between Celsius temperatures and Fahrenheit temperatures."},{"Start":"00:19.559 ","End":"00:24.885","Text":"The temperature in degrees Celsius equals the temperature in degrees Fahrenheit,"},{"Start":"00:24.885 ","End":"00:29.775","Text":"minus 32, divided by 1.8."},{"Start":"00:29.775 ","End":"00:32.580","Text":"If we\u0027re looking at the first temperature,"},{"Start":"00:32.580 ","End":"00:34.245","Text":"which is 20 degrees Fahrenheit,"},{"Start":"00:34.245 ","End":"00:44.510","Text":"our temperature in degrees Celsius will equal 20 minus 32 divided by 1.8,"},{"Start":"00:44.510 ","End":"00:50.730","Text":"which equals minus 6.67 degrees Celsius."},{"Start":"00:50.930 ","End":"00:54.995","Text":"Our second temperature is 120 degrees Fahrenheit."},{"Start":"00:54.995 ","End":"01:03.155","Text":"Temperature in degrees Celsius equals 120 minus 32 divided by 1.8."},{"Start":"01:03.155 ","End":"01:09.424","Text":"Here we get 48.89 degrees Celsius."},{"Start":"01:09.424 ","End":"01:13.120","Text":"The temperature, which is equivalent to the 20 degrees Fahrenheit,"},{"Start":"01:13.120 ","End":"01:18.260","Text":"is minus 6.67 degrees Celsius and the temperature,"},{"Start":"01:18.260 ","End":"01:20.885","Text":"which is equivalent to 120 degrees Fahrenheit,"},{"Start":"01:20.885 ","End":"01:24.575","Text":"is 48.89 degrees Celsius."},{"Start":"01:24.575 ","End":"01:27.815","Text":"Those are our final answers."},{"Start":"01:27.815 ","End":"01:30.540","Text":"Thank you very much for listening."}],"ID":17626},{"Watched":false,"Name":"Exercise 8","Duration":"2m 54s","ChapterTopicVideoID":16881,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16881.jpeg","UploadDate":"2019-02-19T05:40:05.5700000","DurationForVideoObject":"PT2M54S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.050 ","End":"00:03.419","Text":"Hi. We are going to solve the following exercise."},{"Start":"00:03.419 ","End":"00:07.800","Text":"A non-SI unit used in pharmaceutical work is the grain, GR."},{"Start":"00:07.800 ","End":"00:10.560","Text":"16 grains equals 1 gram."},{"Start":"00:10.560 ","End":"00:14.160","Text":"An aspirin tablet contains 6 grains of aspirin."},{"Start":"00:14.160 ","End":"00:17.940","Text":"A 160-pound individual takes 2 aspirin tablets a day."},{"Start":"00:17.940 ","End":"00:22.855","Text":"A, what is the quantity of aspirin in 2 tablets expressed in milligrams?"},{"Start":"00:22.855 ","End":"00:25.500","Text":"B, what is the dosage rate of aspirin"},{"Start":"00:25.500 ","End":"00:29.264","Text":"expressed in milligrams of aspirin per kilogram of body mass?"},{"Start":"00:29.264 ","End":"00:30.960","Text":"Firstly, we will answer A."},{"Start":"00:30.960 ","End":"00:34.815","Text":"What is the quantity of aspirin in 2 tablets expressed in milligrams?"},{"Start":"00:34.815 ","End":"00:37.920","Text":"So we have 2 tablets as written,"},{"Start":"00:37.920 ","End":"00:40.815","Text":"and we want to know how many milligrams we have."},{"Start":"00:40.815 ","End":"00:42.359","Text":"In 2 tablets,"},{"Start":"00:42.359 ","End":"00:46.217","Text":"we know that in each aspirin tablet we have 6 grains of aspirin,"},{"Start":"00:46.217 ","End":"00:49.268","Text":"so it\u0027s 2 times 6 grains of aspirin."},{"Start":"00:49.268 ","End":"00:51.221","Text":"But we want the answer in milligrams."},{"Start":"00:51.221 ","End":"00:57.020","Text":"Therefore, we\u0027ll use our conversion factor in order to convert this into grams."},{"Start":"00:57.020 ","End":"01:00.316","Text":"1 gram contains 16 grains,"},{"Start":"01:00.316 ","End":"01:02.380","Text":"so we will multiply by the conversion factor,"},{"Start":"01:02.380 ","End":"01:04.865","Text":"1 gram per 16 grains."},{"Start":"01:04.865 ","End":"01:06.440","Text":"Grains cancel out."},{"Start":"01:06.440 ","End":"01:10.385","Text":"Our answer is 0.75 grams."},{"Start":"01:10.385 ","End":"01:12.980","Text":"Since we want our answer in milligrams,"},{"Start":"01:12.980 ","End":"01:15.125","Text":"we will multiply by a conversion factor."},{"Start":"01:15.125 ","End":"01:16.310","Text":"For every 1 gram,"},{"Start":"01:16.310 ","End":"01:18.720","Text":"we have 1,000 milligrams."},{"Start":"01:18.720 ","End":"01:20.822","Text":"The grams cancel out,"},{"Start":"01:20.822 ","End":"01:23.270","Text":"and our answer will be in milligrams."},{"Start":"01:23.270 ","End":"01:26.435","Text":"This equals 750 milligrams."},{"Start":"01:26.435 ","End":"01:27.980","Text":"That is our answer for A."},{"Start":"01:27.980 ","End":"01:29.820","Text":"Now we will go on to B."},{"Start":"01:29.820 ","End":"01:33.380","Text":"In B, we were asked, what is the dosage rate of aspirin expressed in"},{"Start":"01:33.380 ","End":"01:37.267","Text":"milligrams of aspirin per kilogram of body mass?"},{"Start":"01:37.267 ","End":"01:42.380","Text":"As we said, we have 750 milligrams in the 2 aspirin tablets,"},{"Start":"01:42.380 ","End":"01:46.040","Text":"which are taken for an individual which weighs 160 pounds."},{"Start":"01:46.040 ","End":"01:48.562","Text":"So 160 pounds is our weight,"},{"Start":"01:48.562 ","End":"01:52.675","Text":"and for this, we have 750 milligrams."},{"Start":"01:52.675 ","End":"01:59.105","Text":"However, the question wants the expression in milligrams per kilogram of body mass."},{"Start":"01:59.105 ","End":"02:04.385","Text":"So first of all, we will convert our body mass into kilograms, 160 pounds."},{"Start":"02:04.385 ","End":"02:06.320","Text":"We will multiply by a conversion factor."},{"Start":"02:06.320 ","End":"02:07.670","Text":"For every 1 pound,"},{"Start":"02:07.670 ","End":"02:11.075","Text":"we have 0.454 kilograms."},{"Start":"02:11.075 ","End":"02:12.845","Text":"The pounds cancel out,"},{"Start":"02:12.845 ","End":"02:18.655","Text":"and this equals 72.64 kilograms."},{"Start":"02:18.655 ","End":"02:24.059","Text":"So 72.64 kilograms is the weight of our individual,"},{"Start":"02:24.059 ","End":"02:28.345","Text":"and the 2 aspirin tablets he takes are 750 milligrams."},{"Start":"02:28.345 ","End":"02:31.594","Text":"Now this is the dosage rate in milligrams per kilogram."},{"Start":"02:31.594 ","End":"02:32.750","Text":"We will take our milligrams,"},{"Start":"02:32.750 ","End":"02:35.650","Text":"which is 750 milligrams,"},{"Start":"02:35.650 ","End":"02:38.085","Text":"and divide it by the weight,"},{"Start":"02:38.085 ","End":"02:41.792","Text":"which is 72.64 kilograms."},{"Start":"02:41.792 ","End":"02:48.450","Text":"This equals 10.32 milligrams of aspirin per kilograms of body mass."},{"Start":"02:49.480 ","End":"02:52.400","Text":"That is our final answer."},{"Start":"02:52.400 ","End":"02:55.110","Text":"Thank you very much for watching."}],"ID":17627},{"Watched":false,"Name":"Density and Percentage Composition","Duration":"9m 57s","ChapterTopicVideoID":16873,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16873.jpeg","UploadDate":"2019-02-19T05:35:16.7000000","DurationForVideoObject":"PT9M57S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.080 ","End":"00:05.640","Text":"In previous videos, we spoke about SI units such as meter,"},{"Start":"00:05.640 ","End":"00:07.770","Text":"kilogram, and second,"},{"Start":"00:07.770 ","End":"00:11.460","Text":"and also about non-SI units such as liter."},{"Start":"00:11.460 ","End":"00:14.520","Text":"We also spoke about conversion factors,"},{"Start":"00:14.520 ","End":"00:18.315","Text":"which help us to get the correct units when solving a problem."},{"Start":"00:18.315 ","End":"00:24.600","Text":"In this video, we\u0027re going to discuss density and how it\u0027s related to mass and volume."},{"Start":"00:24.600 ","End":"00:28.820","Text":"We\u0027ll also see that it can be used as a conversion factor."},{"Start":"00:28.820 ","End":"00:31.760","Text":"Afterwards, we will talk about how we could use"},{"Start":"00:31.760 ","End":"00:35.930","Text":"percentage composition as a conversion factor too."},{"Start":"00:35.930 ","End":"00:38.900","Text":"First, let us discuss the density."},{"Start":"00:38.900 ","End":"00:43.460","Text":"The density of a substance is the mass per unit volume."},{"Start":"00:43.460 ","End":"00:45.770","Text":"This can be written as an equation."},{"Start":"00:45.770 ","End":"00:48.980","Text":"We can write that the density represented by"},{"Start":"00:48.980 ","End":"00:54.135","Text":"letter d is equal to the mass represented by small m,"},{"Start":"00:54.135 ","End":"00:55.605","Text":"divided by V,"},{"Start":"00:55.605 ","End":"00:58.430","Text":"capital V which is a volume."},{"Start":"00:58.430 ","End":"01:03.500","Text":"This equation gives us a density in terms of the mass and the volume."},{"Start":"01:03.500 ","End":"01:07.050","Text":"If we know we have a particular object,"},{"Start":"01:07.050 ","End":"01:08.850","Text":"and we know its mass,"},{"Start":"01:08.850 ","End":"01:10.485","Text":"and we know its volume,"},{"Start":"01:10.485 ","End":"01:12.750","Text":"we can easily measure its density."},{"Start":"01:12.750 ","End":"01:15.765","Text":"We\u0027ll also see that if we know the density,"},{"Start":"01:15.765 ","End":"01:17.785","Text":"we can calculate the mass,"},{"Start":"01:17.785 ","End":"01:19.985","Text":"if we know the volume, of course."},{"Start":"01:19.985 ","End":"01:22.565","Text":"If we know the density and the mass,"},{"Start":"01:22.565 ","End":"01:24.710","Text":"we can calculate the volume."},{"Start":"01:24.710 ","End":"01:26.435","Text":"Let\u0027s take an example."},{"Start":"01:26.435 ","End":"01:34.110","Text":"The first point to notice is that the density is an intensive property."},{"Start":"01:35.350 ","End":"01:39.170","Text":"What does this mean? This means that has"},{"Start":"01:39.170 ","End":"01:43.130","Text":"the same value regardless of how much matter we\u0027re talking about."},{"Start":"01:43.130 ","End":"01:46.730","Text":"For example, a small bottle of lead will have"},{"Start":"01:46.730 ","End":"01:51.635","Text":"the same density as a large cannon ball made of lead."},{"Start":"01:51.635 ","End":"01:56.360","Text":"It makes no difference that 1 is small while the other 1 is large."},{"Start":"01:56.360 ","End":"01:58.880","Text":"They both have the identical density,"},{"Start":"01:58.880 ","End":"02:01.540","Text":"that\u0027s called an intensive property."},{"Start":"02:01.540 ","End":"02:05.780","Text":"Now, what units are we going to use to express the density?"},{"Start":"02:05.780 ","End":"02:08.120","Text":"Let\u0027s first consider liquid."},{"Start":"02:08.120 ","End":"02:11.600","Text":"If we have a liquid whose mass is expressed in"},{"Start":"02:11.600 ","End":"02:15.515","Text":"grams and whose volume is expressed in milliliters,"},{"Start":"02:15.515 ","End":"02:23.070","Text":"then the unit of density is g/mL often written as g(mL)^-1."},{"Start":"02:24.890 ","End":"02:28.110","Text":"This is what we use for liquids."},{"Start":"02:28.110 ","End":"02:30.590","Text":"But supposing we have a solid."},{"Start":"02:30.590 ","End":"02:32.960","Text":"A solid, once again,"},{"Start":"02:32.960 ","End":"02:40.925","Text":"the mass is expressed in grams and the volume this time is in cm^3 or cubic centimeters."},{"Start":"02:40.925 ","End":"02:47.540","Text":"The units for the density are g/cm^3,"},{"Start":"02:47.540 ","End":"02:52.125","Text":"often written as g(cm)^-3."},{"Start":"02:52.125 ","End":"02:54.815","Text":"We\u0027ll use both versions in this course."},{"Start":"02:54.815 ","End":"02:58.400","Text":"Of course, these 2 ways of discussing"},{"Start":"02:58.400 ","End":"03:03.185","Text":"the density of these two sets of units are not really different."},{"Start":"03:03.185 ","End":"03:10.110","Text":"Because we learned before that a centimeter is just the same as a milliliter."},{"Start":"03:10.580 ","End":"03:17.950","Text":"Let\u0027s consider an example of how we can use this density as a conversion unit."},{"Start":"03:17.950 ","End":"03:21.125","Text":"The density of iron,"},{"Start":"03:21.125 ","End":"03:24.195","Text":"which we expressed as d,"},{"Start":"03:24.195 ","End":"03:33.940","Text":"is 11.34 g/cm^3, or 11.34 g(cm)^-3."},{"Start":"03:33.940 ","End":"03:38.635","Text":"Supposing we have a lump of lead and its mass is 100 grams,"},{"Start":"03:38.635 ","End":"03:41.930","Text":"and we\u0027re asked what is its volume?"},{"Start":"03:41.930 ","End":"03:45.205","Text":"We will recall that immediately."},{"Start":"03:45.205 ","End":"03:50.050","Text":"That we know how to write the density in terms of the mass and the volume."},{"Start":"03:50.050 ","End":"03:58.215","Text":"We know that the density is equal to the mass divided by volume."},{"Start":"03:58.215 ","End":"04:01.220","Text":"What we can do is to rearrange"},{"Start":"04:01.220 ","End":"04:07.790","Text":"this equation so that we get the volume in terms of the density and the mass."},{"Start":"04:07.790 ","End":"04:10.630","Text":"Here it is. The V"},{"Start":"04:10.630 ","End":"04:18.850","Text":"in (cm3)"},{"Start":"04:18.850 ","End":"04:21.785","Text":"= m(g)/d(g/cm3)."},{"Start":"04:21.785 ","End":"04:25.460","Text":"Let\u0027s put in the numbers we have in the problem."},{"Start":"04:25.460 ","End":"04:29.960","Text":"The mass is equal to a 100 grams,"},{"Start":"04:29.960 ","End":"04:34.560","Text":"and the density is 11.34 g(cm)-3."},{"Start":"04:35.320 ","End":"04:42.330","Text":"First let\u0027s get the correct number, 100 divided by 11.34 is 8.82."},{"Start":"04:42.940 ","End":"04:45.410","Text":"What about the units?"},{"Start":"04:45.410 ","End":"04:47.210","Text":"We have gram in the numerator,"},{"Start":"04:47.210 ","End":"04:50.705","Text":"gram in the denominator, so they cancel."},{"Start":"04:50.705 ","End":"04:56.690","Text":"We\u0027re left with 1/cm^-3."},{"Start":"04:56.690 ","End":"05:02.425","Text":"We know that 1/cm^-3 is cm^3."},{"Start":"05:02.425 ","End":"05:04.640","Text":"Now we have the answer."},{"Start":"05:04.640 ","End":"05:09.240","Text":"The answer is 8.82 cm^3."},{"Start":"05:09.910 ","End":"05:13.310","Text":"Supposing, on the other hand,"},{"Start":"05:13.310 ","End":"05:18.785","Text":"they gave us the volume and they gave us the density."},{"Start":"05:18.785 ","End":"05:21.665","Text":"Then we could easily find the mass."},{"Start":"05:21.665 ","End":"05:24.065","Text":"Here\u0027s the equation for it."},{"Start":"05:24.065 ","End":"05:28.685","Text":"We can find the mass of an object if we\u0027re given its volume and density,"},{"Start":"05:28.685 ","End":"05:37.590","Text":"m(g)=V(cm^3) multiplied by the d(g/cm^3)."},{"Start":"05:37.590 ","End":"05:39.600","Text":"Let\u0027s look at the units,"},{"Start":"05:39.600 ","End":"05:42.180","Text":"cm^3 in the numerator,"},{"Start":"05:42.180 ","End":"05:44.405","Text":"cm^3 in the denominator."},{"Start":"05:44.405 ","End":"05:46.340","Text":"These cancel each other,"},{"Start":"05:46.340 ","End":"05:48.740","Text":"and we\u0027re left just with grams,"},{"Start":"05:48.740 ","End":"05:50.870","Text":"which is mass in grams."},{"Start":"05:50.870 ","End":"05:54.835","Text":"We know we\u0027ve written the equation correctly if we get the right units."},{"Start":"05:54.835 ","End":"05:58.250","Text":"It\u0027s the first test to see that we\u0027ve done it correctly,"},{"Start":"05:58.250 ","End":"06:00.215","Text":"is to get the correct units."},{"Start":"06:00.215 ","End":"06:06.035","Text":"Now, let\u0027s try to look at another conversion factor."},{"Start":"06:06.035 ","End":"06:10.890","Text":"This time we\u0027re going to talk about the percentage composition."},{"Start":"06:14.110 ","End":"06:17.485","Text":"What\u0027s the percentage composition?"},{"Start":"06:17.485 ","End":"06:21.140","Text":"How can we use it as a conversion factor?"},{"Start":"06:21.140 ","End":"06:23.990","Text":"Let\u0027s take an example."},{"Start":"06:23.990 ","End":"06:26.615","Text":"Supposing we buy a bottle of wine."},{"Start":"06:26.615 ","End":"06:28.400","Text":"Everybody likes a bottle of wine."},{"Start":"06:28.400 ","End":"06:32.900","Text":"On the label, it is written 11% alcohol by volume."},{"Start":"06:32.900 ","End":"06:34.670","Text":"If you look at the wine bottles,"},{"Start":"06:34.670 ","End":"06:38.525","Text":"we see that almost all of them are 11% alcohol by volume."},{"Start":"06:38.525 ","End":"06:39.920","Text":"What does this mean?"},{"Start":"06:39.920 ","End":"06:43.685","Text":"It means that every 100 milliliters of wine,"},{"Start":"06:43.685 ","End":"06:46.294","Text":"there are 11 milliliters of alcohol."},{"Start":"06:46.294 ","End":"06:48.250","Text":"Let\u0027s write this down."},{"Start":"06:48.250 ","End":"06:52.694","Text":"The percentage alcohol by volume is equal to the volume of alcohol,"},{"Start":"06:52.694 ","End":"06:58.150","Text":"milliliters alcohol, dived by volume of wine in milliliters wine."},{"Start":"06:58.150 ","End":"07:02.795","Text":"Now why have I written milliliters of alcohol and not just milliliters?"},{"Start":"07:02.795 ","End":"07:06.455","Text":"That\u0027s because I have two sorts of milliliters here,"},{"Start":"07:06.455 ","End":"07:07.730","Text":"two sorts of volumes,"},{"Start":"07:07.730 ","End":"07:09.335","Text":"and milliliters of alcohol,"},{"Start":"07:09.335 ","End":"07:10.655","Text":"and milliliters of wine,"},{"Start":"07:10.655 ","End":"07:12.110","Text":"and they\u0027re not the same."},{"Start":"07:12.110 ","End":"07:17.180","Text":"When there are two different volumes of two different substances,"},{"Start":"07:17.180 ","End":"07:19.925","Text":"I have to write out what the substances are."},{"Start":"07:19.925 ","End":"07:21.875","Text":"Let\u0027s put in the numbers."},{"Start":"07:21.875 ","End":"07:24.980","Text":"The volume of alcohol to the volume of y,"},{"Start":"07:24.980 ","End":"07:27.830","Text":"and that\u0027s percentage alcohol by volume is"},{"Start":"07:27.830 ","End":"07:31.895","Text":"11 milliliters alcohol divided by 100 milliliters of wine."},{"Start":"07:31.895 ","End":"07:34.625","Text":"This is our conversion factor."},{"Start":"07:34.625 ","End":"07:37.280","Text":"We\u0027re going to use it to solve a problem."},{"Start":"07:37.280 ","End":"07:40.880","Text":"Supposing we want to calculate how much alcohol there is"},{"Start":"07:40.880 ","End":"07:45.200","Text":"in a bottle of wine of volume 750 milliliters."},{"Start":"07:45.200 ","End":"07:47.315","Text":"What can we do about that?"},{"Start":"07:47.315 ","End":"07:54.290","Text":"Let\u0027s write out the volume of alcohol in milliliters"},{"Start":"07:54.290 ","End":"07:55.460","Text":"of alcohol is equal to"},{"Start":"07:55.460 ","End":"08:02.285","Text":"the percentage alcohol times the volume of wine in milliliters of wine."},{"Start":"08:02.285 ","End":"08:08.840","Text":"The percentage of alcohol is 11 milliliters of alcohol divided by the 100 mL of wine."},{"Start":"08:08.840 ","End":"08:11.570","Text":"That\u0027s our conversion factor that we had before."},{"Start":"08:11.570 ","End":"08:14.990","Text":"If we multiply that by how much wine we have,"},{"Start":"08:14.990 ","End":"08:21.535","Text":"750 milliliters of wine we get the answer, 82.5."},{"Start":"08:21.535 ","End":"08:26.015","Text":"That\u0027s the number, 11 multiplied by the 750 divided by a 100."},{"Start":"08:26.015 ","End":"08:29.120","Text":"But we have to look and see that we get the right units."},{"Start":"08:29.120 ","End":"08:32.120","Text":"If we look here, we see that we have milliliters of wine in"},{"Start":"08:32.120 ","End":"08:35.570","Text":"the numerator and milliliters of wine in the denominator,"},{"Start":"08:35.570 ","End":"08:39.800","Text":"so that all we have left is milliliters of alcohol."},{"Start":"08:39.800 ","End":"08:42.380","Text":"We have done it correctly because we have"},{"Start":"08:42.380 ","End":"08:45.425","Text":"the volume of alcohol in milliliters of alcohol."},{"Start":"08:45.425 ","End":"08:49.100","Text":"The answer we got was in milliliters of alcohol."},{"Start":"08:49.100 ","End":"08:52.495","Text":"We\u0027ve obviously done something correctly."},{"Start":"08:52.495 ","End":"08:58.220","Text":"The answer to this problem is 82.5 milliliters of alcohol."},{"Start":"08:58.220 ","End":"09:02.150","Text":"Now, we could have been asked the problem slightly differently."},{"Start":"09:02.150 ","End":"09:06.515","Text":"We could\u0027ve been asked supposing for some obscure reason,"},{"Start":"09:06.515 ","End":"09:10.025","Text":"we wanted to drink a certain amount of alcohol."},{"Start":"09:10.025 ","End":"09:13.534","Text":"We wanted to drink 10 milliliters of alcohol."},{"Start":"09:13.534 ","End":"09:17.480","Text":"May ask us how much wine would have to"},{"Start":"09:17.480 ","End":"09:22.160","Text":"drink in order to consume 10 milliliters of alcohol?"},{"Start":"09:22.160 ","End":"09:26.165","Text":"Once again, all you require is to rearrange the equation."},{"Start":"09:26.165 ","End":"09:31.025","Text":"The volume of wine is equal to the volume"},{"Start":"09:31.025 ","End":"09:37.750","Text":"of alcohol divided by the percentage alcohol."},{"Start":"09:37.750 ","End":"09:40.805","Text":"That will give us the correct answer."},{"Start":"09:40.805 ","End":"09:43.580","Text":"Once again, we\u0027ve seen how we can take"},{"Start":"09:43.580 ","End":"09:48.095","Text":"a conversion factor and use it to get the answer we want."},{"Start":"09:48.095 ","End":"09:57.390","Text":"In this video, we discuss density and percentage composition as conversion factors."}],"ID":17628},{"Watched":false,"Name":"Exercise 9","Duration":"2m 22s","ChapterTopicVideoID":16886,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16886.jpeg","UploadDate":"2019-02-19T05:42:19.9930000","DurationForVideoObject":"PT2M22S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.555","Text":"Hi. We are going to solve the following question."},{"Start":"00:03.555 ","End":"00:08.490","Text":"A 3-liter sample of butyric acid has a mass of 2,100 grams."},{"Start":"00:08.490 ","End":"00:12.120","Text":"What is the density of butyric acid in grams per ml?"},{"Start":"00:12.120 ","End":"00:15.795","Text":"We know that the volume of butyric acid is 3 liters,"},{"Start":"00:15.795 ","End":"00:22.325","Text":"we also know that the mass of butyric acid is 2,100 grams,"},{"Start":"00:22.325 ","End":"00:28.160","Text":"and we\u0027re asked to find the density of butyric acid in grams per ml."},{"Start":"00:28.160 ","End":"00:32.004","Text":"In order to do this, we will use the equation d, density,"},{"Start":"00:32.004 ","End":"00:33.825","Text":"equals m, mass,"},{"Start":"00:33.825 ","End":"00:36.065","Text":"divided by v, volume."},{"Start":"00:36.065 ","End":"00:39.845","Text":"Since we\u0027re looking for the density of butyric acid,"},{"Start":"00:39.845 ","End":"00:46.710","Text":"we need the mass of butyric acid divided by the volume of butyric acid."},{"Start":"00:46.850 ","End":"00:51.750","Text":"The mass of butyric acid is given and equals 2,100 grams,"},{"Start":"00:51.750 ","End":"00:55.730","Text":"and the volume of butyric acid is also given and equals 3 liters,"},{"Start":"00:55.730 ","End":"00:59.930","Text":"so this gives us 700 grams per liter."},{"Start":"00:59.930 ","End":"01:03.710","Text":"Now, we were asked to find the density of butyric acid in grams per ml."},{"Start":"01:03.710 ","End":"01:06.620","Text":"In order to do this, we will use a conversion factor."},{"Start":"01:06.620 ","End":"01:11.095","Text":"Recall that 1 liter equals 1,000 ml."},{"Start":"01:11.095 ","End":"01:17.485","Text":"Therefore,1 liter divided 1000 ml equals 1,"},{"Start":"01:17.485 ","End":"01:24.690","Text":"and 1000 ml divided by 1 liter also equals 1."},{"Start":"01:24.690 ","End":"01:26.420","Text":"Now, we have to decide if to use"},{"Start":"01:26.420 ","End":"01:30.365","Text":"the first conversion factor or the second conversion factor."},{"Start":"01:30.365 ","End":"01:32.630","Text":"In order to do this, we look at our units."},{"Start":"01:32.630 ","End":"01:33.995","Text":"We have grams per liter,"},{"Start":"01:33.995 ","End":"01:36.760","Text":"and we want to change the liter to milliliters."},{"Start":"01:36.760 ","End":"01:39.380","Text":"Now, since the liter is in the denominator,"},{"Start":"01:39.380 ","End":"01:41.630","Text":"we will use the conversion factor which the liter is in"},{"Start":"01:41.630 ","End":"01:46.002","Text":"the numerator and the milliliter is in the denominator."},{"Start":"01:46.002 ","End":"01:48.615","Text":"That way the liter will cancel out,"},{"Start":"01:48.615 ","End":"01:51.705","Text":"and we will get our milliliters in the denominator."},{"Start":"01:51.705 ","End":"01:56.510","Text":"So again, the density of butyric acid equals 700 grams per"},{"Start":"01:56.510 ","End":"02:01.550","Text":"liter times our conversion factor,"},{"Start":"02:01.550 ","End":"02:05.130","Text":"1 liter per 1,000 ml."},{"Start":"02:07.880 ","End":"02:13.215","Text":"Here, we get 0.7 grams per ml."},{"Start":"02:13.215 ","End":"02:19.455","Text":"So the density of butyric acid equals 0.7 grams per ml."},{"Start":"02:19.455 ","End":"02:22.720","Text":"Thank you so much for listening. Bye-bye."}],"ID":17629},{"Watched":false,"Name":"Exercise 10","Duration":"3m 44s","ChapterTopicVideoID":16887,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16887.jpeg","UploadDate":"2019-02-19T05:42:48.8730000","DurationForVideoObject":"PT3M44S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.940","Text":"Hi. We are going to answer the following question."},{"Start":"00:02.940 ","End":"00:06.150","Text":"A 16-liter sample of chloroform at 20 degrees"},{"Start":"00:06.150 ","End":"00:09.975","Text":"Celsius has a density of 1.48 grams per milliliter."},{"Start":"00:09.975 ","End":"00:14.505","Text":"What is the mass of the chloroform at 20 degrees Celsius in kilograms?"},{"Start":"00:14.505 ","End":"00:18.585","Text":"From the question, we know that the volume of chloroform equals 16 liters."},{"Start":"00:18.585 ","End":"00:23.100","Text":"We also know that the density of chloroform equals 1.48 grams per milliliter,"},{"Start":"00:23.100 ","End":"00:25.500","Text":"and we are asked to find the mass of the chloroform."},{"Start":"00:25.500 ","End":"00:28.290","Text":"To find the mass, we will use the equation d, density,"},{"Start":"00:28.290 ","End":"00:30.540","Text":"equals m, mass,"},{"Start":"00:30.540 ","End":"00:32.615","Text":"divided by v, volume."},{"Start":"00:32.615 ","End":"00:34.159","Text":"Since we are looking for the mass,"},{"Start":"00:34.159 ","End":"00:36.529","Text":"we will multiply both sides by the volume,"},{"Start":"00:36.529 ","End":"00:39.360","Text":"and we will get the equation mass,"},{"Start":"00:39.580 ","End":"00:43.640","Text":"m, equals d, density, times v, volume."},{"Start":"00:43.640 ","End":"00:46.600","Text":"Since we\u0027re looking for the mass of chloroform,"},{"Start":"00:46.600 ","End":"00:52.139","Text":"we\u0027ll use the density of chloroform and the volume of chloroform."},{"Start":"00:52.780 ","End":"00:55.516","Text":"The density of chloroform is given,"},{"Start":"00:55.516 ","End":"00:57.440","Text":"and it\u0027s 1.48 grams per ml,"},{"Start":"00:57.440 ","End":"01:01.100","Text":"and the volume of chloroform is also given in 16 liters."},{"Start":"01:01.100 ","End":"01:10.505","Text":"This equals 23.68 grams times liters divided by milliliters."},{"Start":"01:10.505 ","End":"01:13.370","Text":"Since we have liters and milliliters in our units,"},{"Start":"01:13.370 ","End":"01:16.880","Text":"we need to use a conversion factor in order to solve this."},{"Start":"01:16.880 ","End":"01:21.500","Text":"So recall that 1 liter equals 1000 milliliters."},{"Start":"01:21.500 ","End":"01:27.625","Text":"If we divide 1 liter by 1000 ml, it equals 1,"},{"Start":"01:27.625 ","End":"01:32.385","Text":"same as 1000 ml divided by 1 liter,"},{"Start":"01:32.385 ","End":"01:36.650","Text":"it also equals 1."},{"Start":"01:36.650 ","End":"01:39.710","Text":"Now we need to decide which conversion factor we need to use,"},{"Start":"01:39.710 ","End":"01:42.200","Text":"the first one or the second one."},{"Start":"01:42.200 ","End":"01:43.310","Text":"In order to answer this,"},{"Start":"01:43.310 ","End":"01:44.765","Text":"we will look at our units."},{"Start":"01:44.765 ","End":"01:47.820","Text":"We have the liters in the numerator,"},{"Start":"01:48.290 ","End":"01:52.106","Text":"and we have the milliliters in the denominator."},{"Start":"01:52.106 ","End":"01:55.400","Text":"Therefore, we will use the conversion factor in which the milliliters"},{"Start":"01:55.400 ","End":"01:59.480","Text":"is in the numerator and the liters is in the denominator."},{"Start":"01:59.480 ","End":"02:03.275","Text":"That way the liters will cancel out and so will the milliliters."},{"Start":"02:03.275 ","End":"02:11.930","Text":"So we will multiply by our conversion factor which is 1000 ml divided by 1 liter."},{"Start":"02:11.930 ","End":"02:15.020","Text":"That way our liters will cancel out and so will our milliliters,"},{"Start":"02:15.020 ","End":"02:22.040","Text":"and then we will get 23,680 grams."},{"Start":"02:22.040 ","End":"02:31.570","Text":"So the mass of chloroform equals 23,680 grams."},{"Start":"02:31.570 ","End":"02:36.440","Text":"However, we were asked to find the mass of the chloroform in kilograms."},{"Start":"02:36.440 ","End":"02:39.440","Text":"In order to do this we will use a conversion factor."},{"Start":"02:39.440 ","End":"02:44.230","Text":"Recall that 1 kilogram equals 1000 grams."},{"Start":"02:44.230 ","End":"02:51.675","Text":"Therefore, 1 kilogram divided by 1000 grams equals 1,"},{"Start":"02:51.675 ","End":"02:57.510","Text":"and 1000 grams divided by 1 kilogram, it also equals 1."},{"Start":"02:57.510 ","End":"03:00.980","Text":"Again, in order to choose which conversion factor will you use,"},{"Start":"03:00.980 ","End":"03:03.650","Text":"the first one or the second one, we look at our units."},{"Start":"03:03.650 ","End":"03:07.067","Text":"We have grams, and we wanted to convert it to kilograms."},{"Start":"03:07.067 ","End":"03:09.410","Text":"Therefore, we will use the conversion factor which"},{"Start":"03:09.410 ","End":"03:12.830","Text":"the kilograms is in the numerator and the grams is in the denominator,"},{"Start":"03:12.830 ","End":"03:18.530","Text":"so 1 kilogram per 1000 grams,"},{"Start":"03:18.530 ","End":"03:23.600","Text":"that way the grams cancels out,"},{"Start":"03:23.600 ","End":"03:29.400","Text":"and we get the answer 23.68 kilograms."},{"Start":"03:32.230 ","End":"03:39.605","Text":"The mass of chloroform equals 23.68 kilograms."},{"Start":"03:39.605 ","End":"03:41.450","Text":"That is our final answer."},{"Start":"03:41.450 ","End":"03:45.630","Text":"Thank you very much for listening. Bye-bye."}],"ID":17630},{"Watched":false,"Name":"Exercise 11","Duration":"3m 13s","ChapterTopicVideoID":16888,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16888.jpeg","UploadDate":"2019-02-19T05:43:08.2730000","DurationForVideoObject":"PT3M13S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.080 ","End":"00:03.645","Text":"Hi. We are going to answer the following question."},{"Start":"00:03.645 ","End":"00:06.990","Text":"A sample of ethanol at 25 degrees Celsius weighs"},{"Start":"00:06.990 ","End":"00:11.880","Text":"340 grams and has a density of 0.789 grams per milliliter."},{"Start":"00:11.880 ","End":"00:16.515","Text":"What is the volume of the sample at 25 degrees Celsius in liters?"},{"Start":"00:16.515 ","End":"00:22.600","Text":"From the question, we know that the mass of ethanol is 340 grams."},{"Start":"00:27.080 ","End":"00:33.550","Text":"We also know that the density of ethanol is 0.789 grams per ml."},{"Start":"00:40.960 ","End":"00:44.300","Text":"We\u0027re asked to find the volume of ethanol."},{"Start":"00:44.300 ","End":"00:46.730","Text":"In order to do this, we will use the equation d,"},{"Start":"00:46.730 ","End":"00:49.020","Text":"density, equals m,"},{"Start":"00:49.020 ","End":"00:51.000","Text":"mass, divided by v, volume."},{"Start":"00:51.000 ","End":"00:52.955","Text":"Since we are looking for the volume,"},{"Start":"00:52.955 ","End":"00:57.020","Text":"we\u0027ll use a simple math manipulation and receive the equation v,"},{"Start":"00:57.020 ","End":"00:59.600","Text":"volume, equals m,"},{"Start":"00:59.600 ","End":"01:02.765","Text":"mass, divided by d, density."},{"Start":"01:02.765 ","End":"01:07.078","Text":"Now the mass is given and equals 340 grams,"},{"Start":"01:07.078 ","End":"01:14.465","Text":"and the density is also given and equals 0.789 grams per ml,"},{"Start":"01:14.465 ","End":"01:18.260","Text":"and this equals"},{"Start":"01:18.260 ","End":"01:28.640","Text":"430.93 ml."},{"Start":"01:28.640 ","End":"01:30.875","Text":"Now, I want to remind you, here,"},{"Start":"01:30.875 ","End":"01:34.130","Text":"we have grams divided by grams per ml."},{"Start":"01:34.130 ","End":"01:36.620","Text":"So we\u0027re actually dividing by a fraction."},{"Start":"01:36.620 ","End":"01:40.565","Text":"I want to remind you that when you divide by a fraction,"},{"Start":"01:40.565 ","End":"01:45.410","Text":"it is the same as multiplying by the inverse fraction,"},{"Start":"01:45.410 ","End":"01:48.155","Text":"meaning milliliters divided by grams."},{"Start":"01:48.155 ","End":"01:50.645","Text":"Here, the grams cancel out,"},{"Start":"01:50.645 ","End":"01:53.097","Text":"and we\u0027ll receive milliliters."},{"Start":"01:53.097 ","End":"01:55.745","Text":"Therefore, our units are in milliliters."},{"Start":"01:55.745 ","End":"02:01.040","Text":"Now, in the question, we were asked to find the volume of ethanol in liters."},{"Start":"02:01.040 ","End":"02:03.080","Text":"In order to find the volume in liters,"},{"Start":"02:03.080 ","End":"02:04.878","Text":"we will use a conversion factor."},{"Start":"02:04.878 ","End":"02:09.630","Text":"Recall that 1 liter equals 1000 milliliters."},{"Start":"02:09.790 ","End":"02:17.402","Text":"Therefore, 1 liter divided by 1000 milliliters equals 1,"},{"Start":"02:17.402 ","End":"02:22.795","Text":"and 1000 milliliters divided by 1 liter also equals 1."},{"Start":"02:22.795 ","End":"02:25.730","Text":"Now, in order to know which conversion factor"},{"Start":"02:25.730 ","End":"02:28.730","Text":"we are to use the first one or the second one,"},{"Start":"02:28.730 ","End":"02:30.295","Text":"we will look at our units."},{"Start":"02:30.295 ","End":"02:32.120","Text":"We have our units in milliliters,"},{"Start":"02:32.120 ","End":"02:33.785","Text":"and we want to change them to liters."},{"Start":"02:33.785 ","End":"02:36.410","Text":"Therefore, we will use the conversion factor,"},{"Start":"02:36.410 ","End":"02:41.285","Text":"which the liters is in the numerator and the milliliters is in the denominator."},{"Start":"02:41.285 ","End":"02:44.540","Text":"So the volume of ethanol equals"},{"Start":"02:44.540 ","End":"02:55.050","Text":"430.93 milliliters times 1 liter divided by 1000 milliliters."},{"Start":"02:55.050 ","End":"02:57.892","Text":"Our milliliters cancels out,"},{"Start":"02:57.892 ","End":"03:02.420","Text":"and we get the answer 0.43 liters."},{"Start":"03:02.420 ","End":"03:08.780","Text":"So the volume of ethanol equals 0.43 liters."},{"Start":"03:08.780 ","End":"03:11.000","Text":"That is our final answer."},{"Start":"03:11.000 ","End":"03:13.560","Text":"Thank you very much for listening."}],"ID":17631},{"Watched":false,"Name":"Exercise 12","Duration":"3m 33s","ChapterTopicVideoID":16894,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16894.jpeg","UploadDate":"2019-02-19T05:47:49.6330000","DurationForVideoObject":"PT3M33S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.390","Text":"Hi. We are going to solve the following exercise."},{"Start":"00:03.390 ","End":"00:05.430","Text":"A square piece of aluminum foil,"},{"Start":"00:05.430 ","End":"00:09.255","Text":"10 inches on a side, weighs 2.673 grams."},{"Start":"00:09.255 ","End":"00:11.445","Text":"What is the thickness of this foil?"},{"Start":"00:11.445 ","End":"00:15.480","Text":"The density of aluminum is 2.70 grams per centimeters cubed."},{"Start":"00:15.480 ","End":"00:19.000","Text":"We have a square piece of aluminum foil,"},{"Start":"00:20.600 ","End":"00:24.315","Text":"and we know that it\u0027s 10 inches on each side."},{"Start":"00:24.315 ","End":"00:26.770","Text":"Here, 10 inches, and here, 10 inches,"},{"Start":"00:26.770 ","End":"00:30.844","Text":"and this foil has a certain thickness,"},{"Start":"00:30.844 ","End":"00:32.720","Text":"and we have to find this thickness."},{"Start":"00:32.720 ","End":"00:36.835","Text":"We also know that the foil weighs 2.673 grams,"},{"Start":"00:36.835 ","End":"00:39.400","Text":"so the mass equals 2.673"},{"Start":"00:39.400 ","End":"00:48.120","Text":"grams and that the density of aluminum is 2.70 grams per centimeters cubed."},{"Start":"00:54.610 ","End":"00:57.980","Text":"First of all, we will use the equation of density"},{"Start":"00:57.980 ","End":"01:00.590","Text":"in order to find the volume of this piece of aluminum."},{"Start":"01:00.590 ","End":"01:01.790","Text":"Recall that d,"},{"Start":"01:01.790 ","End":"01:03.420","Text":"density, equals m,"},{"Start":"01:03.420 ","End":"01:06.950","Text":"mass, divided by v, the volume."},{"Start":"01:06.950 ","End":"01:08.960","Text":"By simple math manipulation,"},{"Start":"01:08.960 ","End":"01:13.444","Text":"we find that the volume equals mass divided by the density."},{"Start":"01:13.444 ","End":"01:17.910","Text":"So the mass is given and is 2.673 grams,"},{"Start":"01:20.350 ","End":"01:22.760","Text":"and the density is also given,"},{"Start":"01:22.760 ","End":"01:26.040","Text":"2.70 grams per centimeter cubed."},{"Start":"01:28.960 ","End":"01:35.675","Text":"This equals 0.99 centimeters cubed."},{"Start":"01:35.675 ","End":"01:38.675","Text":"That is the volume of a square piece of aluminum."},{"Start":"01:38.675 ","End":"01:43.250","Text":"Recall that the volume of a bar equals the length times the width,"},{"Start":"01:43.250 ","End":"01:45.995","Text":"times the height of the bar."},{"Start":"01:45.995 ","End":"01:48.770","Text":"Now, in our case, the length and the width are equal."},{"Start":"01:48.770 ","End":"01:51.065","Text":"We can say that the length is squared."},{"Start":"01:51.065 ","End":"01:55.190","Text":"In our case, the height is actually the thickness of"},{"Start":"01:55.190 ","End":"02:00.020","Text":"our square piece of aluminum and this equals the length and the width are 10 inches,"},{"Start":"02:00.020 ","End":"02:06.110","Text":"so it\u0027s 10 inches squared times the height,"},{"Start":"02:06.110 ","End":"02:08.180","Text":"which is actually our thickness."},{"Start":"02:08.180 ","End":"02:10.400","Text":"The volume of the square piece of aluminum,"},{"Start":"02:10.400 ","End":"02:14.460","Text":"which we found equals 0.99 centimeters cubed."},{"Start":"02:16.280 ","End":"02:24.080","Text":"This equals the length of our square piece of aluminum squared."},{"Start":"02:24.080 ","End":"02:28.910","Text":"So it\u0027s 10 inches squared times the height,"},{"Start":"02:28.910 ","End":"02:31.265","Text":"which is actually our thickness."},{"Start":"02:31.265 ","End":"02:35.615","Text":"Our thickness equals 0.99"},{"Start":"02:35.615 ","End":"02:42.755","Text":"centimeters cubed divided by 10 inches squared."},{"Start":"02:42.755 ","End":"02:46.055","Text":"Since we have centimeters and inches in our equation,"},{"Start":"02:46.055 ","End":"02:50.240","Text":"we are going to use a conversion factor in order to convert the inches into centimeters."},{"Start":"02:50.240 ","End":"02:53.095","Text":"In every 1 inch,"},{"Start":"02:53.095 ","End":"02:56.580","Text":"we have 2.54 centimeters,"},{"Start":"02:56.580 ","End":"02:59.015","Text":"and since the 10 inches is squared,"},{"Start":"02:59.015 ","End":"03:02.000","Text":"we\u0027re going to square our conversion factor also."},{"Start":"03:02.000 ","End":"03:11.960","Text":"This comes to 0.99 centimeters cubed divided by 645.16 centimeters squared."},{"Start":"03:11.960 ","End":"03:14.855","Text":"Since our inches canceled out,"},{"Start":"03:14.855 ","End":"03:20.540","Text":"and this equals 0.00153 centimeters."},{"Start":"03:20.540 ","End":"03:29.300","Text":"The thickness of a piece of foil equals 0.00153 centimeters."},{"Start":"03:29.300 ","End":"03:31.115","Text":"That is our final answer."},{"Start":"03:31.115 ","End":"03:33.840","Text":"Thank you very much for watching."}],"ID":17632},{"Watched":false,"Name":"Exercise 13","Duration":"4m 11s","ChapterTopicVideoID":16895,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16895.jpeg","UploadDate":"2019-02-19T05:48:26.9770000","DurationForVideoObject":"PT4M11S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:03.270","Text":"Hi. We are going to solve the following exercise."},{"Start":"00:03.270 ","End":"00:05.160","Text":"Which of the following has a greater mass: A,"},{"Start":"00:05.160 ","End":"00:08.115","Text":"a rectangular bar of iron,"},{"Start":"00:08.115 ","End":"00:14.685","Text":"80 centimeters times 2.5 centimeters times 1.5 centimeters, or B,"},{"Start":"00:14.685 ","End":"00:16.020","Text":"sheet of aluminum foil,"},{"Start":"00:16.020 ","End":"00:21.945","Text":"12.5 meters times 3.5 meters times 0.05 centimeters?"},{"Start":"00:21.945 ","End":"00:24.190","Text":"The following densities are given: iron,"},{"Start":"00:24.190 ","End":"00:30.060","Text":"7.86 grams per centimeters cubed and aluminum 2.70 grams per centimeter cubed."},{"Start":"00:30.060 ","End":"00:33.990","Text":"First, we are going to calculate the mass of A."},{"Start":"00:33.990 ","End":"00:38.445","Text":"Assuming that we have a rectangular bar and we know its length, width, and height,"},{"Start":"00:38.445 ","End":"00:44.895","Text":"so the volume of a bar equals length times width times height and this equals"},{"Start":"00:44.895 ","End":"00:53.434","Text":"80 centimeters times 2.5 centimeters times 1.5 centimeters,"},{"Start":"00:53.434 ","End":"00:57.860","Text":"and this equals 300 centimeters cubed."},{"Start":"00:57.860 ","End":"00:59.720","Text":"In order to find its mass,"},{"Start":"00:59.720 ","End":"01:02.030","Text":"we\u0027re going to use that equation d,"},{"Start":"01:02.030 ","End":"01:03.800","Text":"density equals m, mass,"},{"Start":"01:03.800 ","End":"01:06.235","Text":"divided by v, volume."},{"Start":"01:06.235 ","End":"01:10.040","Text":"When we multiply both sides by the volume, we get m,"},{"Start":"01:10.040 ","End":"01:11.420","Text":"the mass, equals d,"},{"Start":"01:11.420 ","End":"01:13.650","Text":"density, times the volume."},{"Start":"01:13.650 ","End":"01:18.800","Text":"The density is given and equals 7.86 grams per"},{"Start":"01:18.800 ","End":"01:24.680","Text":"centimeters cubed times the volume which we calculated,"},{"Start":"01:24.680 ","End":"01:28.415","Text":"which is 300 centimeters cubed."},{"Start":"01:28.415 ","End":"01:30.800","Text":"Centimeters cubed cancels out,"},{"Start":"01:30.800 ","End":"01:36.270","Text":"and we get 2,358 grams,"},{"Start":"01:36.270 ","End":"01:38.440","Text":"so that is our mass for A."},{"Start":"01:38.440 ","End":"01:41.660","Text":"Now, we will calculate the mass for B."},{"Start":"01:41.660 ","End":"01:44.140","Text":"In B, we have a sheet of aluminum foil."},{"Start":"01:44.140 ","End":"01:46.915","Text":"We have a length, and the width, and the thickness."},{"Start":"01:46.915 ","End":"01:50.240","Text":"So again, v of the sheet, it\u0027s similar to a bar,"},{"Start":"01:50.240 ","End":"01:54.570","Text":"so we\u0027ll just write bar equals length times width times height."},{"Start":"01:54.570 ","End":"01:56.900","Text":"But keep in mind that we\u0027re talking about thickness"},{"Start":"01:56.900 ","End":"02:00.040","Text":"here because it\u0027s a sheet of aluminum foil."},{"Start":"02:00.040 ","End":"02:08.555","Text":"So here it is, 12.5 meters times 3.5 meters times 0.05 centimeters."},{"Start":"02:08.555 ","End":"02:15.200","Text":"This equals 0.21875 meter"},{"Start":"02:15.200 ","End":"02:19.820","Text":"squared centimeters because we have meters times meters times centimeters."},{"Start":"02:19.820 ","End":"02:22.985","Text":"We\u0027re interested to convert everything to centimeters,"},{"Start":"02:22.985 ","End":"02:25.505","Text":"therefore, we\u0027ll multiply by a conversion factor."},{"Start":"02:25.505 ","End":"02:26.795","Text":"In every 1 meter,"},{"Start":"02:26.795 ","End":"02:28.625","Text":"we have 100 centimeters,"},{"Start":"02:28.625 ","End":"02:31.115","Text":"and since we have meters squared,"},{"Start":"02:31.115 ","End":"02:33.800","Text":"we will also square our conversion factor,"},{"Start":"02:33.800 ","End":"02:41.404","Text":"so this equals 0.21875 meters squared centimeters times"},{"Start":"02:41.404 ","End":"02:50.480","Text":"10^4 centimeters squared divided by 1 meter squared."},{"Start":"02:50.480 ","End":"02:52.895","Text":"I just took the conversion factor, and I opened it up,"},{"Start":"02:52.895 ","End":"02:58.335","Text":"100 squared equals 10^4 centimeters squared,"},{"Start":"02:58.335 ","End":"03:00.165","Text":"and we also get meter squared."},{"Start":"03:00.165 ","End":"03:02.129","Text":"So now, our meter squared cancels out,"},{"Start":"03:02.129 ","End":"03:05.060","Text":"and we have centimeter squared times centimeters,"},{"Start":"03:05.060 ","End":"03:07.715","Text":"so we get centimeters cubed in our answer,"},{"Start":"03:07.715 ","End":"03:10.840","Text":"and the centimeter squared is times the centimeters,"},{"Start":"03:10.840 ","End":"03:13.310","Text":"so we get centimeters cubed in our answer,"},{"Start":"03:13.310 ","End":"03:18.959","Text":"so this comes to 2,187.5 centimeters cubed."},{"Start":"03:18.959 ","End":"03:20.750","Text":"That is the volume of our sheet."},{"Start":"03:20.750 ","End":"03:24.620","Text":"Now, we will use the same equation in order to find the mass that we did for A."},{"Start":"03:24.620 ","End":"03:26.240","Text":"So mass equals d,"},{"Start":"03:26.240 ","End":"03:27.350","Text":"density, times v,"},{"Start":"03:27.350 ","End":"03:30.250","Text":"volume, and this time,"},{"Start":"03:30.250 ","End":"03:31.630","Text":"we\u0027ll use the density of aluminum,"},{"Start":"03:31.630 ","End":"03:36.700","Text":"which is 2.70 grams per centimeters cubed times the volume which we calculated,"},{"Start":"03:36.700 ","End":"03:43.240","Text":"which is 2,187.5 centimeters cubed."},{"Start":"03:43.240 ","End":"03:46.000","Text":"Centimeters cubed cancels out,"},{"Start":"03:46.000 ","End":"03:51.595","Text":"and we\u0027re left with 5,906.25 grams,"},{"Start":"03:51.595 ","End":"03:58.015","Text":"so the mass that we found for the aluminum sheet equals 5,906.25 grams."},{"Start":"03:58.015 ","End":"04:02.350","Text":"As you can see, this mass is greater than the mass we found in A, therefore,"},{"Start":"04:02.350 ","End":"04:07.750","Text":"the mass of the aluminum sheet is greater than the mass of the iron bar."},{"Start":"04:07.750 ","End":"04:09.223","Text":"That is our final answer."},{"Start":"04:09.223 ","End":"04:11.900","Text":"Thank you very much for watching."}],"ID":17633},{"Watched":false,"Name":"Exercise 14","Duration":"3m 43s","ChapterTopicVideoID":16889,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16889.jpeg","UploadDate":"2019-02-19T05:43:33.9100000","DurationForVideoObject":"PT3M43S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.820","Text":"Hi. We are going to answer the following question."},{"Start":"00:02.820 ","End":"00:06.780","Text":"To determine the mass of an irregularly shaped piece of copper,"},{"Start":"00:06.780 ","End":"00:09.150","Text":"the following experiment is performed."},{"Start":"00:09.150 ","End":"00:14.355","Text":"100 pieces of copper are added to 8.5 milliliters of water in a graduated cylinder."},{"Start":"00:14.355 ","End":"00:16.995","Text":"The total volume becomes 9 milliliters."},{"Start":"00:16.995 ","End":"00:20.820","Text":"The density of copper is 8.92 grams per centimeters cubed."},{"Start":"00:20.820 ","End":"00:23.430","Text":"Determine the mass of a single piece of copper,"},{"Start":"00:23.430 ","End":"00:26.445","Text":"assuming that all the pieces are of the same dimensions."},{"Start":"00:26.445 ","End":"00:31.780","Text":"From the question, we know that the initial volume of water is 8.5 milliliters."},{"Start":"00:34.340 ","End":"00:39.930","Text":"We also know that the final volume of water equals 9 ml."},{"Start":"00:41.500 ","End":"00:47.581","Text":"We know that this change in volume is caused by the addition of 100 pieces of copper."},{"Start":"00:47.581 ","End":"00:53.685","Text":"So the number of pieces of copper is 100 pieces."},{"Start":"00:53.685 ","End":"00:55.820","Text":"We are also given the density of copper,"},{"Start":"00:55.820 ","End":"00:59.550","Text":"which is 8.92 grams per centimeters cubed."},{"Start":"01:03.950 ","End":"01:07.625","Text":"Now, we are asked to find the mass of a single piece of copper."},{"Start":"01:07.625 ","End":"01:12.110","Text":"As we said, the difference in volume caused by 100 pieces of"},{"Start":"01:12.110 ","End":"01:18.170","Text":"copper equals the final volume of the water minus the initial volume of the water,"},{"Start":"01:18.170 ","End":"01:23.420","Text":"which equals 9 milliliters minus 8.5 ml,"},{"Start":"01:23.420 ","End":"01:26.530","Text":"which equals 0.5 ml."},{"Start":"01:26.530 ","End":"01:30.902","Text":"So the change in volume is 0.5 milliliters and this is the change that was [inaudible]."},{"Start":"01:30.902 ","End":"01:37.750","Text":"Since we are interested in finding the mass of a single piece of copper,"},{"Start":"01:37.750 ","End":"01:40.904","Text":"we will now calculate the volume of a single piece of copper."},{"Start":"01:40.904 ","End":"01:47.070","Text":"So the volume of 1 single piece of copper equals the total volume of 100 pieces"},{"Start":"01:47.070 ","End":"01:53.860","Text":"of copper divided by the number of pieces of copper, which is 100."},{"Start":"01:53.860 ","End":"02:00.370","Text":"This equals 0.5 ml divided by 100,"},{"Start":"02:00.370 ","End":"02:06.622","Text":"which equals 0.005 milliliters."},{"Start":"02:06.622 ","End":"02:13.640","Text":"So 0.005 milliliters is the volume that is added for every single piece of copper."},{"Start":"02:13.640 ","End":"02:17.120","Text":"Now, we\u0027re asked to find the mass of a single piece of copper."},{"Start":"02:17.120 ","End":"02:19.535","Text":"In order to do so, we will use the equation d,"},{"Start":"02:19.535 ","End":"02:21.150","Text":"density, equals m,"},{"Start":"02:21.150 ","End":"02:24.475","Text":"mass, divided by v, the volume."},{"Start":"02:24.475 ","End":"02:28.775","Text":"In order to find the mass, we will multiply both sides by the volume."},{"Start":"02:28.775 ","End":"02:33.455","Text":"The mass of a single piece of copper equals the density"},{"Start":"02:33.455 ","End":"02:38.180","Text":"of a single piece of copper times the volume of a single piece of copper."},{"Start":"02:38.180 ","End":"02:41.930","Text":"The density is the same density as the density of copper,"},{"Start":"02:41.930 ","End":"02:45.065","Text":"which equals 8.92 grams per centimeters cubed,"},{"Start":"02:45.065 ","End":"02:53.960","Text":"so 8.92 grams per centimeters cubed times the volume of a single piece of copper,"},{"Start":"02:53.960 ","End":"03:00.320","Text":"which we calculated here, 0.005 milliliters,"},{"Start":"03:00.320 ","End":"03:06.945","Text":"so this equals 0.0446 grams."},{"Start":"03:06.945 ","End":"03:09.240","Text":"Centimeters cubed is in the denominator,"},{"Start":"03:09.240 ","End":"03:12.560","Text":"and in the numerator, we have milliliters."},{"Start":"03:12.560 ","End":"03:15.140","Text":"You see that we have here in the units,"},{"Start":"03:15.140 ","End":"03:16.520","Text":"milliliters and centimeters cubed."},{"Start":"03:16.520 ","End":"03:21.335","Text":"Recall that 1 milliliter equals 1 centimeters cubed."},{"Start":"03:21.335 ","End":"03:24.500","Text":"So the milliliter and centimeters cubed cancels out,"},{"Start":"03:24.500 ","End":"03:30.390","Text":"and we get 0.0446 grams."},{"Start":"03:30.390 ","End":"03:38.315","Text":"So the mass of 1 single piece of copper equals 0.0446 grams."},{"Start":"03:38.315 ","End":"03:40.625","Text":"That is our final answer."},{"Start":"03:40.625 ","End":"03:43.830","Text":"Thank you very much for listening."}],"ID":17634},{"Watched":false,"Name":"Exercise 15","Duration":"3m 24s","ChapterTopicVideoID":16890,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16890.jpeg","UploadDate":"2019-02-19T05:43:55.8500000","DurationForVideoObject":"PT3M24S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.020 ","End":"00:03.540","Text":"Hi. We are going to solve the following question."},{"Start":"00:03.540 ","End":"00:06.810","Text":"To determine the volume of an irregularly shaped vessel,"},{"Start":"00:06.810 ","End":"00:08.445","Text":"the vessel was weighed empty,"},{"Start":"00:08.445 ","End":"00:13.755","Text":"120 grams, and when filled with carbon tetrachloride, 282.5 grams."},{"Start":"00:13.755 ","End":"00:16.995","Text":"What is the volume capacity of the vessel in milliliters?"},{"Start":"00:16.995 ","End":"00:21.735","Text":"The density of carbon tetrachloride is 1.59 grams per milliliters."},{"Start":"00:21.735 ","End":"00:24.840","Text":"From the question, we know the density of"},{"Start":"00:24.840 ","End":"00:33.700","Text":"carbon tetrachloride equals 1.59 grams per ml."},{"Start":"00:33.740 ","End":"00:38.340","Text":"We also know that the mass of the empty vessel equals"},{"Start":"00:38.340 ","End":"00:48.150","Text":"120 grams and that the mass of the filled vessel equals 282.5 grams."},{"Start":"00:50.740 ","End":"00:55.130","Text":"We are asked to find the volume capacity of the vessel."},{"Start":"00:55.130 ","End":"01:01.805","Text":"The volume of the vessel equals the volume of the carbon tetrachloride which filled it."},{"Start":"01:01.805 ","End":"01:04.190","Text":"In order to determine the volume of the vessel,"},{"Start":"01:04.190 ","End":"01:05.990","Text":"we will use the equation d,"},{"Start":"01:05.990 ","End":"01:08.405","Text":"density, equals m,"},{"Start":"01:08.405 ","End":"01:11.435","Text":"mass, divided by v, volume."},{"Start":"01:11.435 ","End":"01:17.315","Text":"The units which are most commonly used for density are grams per centimeters cubed,"},{"Start":"01:17.315 ","End":"01:20.975","Text":"which equals grams per ml."},{"Start":"01:20.975 ","End":"01:24.200","Text":"Now since we are looking for the volume of the vessel,"},{"Start":"01:24.200 ","End":"01:25.835","Text":"we will use the equation,"},{"Start":"01:25.835 ","End":"01:32.000","Text":"volume equals mass divided by density."},{"Start":"01:32.000 ","End":"01:35.165","Text":"Since we are looking for the volume of the carbon tetrachloride,"},{"Start":"01:35.165 ","End":"01:39.975","Text":"we will use the mass of carbon tetrachloride and the density of carbon tetrachloride."},{"Start":"01:39.975 ","End":"01:45.890","Text":"The density of carbon tetrachloride is given and equals 1.59 grams per milliliter."},{"Start":"01:45.890 ","End":"01:51.170","Text":"The mass of carbon tetrachloride equals the mass of"},{"Start":"01:51.170 ","End":"01:56.285","Text":"the filled vessel minus the mass of the empty vessel,"},{"Start":"01:56.285 ","End":"01:59.840","Text":"which equals 282.5 grams,"},{"Start":"01:59.840 ","End":"02:03.035","Text":"minus 120 grams,"},{"Start":"02:03.035 ","End":"02:06.935","Text":"which equals 162.5 grams."},{"Start":"02:06.935 ","End":"02:09.304","Text":"So now, we can go back to the equation."},{"Start":"02:09.304 ","End":"02:15.560","Text":"The volume of carbon tetrachloride equals the mass of carbon tetrachloride,"},{"Start":"02:15.560 ","End":"02:19.050","Text":"which equals 162.5 grams,"},{"Start":"02:20.620 ","End":"02:24.649","Text":"divided by the density of carbon tetrachloride,"},{"Start":"02:24.649 ","End":"02:29.774","Text":"which equals 1.59 grams per milliliter,"},{"Start":"02:29.774 ","End":"02:35.180","Text":"and this equals 102.2."},{"Start":"02:35.180 ","End":"02:37.835","Text":"Now, if we take a look at the units,"},{"Start":"02:37.835 ","End":"02:44.660","Text":"we need to divide grams by a fraction, grams per milliliter."},{"Start":"02:45.300 ","End":"02:51.250","Text":"Now, recall that dividing by a fraction is the same as multiplying by its reciprocal."},{"Start":"02:51.250 ","End":"02:57.665","Text":"So it\u0027s the same as grams times milliliter divided by grams."},{"Start":"02:57.665 ","End":"03:00.440","Text":"In this case, the grams cancel out,"},{"Start":"03:00.440 ","End":"03:03.215","Text":"and the final units we get are milliliters."},{"Start":"03:03.215 ","End":"03:07.370","Text":"So the answer is 102.2 milliliters."},{"Start":"03:07.370 ","End":"03:12.665","Text":"So the final answer that we got is that the volume of carbon tetrachloride,"},{"Start":"03:12.665 ","End":"03:18.578","Text":"which equals the volume of the vessel, equals 102.2 milliliters."},{"Start":"03:18.578 ","End":"03:20.135","Text":"That is our final answer."},{"Start":"03:20.135 ","End":"03:22.242","Text":"Thank you very much for listening."},{"Start":"03:22.242 ","End":"03:24.660","Text":"We hope to see you next time."}],"ID":17635},{"Watched":false,"Name":"Exercise 16","Duration":"4m 17s","ChapterTopicVideoID":16891,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16891.jpeg","UploadDate":"2019-02-19T05:44:22.8800000","DurationForVideoObject":"PT4M17S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.715","Text":"Hi. We are going to answer the following question."},{"Start":"00:02.715 ","End":"00:06.390","Text":"A solution consisting of 7 percent acetone and 93 percent water"},{"Start":"00:06.390 ","End":"00:10.560","Text":"by mass has a density of 0.9867 grams per ml."},{"Start":"00:10.560 ","End":"00:16.155","Text":"What mass of acetone in kilograms is present in 7.5 liters of solution?"},{"Start":"00:16.155 ","End":"00:22.780","Text":"From the question, we know that the density of the solution equals 0.9867 grams per ml."},{"Start":"00:28.820 ","End":"00:35.900","Text":"We also know that the volume of the solution equals 7.5 liters,"},{"Start":"00:37.800 ","End":"00:42.460","Text":"and we know that if we have 100 grams of solution,"},{"Start":"00:42.890 ","End":"00:45.495","Text":"7 percent is acetone."},{"Start":"00:45.495 ","End":"00:49.760","Text":"Therefore, 7 grams will be acetone and 93 percent water,"},{"Start":"00:49.760 ","End":"00:53.885","Text":"meaning, 93 grams of water."},{"Start":"00:53.885 ","End":"00:56.705","Text":"Now, we\u0027re asked to find the mass of acetone,"},{"Start":"00:56.705 ","End":"01:00.380","Text":"which are present in 7.5 liters of solution."},{"Start":"01:00.380 ","End":"01:03.200","Text":"First, we have to find the mass of the solution."},{"Start":"01:03.200 ","End":"01:05.765","Text":"In order to do so, we will use the equation d,"},{"Start":"01:05.765 ","End":"01:07.520","Text":"density, equals m, mass,"},{"Start":"01:07.520 ","End":"01:09.950","Text":"divided by v. Since we are interested in the mass,"},{"Start":"01:09.950 ","End":"01:12.020","Text":"we will multiply both sides by the volume."},{"Start":"01:12.020 ","End":"01:14.840","Text":"Therefore, the mass of the solution equals the density of"},{"Start":"01:14.840 ","End":"01:18.170","Text":"the solution times the volume of the solution."},{"Start":"01:18.170 ","End":"01:22.010","Text":"The density of the solution is given and equals 0.9867"},{"Start":"01:22.010 ","End":"01:26.300","Text":"grams per ml times the volume of the solution,"},{"Start":"01:26.300 ","End":"01:28.705","Text":"which equals 7.5 liters."},{"Start":"01:28.705 ","End":"01:35.815","Text":"This equals 7.4 grams times liter divided by milliliter."},{"Start":"01:35.815 ","End":"01:38.603","Text":"Now, here in the units, we have liters and milliliters."},{"Start":"01:38.603 ","End":"01:43.130","Text":"Recall that 1 liter equals 1,000 milliliters, so therefore,"},{"Start":"01:43.130 ","End":"01:52.767","Text":"this equals 7.4 grams times 1,000 milliliters divided by milliliters."},{"Start":"01:52.767 ","End":"01:55.560","Text":"So milliliters cancel out,"},{"Start":"01:55.560 ","End":"02:02.100","Text":"and here we get 7,400 grams,"},{"Start":"02:02.100 ","End":"02:08.600","Text":"so the mass of the solution equals 7,400 grams."},{"Start":"02:08.600 ","End":"02:12.050","Text":"Now we\u0027re asked to find the mass of acetone in kilograms."},{"Start":"02:12.050 ","End":"02:19.690","Text":"The mass of acetone equals the mass of the solution,"},{"Start":"02:20.180 ","End":"02:23.300","Text":"and here we will use the fact that,"},{"Start":"02:23.300 ","End":"02:25.850","Text":"in 100 grams of solution,"},{"Start":"02:25.850 ","End":"02:31.670","Text":"we have 7 grams of acetone."},{"Start":"02:31.670 ","End":"02:35.925","Text":"This can also be used as a conversion factor, meaning,"},{"Start":"02:35.925 ","End":"02:40.750","Text":"the mass of acetone equals the mass of the solution times"},{"Start":"02:40.750 ","End":"02:48.114","Text":"7 grams of acetone per 100 grams of solution."},{"Start":"02:48.114 ","End":"02:55.850","Text":"This equals 7,400 grams of solution times 7 grams"},{"Start":"02:55.850 ","End":"03:02.972","Text":"of acetone divided by 100 grams of solution."},{"Start":"03:02.972 ","End":"03:05.075","Text":"Grams of solution cancel out,"},{"Start":"03:05.075 ","End":"03:13.535","Text":"and we get 518.0175 grams of acetone,"},{"Start":"03:13.535 ","End":"03:20.369","Text":"which equals 518.02 grams of acetone."},{"Start":"03:20.369 ","End":"03:23.163","Text":"So we have the mass of acetone in grams."},{"Start":"03:23.163 ","End":"03:26.571","Text":"But remember, we were asked to find the mass of acetone in kilograms."},{"Start":"03:26.571 ","End":"03:31.677","Text":"Recall that 1 kilogram equals 1000 grams."},{"Start":"03:31.677 ","End":"03:36.850","Text":"Therefore, 1 kilogram divided by 1000 grams equals 1,"},{"Start":"03:36.920 ","End":"03:43.635","Text":"and 1,000 grams divided by 1 kilogram also equals 1."},{"Start":"03:43.635 ","End":"03:51.480","Text":"So again, the mass of acetone equals 518.02 grams,"},{"Start":"03:51.480 ","End":"03:53.965","Text":"and we want to change the grams to kilograms."},{"Start":"03:53.965 ","End":"03:58.330","Text":"So we will use the conversion factor in which the grams is in the denominator"},{"Start":"03:58.330 ","End":"04:03.397","Text":"so times 1 kilogram divided by 1000 grams."},{"Start":"04:03.397 ","End":"04:05.525","Text":"This way, the grams cancel out,"},{"Start":"04:05.525 ","End":"04:07.250","Text":"and we are left with kilograms."},{"Start":"04:07.250 ","End":"04:13.139","Text":"So the mass of acetone equals 0.518 kilograms."},{"Start":"04:13.139 ","End":"04:15.200","Text":"That is our final answer."},{"Start":"04:15.200 ","End":"04:18.180","Text":"Thank you very much for listening."}],"ID":17636},{"Watched":false,"Name":"Exercise 17","Duration":"4m 22s","ChapterTopicVideoID":16892,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16892.jpeg","UploadDate":"2019-02-19T05:44:50.5400000","DurationForVideoObject":"PT4M22S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.895","Text":"We are going to answer the following question."},{"Start":"00:02.895 ","End":"00:06.210","Text":"A solution of sucrose in water is 28 percent sucrose by"},{"Start":"00:06.210 ","End":"00:10.015","Text":"mass and has a density of 1.118 grams per milliliter."},{"Start":"00:10.015 ","End":"00:13.200","Text":"What volume of the solution in liters must be used in"},{"Start":"00:13.200 ","End":"00:17.294","Text":"an application requiring 1.095 kilograms of sucrose?"},{"Start":"00:17.294 ","End":"00:20.025","Text":"From the question, we know that the solution of sucrose"},{"Start":"00:20.025 ","End":"00:22.678","Text":"in water is 28 percent sucrose by mass,"},{"Start":"00:22.678 ","End":"00:25.755","Text":"meaning that at every 100 grams of solution,"},{"Start":"00:25.755 ","End":"00:28.990","Text":"we have 28 grams of sucrose."},{"Start":"00:29.320 ","End":"00:39.523","Text":"We also know that the density of the solution equals 1.118 grams per ml,"},{"Start":"00:39.523 ","End":"00:41.690","Text":"and we know that,"},{"Start":"00:41.690 ","End":"00:43.505","Text":"for a specific application,"},{"Start":"00:43.505 ","End":"00:46.700","Text":"1.095 kilograms of sucrose are required."},{"Start":"00:46.700 ","End":"00:51.319","Text":"So the mass of sucrose that is required equals 1.095 kilograms."},{"Start":"00:51.319 ","End":"00:53.480","Text":"We are asked to find the volume of"},{"Start":"00:53.480 ","End":"00:57.755","Text":"the solution which is required for the specific application."},{"Start":"00:57.755 ","End":"01:00.580","Text":"First, we will find the mass of the solution."},{"Start":"01:00.580 ","End":"01:03.300","Text":"To find the mass of the solution,"},{"Start":"01:03.300 ","End":"01:07.895","Text":"we will use the relationship of mass between the solution and sucrose."},{"Start":"01:07.895 ","End":"01:10.130","Text":"So the mass of the solution equals the mass of"},{"Start":"01:10.130 ","End":"01:16.025","Text":"sucrose times the relationship between solution and sucrose,"},{"Start":"01:16.025 ","End":"01:18.485","Text":"so times 100 grams of solution,"},{"Start":"01:18.485 ","End":"01:22.855","Text":"divided by 28 grams of sucrose."},{"Start":"01:22.855 ","End":"01:28.419","Text":"The mass of sucrose equals 1.095 kilograms."},{"Start":"01:30.170 ","End":"01:36.420","Text":"Here, we get 3.91 kilograms of sucrose times grams of"},{"Start":"01:36.420 ","End":"01:42.030","Text":"solution divided by grams of sucrose."},{"Start":"01:42.030 ","End":"01:45.805","Text":"Here, we have kilograms of sucrose divided by grams of sucrose."},{"Start":"01:45.805 ","End":"01:52.605","Text":"Now, keep in mind that 1 kilogram equals 1,000 grams."},{"Start":"01:52.605 ","End":"01:57.920","Text":"Therefore, 1 kilogram divided by a gram equals 1,000."},{"Start":"01:57.920 ","End":"02:02.065","Text":"So instead of writing kilograms of sucrose divided by grams of sucrose,"},{"Start":"02:02.065 ","End":"02:05.010","Text":"we can multiply by 1,000."},{"Start":"02:05.010 ","End":"02:12.195","Text":"So we get that the mass of the solution equals 3,910 grams of solution."},{"Start":"02:12.195 ","End":"02:14.799","Text":"Here we\u0027re asked to find the volume of the solution."},{"Start":"02:14.799 ","End":"02:16.765","Text":"In order to find the volume of the solution,"},{"Start":"02:16.765 ","End":"02:18.513","Text":"we will use the equation d,"},{"Start":"02:18.513 ","End":"02:20.520","Text":"density equals m,"},{"Start":"02:20.520 ","End":"02:23.185","Text":"mass, divided by v, the volume."},{"Start":"02:23.185 ","End":"02:25.000","Text":"Since we are looking for the volume,"},{"Start":"02:25.000 ","End":"02:32.660","Text":"a simple math manipulation will give us volume equals mass divided by the density."},{"Start":"02:32.660 ","End":"02:35.420","Text":"So the volume of the solution equals the mass of"},{"Start":"02:35.420 ","End":"02:39.350","Text":"the solution divided by the density of the solution."},{"Start":"02:39.350 ","End":"02:42.500","Text":"The mass of the solution is what we calculated,"},{"Start":"02:42.500 ","End":"02:49.640","Text":"3,910 grams, divided by the density of the solution,"},{"Start":"02:49.640 ","End":"02:53.630","Text":"which is given, and equals 1.118 grams per ml."},{"Start":"02:53.630 ","End":"03:03.360","Text":"So this equals 3,497.32 grams divided by grams per ml."},{"Start":"03:03.360 ","End":"03:05.960","Text":"Now recall that, when we are dividing by a fraction,"},{"Start":"03:05.960 ","End":"03:10.490","Text":"it is the same as multiplying by the reciprocal of the fraction, meaning,"},{"Start":"03:10.490 ","End":"03:14.780","Text":"grams per grams per ml equals grams times"},{"Start":"03:14.780 ","End":"03:20.600","Text":"milliliter divided by grams, which equals milliliters."},{"Start":"03:20.600 ","End":"03:29.435","Text":"So our answer, the volume of the solution, equals 3,497.32 milliliters."},{"Start":"03:29.435 ","End":"03:34.055","Text":"Now we are asked to find the volume of the solution in liters."},{"Start":"03:34.055 ","End":"03:37.885","Text":"In order to solve this, we will use a relationship."},{"Start":"03:37.885 ","End":"03:44.370","Text":"1 liter equals 1,000 milliliters, and therefore,"},{"Start":"03:44.370 ","End":"03:51.135","Text":"1 milliliter equals 1 liter divided by 1,000."},{"Start":"03:51.135 ","End":"03:56.700","Text":"Your 3,497.32 milliliters equals"},{"Start":"03:56.700 ","End":"04:05.890","Text":"3,497.32 liters divided by 1,000,"},{"Start":"04:05.950 ","End":"04:10.430","Text":"which comes to 3.5 liters."},{"Start":"04:10.430 ","End":"04:16.310","Text":"So the volume of the solution equals 3.5 liters."},{"Start":"04:16.310 ","End":"04:18.500","Text":"That is our final answer."},{"Start":"04:18.500 ","End":"04:20.668","Text":"Thank you for listening."},{"Start":"04:20.668 ","End":"04:22.740","Text":"We hope to see you again."}],"ID":17637},{"Watched":false,"Name":"Exercise 18","Duration":"3m 2s","ChapterTopicVideoID":16893,"CourseChapterTopicPlaylistID":99001,"HasSubtitles":true,"ThumbnailPath":"https://www.proprep.com/Images/Videos_Thumbnails/16893.jpeg","UploadDate":"2019-02-19T05:46:53.4870000","DurationForVideoObject":"PT3M2S","Description":null,"VideoComments":[],"Subtitles":[{"Start":"00:00.000 ","End":"00:02.820","Text":"Hi. We are going to solve the following exercise."},{"Start":"00:02.820 ","End":"00:08.099","Text":"Ethylene glycol has a density of 1.11 grams per milliliters at 20 degrees Celsius."},{"Start":"00:08.099 ","End":"00:13.935","Text":"1, what is the mass in grams of 465 milliliters of ethylene glycol, 2,"},{"Start":"00:13.935 ","End":"00:18.770","Text":"what is the mass in kilograms of 17.2 liters of ethylene glycol,"},{"Start":"00:18.770 ","End":"00:23.870","Text":"and 3, what is the volume in milliliters occupied by 72 grams of ethylene glycol?"},{"Start":"00:23.870 ","End":"00:25.280","Text":"In 1, we\u0027re asked,"},{"Start":"00:25.280 ","End":"00:29.629","Text":"what is the mass in grams of 465 milliliters of ethylene glycol?"},{"Start":"00:29.629 ","End":"00:32.225","Text":"Recall that d, the density,"},{"Start":"00:32.225 ","End":"00:34.265","Text":"equals mass, m,"},{"Start":"00:34.265 ","End":"00:35.910","Text":"divided by v, the volume."},{"Start":"00:35.910 ","End":"00:37.525","Text":"Here, we are looking for the mass."},{"Start":"00:37.525 ","End":"00:40.010","Text":"Therefore, we will use the equation mass equals"},{"Start":"00:40.010 ","End":"00:43.775","Text":"d times v. You multiply both sides by the volume."},{"Start":"00:43.775 ","End":"00:50.857","Text":"The density is given 1.11 grams per milliliters,"},{"Start":"00:50.857 ","End":"00:55.200","Text":"and the volume is given in Question 1, 465 milliliters."},{"Start":"00:55.200 ","End":"00:57.400","Text":"The milliliters cancel out,"},{"Start":"00:57.400 ","End":"01:01.705","Text":"and we get 516.15 grams."},{"Start":"01:01.705 ","End":"01:03.560","Text":"That is our answer for 1."},{"Start":"01:03.560 ","End":"01:09.250","Text":"In 2, we are asked, what is the mass in kilograms of 17.2 liters of ethylene glycol?"},{"Start":"01:09.250 ","End":"01:10.540","Text":"Again, we\u0027re looking for the mass."},{"Start":"01:10.540 ","End":"01:11.710","Text":"We will use the same equation."},{"Start":"01:11.710 ","End":"01:13.930","Text":"Mass equals density times the volume."},{"Start":"01:13.930 ","End":"01:17.500","Text":"Again, the density is given an equals 1.11 grams per ml,"},{"Start":"01:17.500 ","End":"01:21.620","Text":"and the volume in which we are given a 17.2 liters."},{"Start":"01:22.260 ","End":"01:26.380","Text":"Since we have liters and milliliters in the same answer,"},{"Start":"01:26.380 ","End":"01:28.600","Text":"we have to multiply by a conversion factor,"},{"Start":"01:28.600 ","End":"01:32.815","Text":"so 1 liter contains 1000 milliliters."},{"Start":"01:32.815 ","End":"01:34.270","Text":"The liters cancel out,"},{"Start":"01:34.270 ","End":"01:35.980","Text":"and the milliliters also cancel out,"},{"Start":"01:35.980 ","End":"01:40.745","Text":"and this equals 19,092 grams."},{"Start":"01:40.745 ","End":"01:44.030","Text":"However, we were asked to give the answer in kilograms,"},{"Start":"01:44.030 ","End":"01:46.520","Text":"and therefore, we will multiply by conversion factor."},{"Start":"01:46.520 ","End":"01:48.515","Text":"In every 1 kilogram,"},{"Start":"01:48.515 ","End":"01:51.395","Text":"we have 1,000 grams."},{"Start":"01:51.395 ","End":"01:58.430","Text":"Grams cancel out, and our answer comes to 19.1 kilograms."},{"Start":"01:58.430 ","End":"02:00.350","Text":"That is our answer for Number 2."},{"Start":"02:00.350 ","End":"02:02.120","Text":"Now, we will continue to 3."},{"Start":"02:02.120 ","End":"02:04.700","Text":"In 3, we\u0027re asked, what is the volume in milliliters"},{"Start":"02:04.700 ","End":"02:07.445","Text":"occupied by 72 grams ethylene glycol?"},{"Start":"02:07.445 ","End":"02:09.035","Text":"Here we are asked to find the volume."},{"Start":"02:09.035 ","End":"02:10.640","Text":"Again, d, density,"},{"Start":"02:10.640 ","End":"02:13.160","Text":"equals m, mass, divided by the volume."},{"Start":"02:13.160 ","End":"02:15.529","Text":"Since in this case we are asked to find the volume,"},{"Start":"02:15.529 ","End":"02:18.650","Text":"a simple math manipulation will give us v,"},{"Start":"02:18.650 ","End":"02:20.870","Text":"the volume, equals m,"},{"Start":"02:20.870 ","End":"02:24.860","Text":"which is the mass, divided by d. Now the mass is given in the question,"},{"Start":"02:24.860 ","End":"02:28.190","Text":"72 grams, and d is the density which was already given,"},{"Start":"02:28.190 ","End":"02:31.020","Text":"1.11 grams per ml."},{"Start":"02:34.150 ","End":"02:40.355","Text":"This equals 64.86 milliliters."},{"Start":"02:40.355 ","End":"02:42.020","Text":"Now, just a reminder here,"},{"Start":"02:42.020 ","End":"02:43.864","Text":"when we are dividing by a fraction,"},{"Start":"02:43.864 ","End":"02:46.183","Text":"here, we\u0027re dividing grams by grams per ml,"},{"Start":"02:46.183 ","End":"02:49.420","Text":"it is the same as multiplying by the reciprocal of the fraction,"},{"Start":"02:49.420 ","End":"02:53.015","Text":"so it\u0027s the same as multiplying grams times milliliters per gram."},{"Start":"02:53.015 ","End":"02:54.425","Text":"The grams cancel out,"},{"Start":"02:54.425 ","End":"02:56.285","Text":"and we are left with milliliters."},{"Start":"02:56.285 ","End":"02:58.895","Text":"Therefore, our units are milliliters."},{"Start":"02:58.895 ","End":"03:00.395","Text":"That is our answer for 3."},{"Start":"03:00.395 ","End":"03:03.120","Text":"Thank you very much for watching."}],"ID":17638}],"Thumbnail":null,"ID":99001}]

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1.1

5