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In this video, I'm going to explain how to change units when we have two units in the quantity.

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We are going to use more difficult, more complex conversion factors.

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So, the first example that I'm going to do is this one.

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The speed of sound is 340 meters per second. How much is this in kilometers per hour?

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So, we need to change this number, meters per second, to kilometers per hour.

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notice the difference between this situation in the previous one is that we

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have two units that we need to change so I'm going to study the usual way and I'm

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going to write what I have 340 meters per second okay and I want to end with

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kilometers per hour so I'm going to need two changes so I'm going to write two

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lines to conversion factors the first one is very easy from meters to

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kilometers so meters go here you know meters go over the line and we all know

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that one kilometer is 1,000 meters okay the second one is seconds to hour but

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notice that seconds cannot go here okay seconds sorry hours cannot go here

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because they are below the line so hours I'm going to be below the line in the

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conversion factor the same than in the final unit and seconds I'm going to be

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here and you can check this but one second is 3600 or one hour is at 3600 seconds the reason for

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doing this this way is very obvious meters cancel meters seconds cancel seconds and i am left with

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kilometers and hours like in my final product so what i need to do now is use my calculator so

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So 340 times 3,600 is 1,024,000, and I have 1,000 here.

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So if I do the math, these math are very easy.

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result is that 340 meters per second speed of sound is 1244 kilometers per hour. Really fast,

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as you can see. I'm going to do the second example. The density of mercury, mercury is a

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liquid, it's the only liquid metal, is 13.6 grams per cubic centimeter. So again, I want to change

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this to kilograms per cubic meter. Again, two conversion factors. First, I go from kilograms

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from grams to kilograms, and this is easy. One kilogram is 1000 grams. And then I need

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to go from cubic centimeters to cubic meters, but cubic meters should be below the line,

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and cubic centimeters is over the line. Okay, how do I change from cubic centimeters to

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cubic meters you know that 100 centimeter is one meter but if it has to

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be cubed so I'm going to cube everything okay and 100 cubed is 1 million we will

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learn a easier way to write this so I write these numbers here okay and now

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what I have to do is very easy doing the math by the way grams cancel grams cubic

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centimeters cancel cubic centimeters and I am left with kilograms cubic meters

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that is my final result and I do the match is very easy 13.6 times 1 million

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divided by 1,000 is 13,600 kilograms for cubic meters