12.05.2024 How To Convert Cubic Centimeters to Cubic Meters - cm^3 to m^3 - Volume

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In this video. we're going to talk about how to convert. cubic centimeters. into. cubic meters. so in this example problem we have 500. 000 cubic centimeters. whenever you have cubic units be it. cubic centimeters cubic feet cubic. inches cubic meters. all of these are units of volume. so we're converting from one unit of. volume to another unit of volume. but how do we change it from cubic. centimeters to cubic meters. well for one thing. we need to know that one meter. has the same length as a hundred. centimeters. so what we're going to do is we're going. to start with what we're given which is. 500 cubic centimeters. and then we're going to convert that. into meters. using. the conversion factor that we have here. now there's two parts. to that equation we have one meter on. one side and 100 centimeters on the. other side.

Should we put the 100 centimeters on top. of the second fraction or. on the bottom of the second fraction. what would you say. what would you place it. now notice that we have units of. centimeters on the top left. in order for that unit to cancel we need. to put centimeters on the bottom. so therefore we're going to put 100. centimeters. on the bottom of the second fraction. but we're going to put one meter on top. of the first fraction. now you might be wondering what does it. mean. when we have centimeters cubed how is. that different from centimeters. centimeters cubed mean that. we have three units of centimeters being. multiplied to each other. right now only one will cancel. and we'll still have two more in order. to cancel all three of the centimeter. units on the top left. what we need to do is we need to raise.

This conversion factor to the third. power. if we do that. note what's going to happen. so what's one meter to the third power. if you multiply one meter by one meter. by one meter you're going to get one. cubic meter. now 100 centimeters to the third power. that's 100 centimeters times 100. centimeters times 100 centimeters. which is. 100 to the third power that's a million. so this is going to be. a million. cubic centimeters. so now we could cancel the unit cubic. centimeters. so it's 500 000 divided by a million. which is. .5. cubic meters. so that's how we can convert from cubic. centimeters to cubic meters by the way. one million is equal to ten to the sixth. because there are six zeros here. another way in which you can see that is. you could replace a hundred. with 10 squared. 10 squared is 100 and so when you have.

10 squared raised to the third power you. can multiply the exponents 2 and 3 and. so you could write this as. 10 to the 6. cubic centimeters. if you don't want to write out a million. now let's work on another example let's. say. we have. 2.4 times 10 to the 8. cubic centimeters. and we want to change that into cubic. meters. so feel free to pause the video and try. this example problem based on what we. did in the last problem. so let's begin with what we're given. now based on the last problem we know. that one meter is equal to 100. centimeters i'm going to write it as. 10 squared centimeters. and then just like the last problem. we're going to raise it to the third. power. so this becomes one cubic meter. and then 10 squared raised to the third. power. that's going to be. 10 to the 6. cubic centimeters. so at this point we could cancel the.

unit cubic centimeters and then we could. divide. 10 to the eight by ten to the sixth. when you divide. by a common base in this case base ten. you need to subtract the exponents. so subtracting eight by six gives us two. thus the answer is going to be two point. four 2.4. times 10 to the second power. cubic meters. so now you know how to convert the. volume from. cubic centimeters to cubic meters. so that's basically it for this video. hopefully it really helped you to see. how to convert from one unit of volume. into another unit the key is to cube the. conversion factor if you do that then. that's going to help you to get the. right answer

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