Need help with converting squared and cubed units

[virtuoso735]

I feel really stupid, but I'm having some trouble converting squared and cubed units. How do you convert cm^2 to m^3? For example, how do you convert 5 cm^2 to m^2? How do you convert cm^3 to m^3, and so on? Is there a shortcut?

Edit: Sorry, this should be in the Q&A subforum, but I posted it here by accident. Can a mod move it?

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[jevo]

Just square or cube the powers of 10.

5cm would normally b 0.05m which is the same as 5x10^-2m

So if you go from 5cm^2 to m^2, you would go (5x10^-2) x (10^-2) and then add the 10^-2's

5cm^2 = 5 x 10^-4 m^2

5cm^3 = (5)x(10^-2)^3 = 5x10^-6 m^3

Hopefully this isn't too confusing lol

 

[misseskwee]

This is how I do it.
So first off you multiply it by its conversion factor (1m=100cm), which u must square in order to cancel out your squared units:
5cm^2 x [(1m)/(100cm)]^2 = 5cm^2 x [(1m^2)/(10,000cm^2)] = .0005m^2 = 5x10^-4 m^2

If you need to convert cm^3, same thing, just cube your conversion factor.

 

[SaintJude]

Actually had trouble with this myself for a while. This is the easiest/quickest way for me. I'm gonna be writing this way on all my practice exams to maintain accuracy.

1 cm = 10 ^-2 m
(Now square both sides if you want cm to m^2. Or cube both sides if you want to convert cm to m^3.)

I'll do "cube"

1 cm ^3 = (10^-2m) ^3 = 1 x 10^-6 m^3

Then you can replace any number with the 1. What I like about this method is that you easily convert to anything

nm to m^3 whatever...

 

[MedPR]

I feel really stupid, but I'm having some trouble converting squared and cubed units. How do you convert cm^2 to m^3? For example, how do you convert 5 cm^2 to m^2? How do you convert cm^3 to m^3, and so on? Is there a shortcut?

Edit: Sorry, this should be in the Q&A subforum, but I posted it here by accident. Can a mod move it?

I've actually been confused about this all the way up until last night (which is good because my MCAT is on thursday)!

So 5cm^2 to m^2. You know that 1cm is 10^-2m. If you use the stoichiometry technique you learned in general chemistry, it is very very simple.

So you start with what you know; 5cm^2. Then you convert it to meters (10^-2m/cm). But at this point you've only canceled out one "cm" so in effect you have 5*10^-2m/cm. You need to cancel out cm again (and get m^2). So you multiply by the conversion factor (10^-2m/cm) one more time. Mathematically it looks like this:

(5cm^2)(1*10^-2m/cm)(1*10^-2m/cm) = 5*10^-4m^2.

Obviously my way is slower than other ways that people can do it, but algebra is a pretty weak area for me so I have to do things the long way sometimes. It's not that much slower, and it rules out all doubt from my mind so it doesn't actually slow me down on the test.

 

[new student guest]

This short video will help you understand the concept