How many milliliters are in a cubic meter? (There are 1,000 L in 1 m^3)? The answer is 1 billion, but how would you do this problem in steps? May anyone show me the form where you cancel units and put it in fraction form?

Question

jfraser · Answer

when you square or cube things like cm/m to get cubic cm, you have to cube both the number, and the unit.  Since there are 100cm in 1m, that equality is$$100cm = 1m$$ to get a CUBIC meter, cube both sides, which means cube EVERYTHING$$(100cm)^3 = (1m)^3$$the cube has to work on everything, the number and the unit.

$1^3$ is easy, since it's 1. but $100^3$ is also $(10^2)^3$ or $10^6$ which is 1 millon, not 1 billion. In fraction form it's easy:

$$1m^3 * \frac{(100cm)^3}{(1m)^3} = \frac{(10^2)^3cm^3}{1^3m^3} = 10^6cm^3$$