# Question #c6026

Jan 19, 2015

Unit conversions are a relatively confusing thing for most people, to start with, but after a little bit of practice you will find it to be very simple.

The most important thing to understand about unit conversions is that a unit divided by itself, i.e. $\frac{m e t e r}{m e t e r}$, cancels the unit out by making it equal to 1.

Mathematically this is similar to when you see a unit squared or cubed:
$M e t e r \cdot M e t e r = M e t e {r}^{2}$
or
$M e t e r \cdot M e t e r \cdot M e t e r = M e t e {r}^{3}$

Example: Suppose I asked you to convert 25 centimeters to meters.

You would solve this, and other unit conversion problems, by starting with your given unit (centimeters) and canceling out your units by multiplying by ratios which contain your unit and the unit you're trying to convert to.

For this problem your ratio would be ${10}^{-} 2 m e t e r s = 1 c e n t i m e t e r s$
or
$1 m e t e r = 100 c e n t i m e t e r s$

Starting w/ our given unit we set up our problem like this
$25 c e n t i m e t e r s \cdot \frac{{10}^{- 2} m e t e r s}{1 c e n t i m e t e r s} = 25 \cdot {10}^{-} 2 m e t e r s$

Since our units cancel out correctly, the only units we're left with is $1 \cdot m e t e r s$ or simply $m e t e r s$.

This example only required one step, but there are others that require multiple steps. However, multiple step conversions follow the exact same steps, they just end up w/ more multiplication/division at the end. As long as you cancel out your units correctly, the math will work!