A conversion factor is a fraction that you can use to help you convert a quantity from one unit to another. Conversion factors are always equal to one, so you can multiply a quantity by the conversion factor without changing the quantity's value.

Example One - You know that there are three feet in a yard, right? Here's how we take that information and turn it into a conversion factor. We take the equation: 3 feet = 1 yard and divide both sides by the quantity 1 yard. The result is:

(3 feet)/(1 yard) = 1

Our conversion factor for converting yards to feet is:

(3 feet)/(1 yard).

But wait...what if we had taken the equation and divided it by 3 feet instead?

Well, then we would have (1 yard)/(3 feet) = 1. So it turns out that:

(1 yard)/(3 feet) 

is another conversion factor for feet and yards. This one is helpful for converting feet into yards. (But we'll get into how to actually do that in the next reading)

It turns out that for every pair of units, there aretwo possible conversion factors we can create. 

Example Two - What are the conversion factors for the equation 5280 feet = 1 mile?

Answer - (5280 feet)/(1 mile) and (1 mile)/(5280 feet)

So far we haven't discussed at all how we'll use these conversion factors. We'll get into that in the next reading.