Dimensional Analysis: Unit Conversions

Example 1

60 inches is how many feet?

First of all, we write our conversion factor as a fraction. 12 inches = 1 foot, so the conversion factor is

 or 

Because 12 inches is the same thing as 1 foot, that fraction is equal to 1 - we can multiply by it without changing the actual amount.

So, let's try that on our 60 inches.

The critical thing to note about the above equation is that the units behave like numbers do when you multiply fractions. That is, the inches on top and the inches on the bottom cancel out, leaving feet. Then all you have to worry about is the numbers.

Example 2

Sometimes both the top and bottom units need to be converted:

If you are going 50 miles per hour, how many feet per second are you traveling?

Example 3

Your car's gas tank holds 18.6 gallons and is one quarter full. Your car gets 16 miles/gal. You see a sign saying, "Next gas 73 miles." You're not so sure you can make it and do some quick figuring: