How to convert units with unit multipliers
When a measurement is given in one unit and you need it in another, the units can tell you how to set up the calculation. We’ll start with feet and inches, then use the same idea for two conversions in a row and for square units.
Put the unit you have in the denominator
Since , the fraction represents 1. It changes the unit we use to describe the length while keeping the length the same. To convert feet to inches, put feet in the denominator so the feet cancel.
The same setup works for metric units. Since , use a factor with meters in the denominator.
Use two factors to convert inches to yards
To go from inches to yards, we can stop at feet along the way. Start with a factor that cancels inches, then use one that cancels feet.
Square the conversion factor for area
A square mile has two dimensions measured in miles. Since , use the same factor twice so that both copies of miles cancel.
For cubic units, use the factor three times for the same reason.
To see how two ratios can represent the same relationship, review how ratios and proportions work.
