Student Success Commons: Units and Conversions

UNITS

• The units of a quantity describe what the quantity measures or counts. Units provide crucial context. For example, if you ask a car mechanic how long it will take to have your radiator fixed and they say "5" you need the units to fully understand their meaning. Is it 5 minutes, 5 hours, 5 days, 5 weeks, 5 months? 

• Unit analysis (also called dimensional analysis) is the process of working with units to help solve problems.

• You can cancel units that appear in the top and bottom of one fraction, or in the top of one fraction and in the bottom of another as long as the two fractions are being multiplied (see the Unit analysis (cancelling units) PDF)

• Tip: You generally cannot add or subtract numbers with different units. For example, you couldn't add 3 inches and 5 miles to get 8; what would the unit be? But you can combine different units by converting at least one of the units. (Using the previous example, if we converted 5 miles into inches, we could then add the two values because they would both have the same unit: inches.)

CONVERSIONS

• When you are trying to add or subtract two quantities and the units are not the same you will need to convert at least one of the units.

• A conversion factor is used to change the units of a measured quantity without changing its value. Common conversion factors and how to use them are given on this page, as are additional resources and examples.