Basic Math — Percents

Using Percents

Most students learn to use percents in middle school, but many people still have trouble interpreting information involving percents even as adults. Just what is a percent (%)?

The word percent comes from the Latin per centum meaning “out of one hundred,” so we can think of 22% as “22 out of 100.” Thus a percent is a symbol representing a ratio of the part — in this case 22 — to the whole — 100. A percent must be changed to a number (fraction or decimal) before we can compute with it. Hence 22% is the ratio 22 : 100, which gives:

 22 100
= .22

Other examples:

percent notation ratio notation number notation
30% 30 : 100 30 / 100 = 0.3
8% 8 : 100 8 / 100 = 0.08
63.7% 63.7 : 100 63.7 / 100 = 0.637
100% 100 : 100 100 / 100 = 1
212% 212 : 100 212 / 100 = 2.12
5 3/4% 5 3/4 : 100 or 5.75 : 100 5.75 / 100 = 0.0575

We will most often use the decimal form (in bold above) because it is easy to find on a calculator by dividing by 100. Let’s make some notes from these examples:

• The mechanics of changing a percent to a decimal number involves moving the decimal point two places to the left. The percent symbol can help us remember this: • When we change percents smaller than 10 percent to numbers, we need to place holding 0s — as with 8% and 5 3/4%.
• 100% is 1, reinforcing the idea that x% describes x’s part of “the whole.”
• Percents representing more than 1 are possible (212%) — they are used to talk about something growing really large rather than as “part out of the whole.” ×