# Section 3-2

# Percents

Percent is short for "per centum", which is Latin for "per hundred".

So "15 percent" (written 15%) simply means "fifteen out of a hundred."

Things don't usually come in groups of exactly 100. So, we use percents to indicate proportions. When we say "82% of North Americans drink orange juice", we mean that in a group of *N* North Americans,

## THREE KINDS OF PERCENT PROBLEMS

Consider the statement "*x* percent of *y* is *z*."

If any two of the variables are given, you can use algebra to find out the missing one. This results in three different kinds of problems. In each one, the unknown is in a different position.

- problems where
*x* is the unknown (e.g. "*What percent of 44 is 11?*")
- problems where
*y* is the unknown (e.g. "*58 is 25% of what number?*")
- problems where
*z* is the unknown (e.g. "*What is 88% of 5000**?*")

Example 1:

What percent of 44 is 11?

Write a proportion.

Cross-multiply.

**44***x* = 1100

Divide.

*x* = 25

Example 2:

58 is 25% of what number?

Write a proportion.

Cross multiply.

**25***x *= 5800

Divide.

**x**** = 232 **

Example 3:

What is 88% of 5000?

Write a proportion.

Cross multiply.

**100***x* = 440000

Divide.

**x**** = 4400**

## CONVERTING PERCENTS TO DECIMALS

To convert a percent to a decimal, just remove the % sign, and move the decimal point two places to the left.

Example:

Express 2.5% as a decimal.

Move the decimal point two places to the left.

**2.5% = 0.025**