# Percent

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 for each $100$ North Americans, $82$ drink orange juice.  We can set up a proportion to show this relationship.

## 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.

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

Example 1:

What percent of $44$ is $11$ ?

Write a proportion.

$\frac{x}{100}=\frac{11}{44}$

(Note: You can reduce this fraction now if you want, but we'll be dividing anyway at the end.)

Cross-multiply.

$44x=1100$

Divide.

$x=25$

Example 2:

$58$ is $25%$ of what number?

Write a proportion.

$\frac{25}{100}=\frac{58}{y}$

Cross multiply.

$25y=5800$

Divide.

$y=232$

Example 3:

What is $88%$ of $5000$ ?

Write a proportion.

$\frac{88}{100}=\frac{z}{5000}$

Cross multiply.

$100z=440000$

Divide.

$z=4400$

## Converting Percents to Decimals

To convert a percent to a decimal, just remove the $%$ sign and divide by $100$ . The quick way to do this is to move the decimal point two places to the left .

Example 1:

Express $2.5%$ as a decimal.

Move the decimal point two places to the left.

$2.5%=0.025$

Example 2:

Express $0.7%$ as a decimal.

Move the decimal point two places to the left.

$0.7%=0.007$

## Converting Decimals to Percents

To convert a decimal to a percent, do just the opposite; add a percent sign and multiply by $100$ . The quick way to do this is to move the decimal point two places to the right .

Example 1:

Express $1.005$ as a percent.

Move the decimal point two places to the right.

$1.005=100.5%$