## Converting fractions and decimals into percents

 A percent is a ratio that compares a number to 100. 6% means the ratio "6 to 100". Since ratios can be written as fractions, we can write $$6\mbox{%}=\frac{6}{100}$$ Any fraction with a denominator of 100 can easily be written as a percent: the numerator becomes the percent! $\frac{29}{100}=29\mbox{%}$ or $\frac{99}{100}=99\mbox{%}$ What if the denominator is NOT 100? Or what about decimals?

### Decimals to percents (D ----> P)

 To turn a decimal into a percent you must remember that a decimal can be turned into a fraction. Then after the decimal has been turned into a fraction, you can rename the fraction so its denominator is 100.

Example 1: Convert 0.7 into a percent.

 Method 1: Change into a fraction, then rename. Method 2: Move the decimal to spaces to the right. SHORTCUT ALERT! Notice in the example to the left the decimal moved to places to the right. This will happen every time, so you can use it as a shortcut like this...

Example 2: Convert 0.92 into a percent.

 Change into a fraction, then rename. Move the decimal two spaces to the right.

### Fractions to percents (F ----> P)

There are two ways to turn a fraction into a percent:

1. Rename the fraction so that it has a denominator of 100.
2. Change the fraction into a decimal by dividing, and then change the decimal into a percent.
 Rename Divide

Example 3: Convert $\frac{9}{20}$ into a percent.

 Method 1: Rename denominator Method 2: Divide

For this example, both methods are easy to use. Sometimes, however, one method is easier than the other as is the case in Example 2.

Example 4: Convert $\frac{11}{25}$ into a percent.

 Method 1: Rename denominator Method 2: Divide

In example 2, Method 1 was probably the easier method. Now try example 3.

Example 5: Convert $\frac{7}{8}$ into a percent.

 Method 1: Rename denominator Method 2: Divide

In this example, Method 2 was probably the easier method, since it is not easy to change the denominator of 8 into a 100.

# Self-Check

Question 1

Convert 0.9 into a percent.

Question 2

Convert $\frac{4}{5}$ into a percent.

Question 3

Convert $\frac{25}{40}$ into a percent.

Question 4

Convert 0.125 into a percent.