Converting a Percentage to a Fraction with a Denominator of 100

Definition

A percentage or percent for short is a fraction; a fraction that always has the denominator as 100.

Because the denominator of a percent is always a 100, no matter what the numerator is, we replace 100 with the percent symbol % after the number.

Rule for writing a percentage as a fraction with denominator of 100

• By definition, for any number x, x% = x100�100.
• Alternatively, we replace the percent sign in x% with a 100 in the denominator of the number x as follows, x% = x100�100

Example 1

Convert the following percentage to a fraction with a denominator of 100

9%

Solution

Step 1:

By definition, for any number x, x% = x100�100.

Step 2:

So, 9% = 91009100Example 2

Convert the following percentage to a fraction with a denominator of 100

63%

Solution

Step 1:

By definition, for any number x, x% = x100�100.

Step 2:

So, 63% = 6310063100Example 3

Convert the following percentage to a fraction with a denominator of 100

81%

Solution

Step 1:

By definition, for any number x, x% = x100�100.

Step 2:

So, 81% = 81100