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Converting Between Fractions, Decimal Numbers and Percentages

Fractions and percentages are closely related—both express a part of a whole. Here, you will learn how to convert fractions and decimal numbers to percentages, and back.

Rule

Percentage fraction decimal number

a% = a 100

and to find the decimal number you simply calculate a : 100.

In fact, you can change the percentage symbol to a regular number with the fraction 1 100 in your calculations. Since we’re discussing parts in one hundred, you can write your percentage as a decimal number by using the tenths and hundredths place values. You can do it like this:

7% = 7 1 100 = 7 100 = 0.07

Example 1

Write 20% both as a fraction and a decimal number.

20% = 20 1 100 = 20 100 = 20 : 20 100 : 20 = 1 5
20% = 20 1 100 = 20 100 = 0, 20 = 0, 2

Example 2

Write 65% both as a fraction and a decimal number.

65% = 65 1 100 = 65 100 = 65 : 5 100 : 5 = 13 20
65% = 65 1 100 = 65 100 = 0.65

Rule

Fraction percentage

a 100 = a%

Rule

Decimal number d percentage

d = d 100%

You’re now going to learn how to go the other way, from fractions and decimal numbers to percentages. You can always change the fraction 1 100 to a percentage symbol %. If you have more than 100 %, your decimal number will be larger than 1. Your goal is to make sure that your denominator is 100. You will often have to expand or simplify your fraction.

Example 3

Write 0.25 both as a fraction and a percentage.

0.25 = 25 100 = 25 : 25 100 : 25 = 1 4
0.25 = 0.25 100% = 25%

Example 4

Write 1 10 both as a decimal number and a percentage.

1 10 = 1 10 10 10 = 10 100 = 0.1
1 10 = 1 10 10 10 = 10 100 = 10 1 100 = 10%

Example 5

Write 0.75 both as a fraction and a percentage.

0.75 = 75 100 = 75 : 25 100 : 25 = 3 4
0.75 = 75 100% = 75%

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How to Convert Between Decimal Numbers and Fractions