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 $\to$ fraction $\to$ decimal number

a % = \frac{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

\frac{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 \cdot \frac{1}{100} = \frac{7}{100} = 0.07

Example 1

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

20 % = 20 \cdot \frac{1}{100} = \frac{20}{100} = \frac{20 : 20}{100 : 20} = \frac{1}{5}

20 % = 20 \cdot \frac{1}{100} = \frac{20}{100} = 0.20 = 0.2

Example 2

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

65 % = 65 \cdot \frac{1}{100} = \frac{65}{100} = \frac{65 : 5}{100 : 5} = \frac{13}{20}

65 % = 65 \cdot \frac{1}{100} = \frac{65}{100} = 0.65

Rule

Fraction $\to$ percentage

\frac{a}{100} = a %

Rule

Decimal number $d \to$ percentage

d = d \cdot 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 $\frac{1}{100}$ 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.