How to Convert Percentages to Fractions and Decimal Numbers

Percentages and fractions are closely connected as they both are ways of expressing parts of something. You have to be able to convert between percentages, fractions and decimal numbers.

Rule

Percent $\to$ fraction $\to$ decimal number

a % = \frac{a}{100}

where you find the decimal number by calculating $a : 100$ .

This means that you can change the percentage sign with the fraction

\frac{1}{100}

when calculating. As in percentage we talk about parts of one hundred, you write it as a decimal by using the tenths and hundredths like this:

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

Example 1

Write $25 %$ As a fraction and as a decimal number:

\begin{array}{l} 25 % & = 25 \cdot \frac{1}{100} \\ = \frac{25}{100} \\ = \frac{25 : 5}{100 : 5} \\ = \frac{5}{20} \\ = \frac{5 : 5}{20 : 5} \\ = \frac{1}{4} \\ 25 % & = 25 \cdot \frac{1}{100} = \frac{25}{100} = 0.25 \end{array}

Example 2

Write $75 %$ as a fraction and as a decimal number

\begin{array}{l} 75 % & = 75 \cdot \frac{1}{100} = \frac{75}{100} = \frac{75 : 25}{100 : 25} = \frac{3}{4} \\ 75 % & = 75 \cdot \frac{1}{100} = \frac{75}{100} = 0.75 \end{array}

Example 3

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

\begin{array}{l} 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 \end{array}

Example 4

Write $80 %$ as a fraction and as a decimal number

\begin{array}{l} 80 % & = 80 \cdot \frac{1}{100} = \frac{80}{100} = \frac{80 : 20}{100 : 20} = \frac{4}{5} \\ 80 % & = 80 \cdot \frac{1}{100} = \frac{80}{100} = 0.80 = 0.8 \end{array}

Example 5

Write $10 %$ as a fraction and as a decimal number

\begin{array}{l} 10 % & = 10 \cdot \frac{1}{100} = \frac{10}{100} = \frac{10 : 10}{100 : 10} = \frac{1}{10} \\ 10 % & = 10 \cdot \frac{1}{100} = \frac{10}{100} = 0.10 = 0.1 \end{array}

Example 6

Write $37 %$ as a fraction and as a decimal number

\begin{array}{l} 37 % & = 37 \cdot \frac{1}{100} = \frac{37}{100} \\ 37 % & = 37 \cdot \frac{1}{100} = \frac{37}{100} = 0.37 \end{array}

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How to Convert Fractions and Decimal Numbers to Percentages

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Percent → fraction → decimal number

Percent $\to$ fraction $\to$ decimal number