# 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$\to$decimalnumber

 $a\phantom{\rule{0.33em}{0ex}}\text{%}=\frac{a}{100}$

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:

 $7\phantom{\rule{0.17em}{0ex}}\text{%}=7\cdot \frac{1}{100}=\frac{7}{100}=0.07$

Example 1

Write $\text{}25\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ As a fraction and as a decimal number:

$\begin{array}{llll}\hfill 25\phantom{\rule{0.17em}{0ex}}\text{%}& =25\cdot \frac{1}{100}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{25}{100}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{25:5}{100:5}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{5}{20}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{5:5}{20:5}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{1}{4}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 25\phantom{\rule{0.17em}{0ex}}\text{%}& =25\cdot \frac{1}{100}=\frac{25}{100}=0.25\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

Write $\text{}75\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ as a fraction and as a decimal number

$\begin{array}{llll}\hfill 75\phantom{\rule{0.17em}{0ex}}\text{%}& =75\cdot \frac{1}{100}=\frac{75}{100}=\frac{75:25}{100:25}=\frac{3}{4}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 75\phantom{\rule{0.17em}{0ex}}\text{%}& =75\cdot \frac{1}{100}=\frac{75}{100}=0.75\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 3

Write $\text{}20\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ as a fraction and as a decimal number

$\begin{array}{llll}\hfill 20\phantom{\rule{0.17em}{0ex}}\text{%}& =20\cdot \frac{1}{100}=\frac{20}{100}=\frac{20:20}{100:20}=\frac{1}{5}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 20\phantom{\rule{0.17em}{0ex}}\text{%}& =20\cdot \frac{1}{100}=\frac{20}{100}=0.20=0.2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 4

Write $\text{}80\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ as a fraction and as a decimal number

$\begin{array}{llll}\hfill 80\phantom{\rule{0.17em}{0ex}}\text{%}& =80\cdot \frac{1}{100}=\frac{80}{100}=\frac{80:20}{100:20}=\frac{4}{5}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 80\phantom{\rule{0.17em}{0ex}}\text{%}& =80\cdot \frac{1}{100}=\frac{80}{100}=0.80=0.8\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 5

Write $\text{}10\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ as a fraction and as a decimal number

$\begin{array}{llll}\hfill 10\phantom{\rule{0.17em}{0ex}}\text{%}& =10\cdot \frac{1}{100}=\frac{10}{100}=\frac{10:10}{100:10}=\frac{1}{10}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 10\phantom{\rule{0.17em}{0ex}}\text{%}& =10\cdot \frac{1}{100}=\frac{10}{100}=0.10=0.1\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 6

Write $\text{}37\text{}\phantom{\rule{0.17em}{0ex}}\text{%}$ as a fraction and as a decimal number

$\begin{array}{llll}\hfill 37\phantom{\rule{0.17em}{0ex}}\text{%}& =37\cdot \frac{1}{100}=\frac{37}{100}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 37\phantom{\rule{0.17em}{0ex}}\text{%}& =37\cdot \frac{1}{100}=\frac{37}{100}=0.37\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$