# How to Convert Fractions and Decimal Numbers to Percentages

Now you will learn to go from a fraction and decimal to percentages.

Rule

### Fraction$\to$percent

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

This means that you can change the percentage sign with the fraction $\frac{1}{100}$ in the calculation. As in percentage we talk about parts of one hundred, you write it as a decimal by using the tenths and hundredths.

Example 1

Write $\text{}0.25\text{}$ as a fraction and as percentage.

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

Example 2

Write $\text{}0.75\text{}$ as a fraction and as percentage.

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

Example 3

Write $\text{}0.20\text{}$ as a fraction and as percentage.

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

Example 4

Write $\text{}0.80\text{}$ as a fraction and as percentage.

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

Example 5

Write $\text{}0.10\text{}$ as a fraction and as percentage.

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

Example 6

Write $\text{}0.37\text{}$ as a fraction and as percentage.

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

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# How to Convert Fractions and Decimal Numbers to Percentages

Numbers and QuantitiesAlgebra
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