# How to Convert Between Decimal Numbers and Fractions

Here, you’ll learn to convert decimals to fractions, and back. You will need to use both decimals and fractions to express shares, so you need to understand both types of numbers and how they relate to each other. First, you’ll look at some basic fractions and the connection between fractions and decimals.

An important trick when you convert fractions to decimals and back is to have control over a few basic fractions and how to express them in decimals. You should memorize the fractions above. The line you see above the number $3$ means that there is an infinite number of $3$’s after the decimal point.

The reason you should know these basic correlations is that they make the calculations between fractions and decimals much simpler. Let’s look at a few examples.

Example 1

Write $\frac{3}{4}$ as a decimal number.

 $\frac{3}{4}=3\cdot \frac{1}{4}=3\cdot 0.25=0.75$

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

 $0.75=\frac{75}{100}=\frac{75:25}{100:25}=\frac{3}{4}$

Example 2

Write $\frac{4}{5}$ as a decimal number.

 $\frac{4}{5}=4\cdot \frac{1}{5}=4\cdot 0.20=0.80$

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

 $0.80=\frac{80}{100}=\frac{80:20}{100:20}=\frac{4}{5}$

Example 3

Write $\frac{4}{3}$ as a decimal number.

 $\frac{4}{3}=4\cdot \frac{1}{3}=4\cdot 0.33\overline{3}=1.33\overline{3}$

Write $\text{}1.33\text{}\overline{3}$ as a fraction.

$\begin{array}{llll}\hfill 1.33\overline{3}& =1+0.33\overline{3}=\frac{3}{3}+\frac{1}{3}=\frac{3+1}{3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =\frac{4}{3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $1.33\overline{3}=1+0.33\overline{3}=\frac{3}{3}+\frac{1}{3}=\frac{3+1}{3}=\frac{4}{3}$

There is a line over the last $3$ to show that in reality there are an infinite number of $3$’s after the decimal point.