# #### Fractions to Decimals

It is really easy to convert fractions to decimals, especially if you use a calculator. On this page, I’ll show you how to convert fractions to decimals with step-by-step instructions and examples.

If you need to know how to convert decimals to fractions or how to convert fractions to percents, check out the linked pages. You may also want to check out my page about converting repeating decimals to fractions.

## How to Convert Fractions to Decimals

1. Identify the numerator of the fraction.
2. Identify the denominator of the fraction.
3. Use long division to divide the numerator by the denominator.

It is much easier to convert fractions to decimals if you use a calculator to do the division. Just remember that integrity is always more important than math. So, if your teacher does not allow calculators, then use long division.

## Examples

Convert this fraction to a decimal: $\frac{3}{4}$

What is the numerator of the fraction?

The numerator is 3.

What is the denominator of the fraction?

The denominator is 4.

What is the quotient when you divide 3 by 4?

$\begin{array}{cr} \\ 4 & \\ \\ \\\\ \\ \end{array} \begin{array}{cccc} & 0. & 7 & 5 \\ \hline ) & 3. & 0 & 0 \\ – & 2 & 8 & \\ \hline & & 2 & 0 \\ & -& 2 & 0 \\ \hline & & & 0 \end{array}$

The remainder is 0 after two rounds of long division, so the quotient is a terminating decimal.

$3 \div 4 = 0.75$

$$0.75$$ is the decimal form of $$\frac{3}{4}$$.

Convert this fraction to a decimal: $\frac{9}{5}$

What is the numerator of the fraction?

The numerator is 9.

What is the denominator of the fraction?

The denominator is 5.

What is the quotient when you divide 9 by 5?

$\begin{array}{cr} \\ 5 & \\ \\ \\ \\ \\ \end{array} \begin{array}{ccc} & 1. & 8 \\ \hline ) & 9. & 0 \\ – & 5 \\ \hline & 4 & 0 \\ -& 4 & 0 \\ \hline & & 0 \end{array}$

The remainder is 0 after two rounds of long division, so the quotient is a terminating decimal.

$9 \div 5 = 1.8$

The decimal is greater than 1 because $$\frac{9}{5}$$ is an improper fraction.

$$1.8$$ is the decimal form of $$\frac{9}{5}$$.

Convert this fraction to a decimal: $\frac{5}{11}$

What is the numerator of the fraction?

The numerator is 5.

What is the denominator of the fraction?

The denominator is 11.

What is the quotient when you divide 5 by 11?

$\begin{array}{cr} \\ 11 & \\ \\ \\\\ \\ \\ \\ \\ \\ \end{array} \begin{array}{ccccccc} & 0. & 4 & 5 & 4 & 5 & … \\ \hline ) & 5. & 0 & 0 & 0 & 0 & …\\ – & 4 & 4 \\ \hline & & 6 & 0 \\ & -& 5 & 5 \\ \hline & & & 5 & 0 \\ & & – & 4 & 4 \\ \hline & & & & 6 & 0 \\ & & & – & 5 & 5 \\ \hline & & & & & 5 & …\end{array}$

This long division process will literally go on forever so the quotient is a repeating decimal.

$5 \div 11 = 0.45454545…$

The repeating decimal can be written with a vinculum over the repeating part of the decimal.

$0.45454545…=0.\overline{45}$

The decimal form of $$\frac{5}{11}$$ is $$0.\overline{45}$$.

## Repeating Decimals

When you convert fractions to decimals, it is very common to end up with a repeating decimal. Repeating decimals happen when the long division process cycles through the same remainders over and over again (like the purple example above).

Some repeating decimals like $$\frac{2}{9}=0.22222…$$ have a single repeating number. And others like $$\frac{4}{11}=0.363636…$$ have multiple repeating numbers. And sometimes only part of the decimal repeats like $$\frac{5}{12}=0.4166666…$$

When you write a repeating decimal, you can write an ellipsis to show that the pattern continues ($$0.1252525…$$) Or you can write a vinculum over the part of the decimal that repeats ($$0.1\overline{25}$$)

$\frac{1}{3}=0.3333333…$

Can also be written as $$0.\overline{3}$$

$\frac{4}{9}=0.4444444…$

Can also be written as $$0.\overline{4}$$

$\frac{5}{6}=0.8333333…$

Can also be written as $$0.8\overline{3}$$

$\frac{8}{11}=0.727272…$

Can also be written as $$0.\overline{72}$$

$\frac{419}{3333}=0.12571257…$

Can also be written as $$0.\overline{1257}$$

## Why It Works

As I explain on this page, fractions can be interpreted in several different ways. Most people think of fractions as parts of a whole. But fractions can also be interpreted as division.

For example, if I have the fraction $$\frac{2}{3}$$, I think of it as 2 pizzas being divided up equally  between 3 friends. When I split up the first pizza, each friend gets $$\frac{1}{3}$$ of the pizza. And then when I split up the second pizza, they each get another third.

Ultimately, all three friends each get $$\frac{2}{3}$$ of a pizza. If we use a calculator or long division to divide the 2 pizzas into 3 groups we will get the decimal that is equivalent to $$\frac{2}{3}$$.