Writing fractions as repeating decimals review

Review converting fractions to repeating decimals, and then try some practice problems.

Writing fractions as decimals

To convert a fraction to a decimal, we divide the numerator by the denominator.

Example: $\frac{2}{5}$ ‍

\frac{2}{5} = 2 \div 5

\begin{aligned} 0. 4 \\ 5 & \overset{―}{) 2, 0} \\ \underset{―}{- 0} ↓ \\ 2 0 \\ \underset{―}{- 2 0} \\ 0 \end{aligned}

\frac{2}{5} = 0, 4

Writing fractions as repeating decimals

However, it does not always work out that nicely.

Sometimes, when we divide the numerator by the denominator, it becomes clear that the digits will keep repeating. In this case, we write the answer as a repeating decimal.

In our answer, we write a bar over the repeating digits to show that they repeat.

Example: $\frac{4}{9}$ ‍

\frac{4}{9} = 4 \div 9

\begin{aligned} 0. 4444 \\ 9 & \overset{―}{) 4 .0000} \\ \underset{―}{- 0} ↓ \\ 4 0 \\ \underset{―}{- 3 6} ↓ \\ 4 0 \\ \underset{―}{- 3 6} ↓ \\ 4 0 \\ \underset{―}{- 3 6} \\ 4 \end{aligned}

No matter how long we divide, the

4

will continue to repeat in our quotient.

\frac{4}{9} = 0. \overset{―}{4}

Want to learn more about writing fractions as repeating decimals? Check out this video.

Εξάσκηση

Πρόβλημα 1

Select the decimal that is equivalent to $\frac{2}{3}$ ‍.

Want to try more problems like this? Check out this exercise.

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