# Repeating Decimal Fractions - Examples, Exercises and Solutions

What is a repeating decimal?
A repeating decimal is a number with a fractional part that, after the decimal point, the digits repeat infinitely, in a periodic manner.

### Conversion from Fraction to Repeating Decimal

First step: We will write the fraction as a long division exercise
Second step: We will add the decimal point to the dividend and then $5$ zeros (the value of the number is not affected)
Third step: We will solve the division and copy the decimal point to the result exactly in the same place it was.
Fourth step: we will put ellipses at the result to signal that the number continues.

## Examples with solutions for Repeating Decimal Fractions

### Exercise #1

Write the decimal fraction as a simple fraction:

$0.\overline{5}=$

### Video Solution

$\frac{5}{9}$

### Exercise #2

Write the decimal fraction as a simple fraction:

$0.333=$

### Video Solution

$\frac{1}{3}$

### Exercise #3

Write the decimal fraction as a simple fraction:

$0.\overline{123}=$

### Video Solution

$\frac{41}{333}$

### Exercise #4

Write the decimal fraction as a simple fraction:

$0.\overline{67}=$

### Video Solution

$\frac{67}{99}$

### Exercise #5

Write the decimal fraction as a simple fraction:

$0.\overline{81}=$

### Video Solution

$\frac{9}{11}$

4.8

### Exercise #7

Write the decimal fraction as a simple fraction:

$10.\overline{67}=$

### Video Solution

$10\frac{67}{99}$

### Exercise #8

Write the decimal fraction as a simple fraction:

$0.\overline{352}=$

### Video Solution

$\frac{352}{999}$

13.1

163.1

4.3

7.8

### Exercise #13

Write the decimal fraction as a simple fraction:

$0.\overline{142857}=$

### Video Solution

$\frac{1}{7}$

### Exercise #14

Write the decimal fraction as a simple fraction:

$0.\overline{63}=$

### Video Solution

$\frac{7}{11}$