Repeating Decimal Fractions - Examples, Exercises and Solutions

Question Types:
Repeating Decimal Fractions: Converting from decimal fractions

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 55 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.

Detailed explanation

Suggested Topics to Practice in Advance

  1. Multiplication and Division of Decimal Numbers by 10, 100, etc.
  2. Division of Decimal Numbers
  3. Multiplication of Decimal Numbers
  4. Decimal Measurements

Practice Repeating Decimal Fractions

Question 1

Write the decimal fraction as a simple fraction:

\( 0.\overline{5}= \)

Question 2

Write the decimal fraction as a simple fraction:

\( 0.\overline{67}= \)

Question 3

Write the decimal fraction as a simple fraction:

\( 0.333= \)

Question 4

Write the decimal fraction as a simple fraction:

\( 0.\overline{123}= \)

Question 5

Write the decimal fraction as a simple fraction:

\( 0.\overline{81}= \)

Examples with solutions for Repeating Decimal Fractions

Exercise #1

Write the decimal fraction as a simple fraction:

0.5‾= 0.\overline{5}=

Video Solution

Answer

59 \frac{5}{9}

Exercise #2

Write the decimal fraction as a simple fraction:

0.67‾= 0.\overline{67}=

Video Solution

Answer

6799 \frac{67}{99}

Exercise #3

Write the decimal fraction as a simple fraction:

0.333= 0.333=

Video Solution

Answer

13 \frac{1}{3}

Exercise #4

Write the decimal fraction as a simple fraction:

0.123‾= 0.\overline{123}=

Video Solution

Answer

41333 \frac{41}{333}

Exercise #5

Write the decimal fraction as a simple fraction:

0.81‾= 0.\overline{81}=

Video Solution

Answer

911 \frac{9}{11}

Question 1

Write the decimal fraction as a simple fraction:

\( 10.\overline{67}= \)

Question 2

Write the decimal fraction as a simple fraction:

\( 0.\overline{352}= \)

Question 3

Write the decimal fraction as a simple fraction:

\( 0.\overline{63}= \)

Question 4

Write the decimal fraction as a simple fraction:

\( 0.\overline{142857}= \)

Exercise #6

Write the decimal fraction as a simple fraction:

10.67‾= 10.\overline{67}=

Video Solution

Answer

106799 10\frac{67}{99}

Exercise #7

Write the decimal fraction as a simple fraction:

0.352‾= 0.\overline{352}=

Video Solution

Answer

352999 \frac{352}{999}

Exercise #8

Write the decimal fraction as a simple fraction:

0.63‾= 0.\overline{63}=

Video Solution

Answer

711 \frac{7}{11}

Exercise #9

Write the decimal fraction as a simple fraction:

0.142857‾= 0.\overline{142857}=

Video Solution

Answer

17 \frac{1}{7}

Topics learned in later sections

  1. Decimal Fractions