Periodic decimal fraction - 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 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.

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 Periodic decimal fraction

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:

0.81= 0.\overline{81}=

Video Solution

Answer

911 \frac{9}{11}

Exercise #3

Write the decimal fraction as a simple fraction:

0.123= 0.\overline{123}=

Video Solution

Answer

41333 \frac{41}{333}

Exercise #4

Write the decimal fraction as a simple fraction:

0.333= 0.333=

Video Solution

Answer

13 \frac{1}{3}

Exercise #5

Write the decimal fraction as a simple fraction:

0.67= 0.\overline{67}=

Video Solution

Answer

6799 \frac{67}{99}

Exercise #1

Write the decimal fraction as a simple fraction:

0.352= 0.\overline{352}=

Video Solution

Answer

352999 \frac{352}{999}

Exercise #2

Write the decimal fraction as a simple fraction:

10.67= 10.\overline{67}=

Video Solution

Answer

106799 10\frac{67}{99}

Exercise #3

29.6

Video Solution

Answer

4.8

Exercise #4

Write the decimal fraction as a simple fraction:

0.142857= 0.\overline{142857}=

Video Solution

Answer

17 \frac{1}{7}

Exercise #5

Write the decimal fraction as a simple fraction:

0.63= 0.\overline{63}=

Video Solution

Answer

711 \frac{7}{11}

Exercise #1

3.343.23

Video Solution

Answer

13.1

Exercise #2

970.2

Video Solution

Answer

7.8

Exercise #3

4652.4

Video Solution

Answer

163.1

Exercise #4

1.56.45

Video Solution

Answer

4.3

Exercise #5

2.50.3350

Video Solution

Answer

0.134

Topics learned in later sections

  1. Decimal Fractions