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.

Question Types:

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.

**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.

Question 1

Write the decimal fraction as a simple fraction:

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

Question 2

Write the decimal fraction as a simple fraction:

\( 0.333= \)

Question 3

Write the decimal fraction as a simple fraction:

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

Question 4

Write the decimal fraction as a simple fraction:

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

Question 5

Write the decimal fraction as a simple fraction:

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

Write the decimal fraction as a simple fraction:

$0.\overline{5}=$

$\frac{5}{9}$

Write the decimal fraction as a simple fraction:

$0.333=$

$\frac{1}{3}$

Write the decimal fraction as a simple fraction:

$0.\overline{123}=$

$\frac{41}{333}$

Write the decimal fraction as a simple fraction:

$0.\overline{67}=$

$\frac{67}{99}$

Write the decimal fraction as a simple fraction:

$0.\overline{81}=$

$\frac{9}{11}$

Question 1

Question 2

Write the decimal fraction as a simple fraction:

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

Question 3

Write the decimal fraction as a simple fraction:

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

Question 4

Question 5

4.8

Write the decimal fraction as a simple fraction:

$10.\overline{67}=$

$10\frac{67}{99}$

Write the decimal fraction as a simple fraction:

$0.\overline{352}=$

$\frac{352}{999}$

13.1

163.1

Question 1

Question 2

Question 3

Write the decimal fraction as a simple fraction:

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

Question 4

Write the decimal fraction as a simple fraction:

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

Question 5

4.3

7.8

Write the decimal fraction as a simple fraction:

$0.\overline{142857}=$

$\frac{1}{7}$

Write the decimal fraction as a simple fraction:

$0.\overline{63}=$

$\frac{7}{11}$

0.134