# Conversion of Repeating Decimals to Fraction

Converting decimal to fraction is very easy using our calculator however not all the time we have our calculator handy so it is important to know the basic steps how to do so. To illustrate the method lets cite some examples.

Sample Problem 1:

What is the equivalent fraction of 0.2316161616…

Solution:

the number of 9’s in the denominator  is equal to the number of repeating digits(16) and the number of 0’s in the denominator is equal to the number of non- repeating digits(23)

Equivalent fraction:

=     $\displaystyle\frac{2316-23}{9900}$

=     $\displaystyle\frac{2293}{9900}$

To determine if the fraction is on lowest term, try to divide the numerator by 3,5,11 or 2. If the numerator is not a multiple of any of these numbers then it is on its lowest term.

Sample Problem 2:

Find the equivalent fraction of 0.6213535353535…

Solution:

Equivalent fraction:

=     $\displaystyle\frac{62135-621}{99000}$

=     $\displaystyle\frac{61514}{99000}$

=     $\displaystyle\frac{30757}{49500}$

Sample Problem 3:

Find the equivalent fraction of 1.123123123123

Solution: We rewrite the decimal to 1+ 0.123123123…

= 1+ $\displaystyle\frac{123}{999}$

= 1+ $\displaystyle\frac{41}{333}$

=    $\displaystyle\frac{333+41}{333}$

=    $\displaystyle\frac{374}{333}$

Practice problems:

Convert each repeating decimal to fraction in lowest term.

1. 0.2312121212…

2. 0.67151151151151…

3. 0.452331331331…

4. 3.13131313…

5. 5.41234234234…