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…


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…


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…

Check your answer here



Blogger and a Math enthusiast. Has no interest in Mathematics until MMC came. Aside from doing math, he also loves to travel and watch movies.

Latest posts by Dan (see all)

You may also like...

3 Responses

  1. Youre so cool! I dont suppose Ive read anything in this way before. So good to uncover somebody with some original tips on this topic. realy appreciate starting this up. this excellent website is something that is necessary more than the internet, a person if we do originality. valuable function for bringing something new towards the web!

  2. I am curious to locate out what blog system you’re utilizing? Im having some small security problems with my latest site and Id like to find something a lot more risk-free. Do you’ve any suggestions? Hmm it looks like your weblog ate my initial comment (it was super long) so I guess Ill just sum it up what I wrote and say, Im thoroughly enjoying your weblog. I too am an aspiring weblog blogger but Im still new to everything. Do you’ve any guidelines and hints for rookie weblog writers? Id definitely appreciate it.

  3. Thank you of this blog. That’s all I’m able to say. You undoubtedly have made this web web site into an item thats attention opening in addition to critical. You certainly know a fantastic deal of about the niche, youve covered a multitude of bases. Fantastic stuff from this the main internet. All more than again, thank you for the blog.

Leave a Reply

Your email address will not be published. Required fields are marked *