what is 0.142857 repeating as a fraction.

Guest Sep 9, 2017

3+0 Answers




MIRB16  Sep 9, 2017

I happen to remember what this decimal is represented in a fraction form, but here is the method one can use to convert \(0.\overline{142857}\) into a fraction. 


This first step is very simple; just set it equal to a variable. I'll use the normal x as my variable for this example. Therefore, \(0.\overline{142857}=x\)


The next goal is to get the repeating portion into the whole numbers part. It is probably easier showing by example than by explaining in words:


\(0.\overline{142857}=x\) Multiply by 1000000 on both sides.
\(142857.\overline{142857}=10000000x\) As you can see, the repeating section is now in whole numbers. Now, subtract both equations from each other.
\(142857=999999x\) Now, divide by 999999 on both sides.
\(x=\frac{142857}{999999}\div\frac{142857}{142857}\) It is probably hard to realize here, but the GCF of the numerator and denominator is 142857. 


Look at that! \(0.\overline{142857}=\frac{1}{7}\). That's quite a nice fraction.

TheXSquaredFactor  Sep 9, 2017

Nice job!

MIRB16  Sep 9, 2017

8 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details