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what is 0.142857 repeating as a fraction.

Guest Sep 9, 2017
 #1
avatar+737 
+4

1/7

Yay!!!!!!

MIRB16  Sep 9, 2017
 #2
avatar+2294 
+2

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. 
\(x=\frac{1}{7}\)  
   

 

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

TheXSquaredFactor  Sep 9, 2017
 #3
avatar+737 
+5

Nice job!

MIRB16  Sep 9, 2017

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