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what is 0.142857 repeating as a fraction.

Guest Sep 9, 2017
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#1
+359
+3

1/7

Yay!!!!!!

MIRB16  Sep 9, 2017
#2
+1364
+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
+359
+3

Nice job!

MIRB16  Sep 9, 2017

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