Simplifying Repeating Decimal as a Fraction/Mixed Number?

Question

1) -0.1666...

(.... means repeats)




Here is an example. Although I've been working on this problem and I still dont understand it. Thanks for your help. :)

a) 0.5555...

Let N= 0.555... Then 10N= 5.55... (Multiply N by 10 because one
digit repeats)

10N=5.555...
-1N =0.555... (10N-N=9n)
-------------------
9N= 5 (Divide each side by 9)

N= 5/9



~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Hope this example helps! Thanks to all who helps :)

Answer 1

As the example implies, you need to multiply by 10 if one digit repeats, 100 if two digits repeat, 1000 if three, etc.

With -0.16666, you only have one repeating digit. Note - don't worry about the 1 at the start; thats not important.

So,
N = -0.166666
10N = -1.66666
Subtract:
9N = -1.5
So N = -1.5/9.
Thats not a proper fraction, so multiply top and bottom by 2:
N = -3/18, or -1/6.

If it was 0.2131313.. for example:
N = 0.21313131
100N = 21.313131
99N = 21.1
N = 21.1/99
= 211/990 (multiplying top and bottom by 10)

Answer 2

I just have only one hint for you: Multiply by 2 and then follow your example...

The exact answer is -1/6 if you want to check your answer.