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2014-06-25T23:11:05+08:00

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So, for example we have the number 0.272727.... Let that be equal to x.
                   
x = 0.272727...

If we multiply both sides by 100, we will have:
                      
100x = 27.2727...

Subtract the first equation from the second:
                   
100x = 27.272727...
 -   x =   0.272727...
  90x = 27.000000...

Isolate x:

x =  \frac{27}{99} =  \frac{7}{11}
                 
                                      
Another example: 0.16666...
Let x = 0.1666...
10x = 1.666...

10x = 1.666...
-  x = 0.1666...
9x = 1.5000...

x =  \frac{1.5}{9} =  \frac{15}{90} =  \frac{1}{6}
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