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:
[tex]x = \frac{27}{99} = \frac{7}{11} [/tex]
Another example: 0.16666...
Let x = 0.1666...
10x = 1.666...
10x = 1.666...
- x = 0.1666...
9x = 1.5000...
[tex]x = \frac{1.5}{9} = \frac{15}{90} = \frac{1}{6} [/tex]
