Answer:
2/11
Step-by-step explanation:
Let's say our fraction is x = 0.1818181818...
The trick is to multiply x by 10²=100 in this case, since there are two repeating digits, and then subtract the original x.
So, in fact you are subtracting 0.181818 from 18.181818 which effectively cancels the entire bit after the decimal point.
You get:
100x - x = 18
Which you can solve:
99x = 18
x = 18/99 = 2/11
