Solution
0.18181818…=
11
2
Explanation:
Let’s begin by setting x equal to our repeating fraction
x=0.18181818…
The next step is a bit of a trick where we multiply by a power of 10 such that what remains to the right of the decimal is the repeating fraction itself, i.e.
100x=18.1818181818…=18+0.18181818…
which can be re-written
100x=18+x
subtracting x from both sides we get
99x=18
and finally
x=
99
18
=
11
2