Question

What fraction is equivalent to the repeating decimal 0.18

Answer 1

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

taking x to the left-hand side we get

99x=18

and finally

x=18/99=2/11

Hope this helps!

Answer 2

18/99 can be reduced, it becomes 2/11

Therefore the answer is 2/11!!

Hope this helps!!! :)

P.S. You can check it if you wish by dividing 2 by 11!