Question

How do you convert 0.18 (18 repeating) to a fraction?

Answer 1

`0.18181818... = 2/11`

Explanation:

Let's begin by setting `x` equal to our repeating fraction

`x = \color(red)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 + \color(red)0.18181818...`

which can be re-written

`100x = 18 + x`

subtracting `x` from both sides we get

`99x = 18`

and finally

`x = 18/99 = 2/11`