How do you convert a repeating decimal to fraction?

Answer 1

1. Find the length of the repeating digits
2. Put the repeating digits over the same number of 9s as the result of step 1
3. reduce to simplest form.

Example, for 0.181818...

1. '18' repeats, so length is 2 digits
2. 18/99 (the repeating digits '18' over two '9's)
3. 2/11 (divide top and bottom by 9)

So for 0.333...

1. '3' repeats, so length is 1 digit
2. 3/9 (the repeating digit '3' over one '9')
3. 1/3 (divide top and bottom by 3)