How do you write the repeating decimal 0.5555555 as a fraction?

5/9

The trick to figuring this out is simply to take the number that repeats and put it over a 9 if it's one digit, 99 if it's two digits, 999 if it's three digits, etc.

For example:

.2222222222... = 2/9

.1313131313... = 13/99

.2727272727... = 27/99 = 3/11

.123123123123... = 123/999 = 41/333