5.555… as a Fraction

5.555… (5.5 repeating) as a fraction is 50/9. As a mixed number that is 5 5/9.

How to convert 5.555… to a fraction

  1. Let x = 5.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 55.555...
  3. Subtract to cancel the repeating tail: 10x − x = 55 − 5, so 9x = 50.
  4. Solve: x = 50/9. The greatest common divisor is 1, so x = 50/9 (already in lowest terms).

Since 50 is larger than 9, it can also be written as the mixed number 5 5/9.

Check

Divide 50 by 9 on a calculator: 50 ÷ 9 = 5.5555555556… which matches 5.555….

Similar repeating decimals

DecimalFraction
5.111…46/9
5.222…47/9
5.333…16/3
5.444…49/9
5.666…17/3
5.777…52/9
5.888…53/9
6.111…55/9

See also: 50/9 as a mixed number.

Another decimal? Browse the repeating decimal to fraction chart, the terminating decimal chart, or use the decimal to fraction converter.