6.555… as a Fraction

6.555… (6.5 repeating) as a fraction is 59/9. As a mixed number that is 6 5/9.

How to convert 6.555… to a fraction

  1. Let x = 6.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 65.555...
  3. Subtract to cancel the repeating tail: 10x − x = 65 − 6, so 9x = 59.
  4. Solve: x = 59/9. The greatest common divisor is 1, so x = 59/9 (already in lowest terms).

Since 59 is larger than 9, it can also be written as the mixed number 6 5/9.

Check

Divide 59 by 9 on a calculator: 59 ÷ 9 = 6.5555555556… which matches 6.555….

Similar repeating decimals

DecimalFraction
6.111…55/9
6.222…56/9
6.333…19/3
6.444…58/9
6.666…20/3
6.777…61/9
6.888…62/9
7.111…64/9

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