2.555… as a Fraction

2.555… (2.5 repeating) as a fraction is 23/9. As a mixed number that is 2 5/9.

How to convert 2.555… to a fraction

  1. Let x = 2.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 25.555...
  3. Subtract to cancel the repeating tail: 10x − x = 25 − 2, so 9x = 23.
  4. Solve: x = 23/9. The greatest common divisor is 1, so x = 23/9 (already in lowest terms).

Since 23 is larger than 9, it can also be written as the mixed number 2 5/9.

Check

Divide 23 by 9 on a calculator: 23 ÷ 9 = 2.5555555556… which matches 2.555….

Similar repeating decimals

DecimalFraction
2.1666…13/6
2.222…20/9
2.333…7/3
2.444…22/9
2.5333…38/15
2.666…8/3
2.777…25/9
2.888…26/9

See also: 23/9 as a mixed number.

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