0.2555… as a Fraction

0.2555… (0.25 repeating) as a fraction is 23/90.

How to convert 0.2555… to a fraction

  1. Let x = 0.2555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 25.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 25 − 2, so 90x = 23.
  5. Solve: x = 23/90. The greatest common divisor is 1, so x = 23/90 (already in lowest terms).

Check

Divide 23 by 90 on a calculator: 23 ÷ 90 = 0.2555555556… which matches 0.2555….

Similar repeating decimals

DecimalFraction
0.2333…7/30
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0.252525…25/99
0.262626…26/99
0.2666…4/15
0.272727…3/11

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