0.252525… as a Fraction

0.252525… (0.25 repeating) as a fraction is 25/99.

How to convert 0.252525… to a fraction

  1. Let x = 0.252525... (the underlined part, 25, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 25.252525...
  3. Subtract to cancel the repeating tail: 100x − x = 25 − 0, so 99x = 25.
  4. Solve: x = 25/99. The greatest common divisor is 1, so x = 25/99 (already in lowest terms).

Check

Divide 25 by 99 on a calculator: 25 ÷ 99 = 0.2525252525… which matches 0.252525….

Similar repeating decimals

DecimalFraction
0.2333…7/30
0.234234234…26/111
0.242424…8/33
0.2444…11/45
0.2555…23/90
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.