0.525252… as a Fraction

0.525252… (0.52 repeating) as a fraction is 52/99.

How to convert 0.525252… to a fraction

  1. Let x = 0.525252... (the underlined part, 52, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 52.525252...
  3. Subtract to cancel the repeating tail: 100x − x = 52 − 0, so 99x = 52.
  4. Solve: x = 52/99. The greatest common divisor is 1, so x = 52/99 (already in lowest terms).

Check

Divide 52 by 99 on a calculator: 52 ÷ 99 = 0.5252525253… which matches 0.525252….

Similar repeating decimals

DecimalFraction
0.5111…23/45
0.515151…17/33
0.5222…47/90
0.5333…8/15
0.535353…53/99
0.538538538…538/999
0.5444…49/90
0.545454…6/11

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