0.535353… as a Fraction

0.535353… (0.53 repeating) as a fraction is 53/99.

How to convert 0.535353… to a fraction

  1. Let x = 0.535353... (the underlined part, 53, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 53.535353...
  3. Subtract to cancel the repeating tail: 100x − x = 53 − 0, so 99x = 53.
  4. Solve: x = 53/99. The greatest common divisor is 1, so x = 53/99 (already in lowest terms).

Check

Divide 53 by 99 on a calculator: 53 ÷ 99 = 0.5353535354… which matches 0.535353….

Similar repeating decimals

DecimalFraction
0.515151…17/33
0.5222…47/90
0.525252…52/99
0.5333…8/15
0.538538538…538/999
0.5444…49/90
0.545454…6/11
0.555…5/9

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