0.538538538… as a Fraction

0.538538538… (0.538 repeating) as a fraction is 538/999.

How to convert 0.538538538… to a fraction

  1. Let x = 0.538538538... (the underlined part, 538, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 538.538538538...
  3. Subtract to cancel the repeating tail: 1000x − x = 538 − 0, so 999x = 538.
  4. Solve: x = 538/999. The greatest common divisor is 1, so x = 538/999 (already in lowest terms).

Check

Divide 538 by 999 on a calculator: 538 ÷ 999 = 0.5385385385… which matches 0.538538538….

Similar repeating decimals

DecimalFraction
0.515151…17/33
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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.