0.515151… as a Fraction

0.515151… (0.51 repeating) as a fraction is 17/33.

How to convert 0.515151… to a fraction

  1. Let x = 0.515151... (the underlined part, 51, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 51.515151...
  3. Subtract to cancel the repeating tail: 100x − x = 51 − 0, so 99x = 51.
  4. Solve: x = 51/99. The greatest common divisor is 3, so x = 17/33.

Check

Divide 17 by 33 on a calculator: 17 ÷ 33 = 0.5151515152… which matches 0.515151….

Similar repeating decimals

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0.494949…49/99
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0.5222…47/90
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0.5333…8/15
0.535353…53/99
0.538538538…538/999

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