0.5111… as a Fraction

0.5111… (0.51 repeating) as a fraction is 23/45.

How to convert 0.5111… to a fraction

  1. Let x = 0.5111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 51.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 51 − 5, so 90x = 46.
  5. Solve: x = 46/90. The greatest common divisor is 2, so x = 23/45.

Check

Divide 23 by 45 on a calculator: 23 ÷ 45 = 0.5111111111… which matches 0.5111….

Similar repeating decimals

DecimalFraction
0.4888…22/45
0.494949…49/99
0.505050…50/99
0.515151…17/33
0.5222…47/90
0.525252…52/99
0.5333…8/15
0.535353…53/99

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