0.076923076923076923… as a Fraction

0.076923076923076923… (0.076923 repeating) as a fraction is 1/13.

How to convert 0.076923076923076923… to a fraction

  1. Let x = 0.076923076923076923... (the underlined part, 076923, repeats forever).
  2. Move the decimal point past one full repeating block: 1000000x = 76923.076923076923076923...
  3. Subtract to cancel the repeating tail: 1000000x − x = 76923 − 0, so 999999x = 76923.
  4. Solve: x = 76923/999999. The greatest common divisor is 76923, so x = 1/13.

Check

Divide 1 by 13 on a calculator: 1 ÷ 13 = 0.0769230769… which matches 0.076923076923076923….

Similar repeating decimals

DecimalFraction
0.070707…7/99
0.074074074…2/27
0.076076076…76/999
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.08666…13/150

See also: 1/13 as a decimal.

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