0.08333… as a Fraction

0.08333… (0.083 repeating) as a fraction is 1/12.

How to convert 0.08333… to a fraction

  1. Let x = 0.08333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 83.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 8.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 83 − 8, so 900x = 75.
  5. Solve: x = 75/900. The greatest common divisor is 75, so x = 1/12.

Check

Divide 1 by 12 on a calculator: 1 ÷ 12 = 0.0833333333… which matches 0.08333….

Similar repeating decimals

DecimalFraction
0.076076076…76/999
0.076923076923076923…1/13
0.0777…7/90
0.080808…8/99
0.081081081…3/37
0.08666…13/150
0.0888…4/45
0.090909…1/11

See also: 1/12 as a decimal.

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