0.58333… as a Fraction

0.58333… (0.583 repeating) as a fraction is 7/12.

How to convert 0.58333… to a fraction

  1. Let x = 0.58333... (the underlined part, 3, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 583.333...
  3. Move the decimal point past the non-repeating digits too: 100x = 58.3333...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 583 − 58, so 900x = 525.
  5. Solve: x = 525/900. The greatest common divisor is 75, so x = 7/12.

Check

Divide 7 by 12 on a calculator: 7 ÷ 12 = 0.5833333333… which matches 0.58333….

Similar repeating decimals

DecimalFraction
0.567567567…21/37
0.571571571…571/999
0.575757…19/33
0.5777…26/45
0.585858…58/99
0.58666…44/75
0.5888…53/90
0.595959…59/99

See also: 7/12 as a decimal.

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