0.58666… as a Fraction

0.58666… (0.586 repeating) as a fraction is 44/75.

How to convert 0.58666… to a fraction

  1. Let x = 0.58666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 586.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 58.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 586 − 58, so 900x = 528.
  5. Solve: x = 528/900. The greatest common divisor is 12, so x = 44/75.

Check

Divide 44 by 75 on a calculator: 44 ÷ 75 = 0.5866666667… which matches 0.58666….

Similar repeating decimals

DecimalFraction
0.567567567…21/37
0.571571571…571/999
0.575757…19/33
0.5777…26/45
0.58333…7/12
0.585858…58/99
0.5888…53/90
0.595959…59/99

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