0.585858… as a Fraction

0.585858… (0.58 repeating) as a fraction is 58/99.

How to convert 0.585858… to a fraction

  1. Let x = 0.585858... (the underlined part, 58, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 58.585858...
  3. Subtract to cancel the repeating tail: 100x − x = 58 − 0, so 99x = 58.
  4. Solve: x = 58/99. The greatest common divisor is 1, so x = 58/99 (already in lowest terms).

Check

Divide 58 by 99 on a calculator: 58 ÷ 99 = 0.5858585859… which matches 0.585858….

Similar repeating decimals

DecimalFraction
0.567567567…21/37
0.571571571…571/999
0.575757…19/33
0.5777…26/45
0.58333…7/12
0.58666…44/75
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.