0.595959… as a Fraction

0.595959… (0.59 repeating) as a fraction is 59/99.

How to convert 0.595959… to a fraction

  1. Let x = 0.595959... (the underlined part, 59, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 59.595959...
  3. Subtract to cancel the repeating tail: 100x − x = 59 − 0, so 99x = 59.
  4. Solve: x = 59/99. The greatest common divisor is 1, so x = 59/99 (already in lowest terms).

Check

Divide 59 by 99 on a calculator: 59 ÷ 99 = 0.595959596… which matches 0.595959….

Similar repeating decimals

DecimalFraction
0.5777…26/45
0.58333…7/12
0.585858…58/99
0.58666…44/75
0.5888…53/90
0.606060…20/33
0.6111…11/18
0.615615615…205/333

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