0.575757… as a Fraction

0.575757… (0.57 repeating) as a fraction is 19/33.

How to convert 0.575757… to a fraction

  1. Let x = 0.575757... (the underlined part, 57, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 57.575757...
  3. Subtract to cancel the repeating tail: 100x − x = 57 − 0, so 99x = 57.
  4. Solve: x = 57/99. The greatest common divisor is 3, so x = 19/33.

Check

Divide 19 by 33 on a calculator: 19 ÷ 33 = 0.5757575758… which matches 0.575757….

Similar repeating decimals

DecimalFraction
0.565656…56/99
0.5666…17/30
0.567567567…21/37
0.571571571…571/999
0.5777…26/45
0.58333…7/12
0.585858…58/99
0.58666…44/75

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