0.5777… as a Fraction

0.5777… (0.57 repeating) as a fraction is 26/45.

How to convert 0.5777… to a fraction

  1. Let x = 0.5777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 57.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 57 − 5, so 90x = 52.
  5. Solve: x = 52/90. The greatest common divisor is 2, so x = 26/45.

Check

Divide 26 by 45 on a calculator: 26 ÷ 45 = 0.5777777778… which matches 0.5777….

Similar repeating decimals

DecimalFraction
0.5666…17/30
0.567567567…21/37
0.571571571…571/999
0.575757…19/33
0.58333…7/12
0.585858…58/99
0.58666…44/75
0.5888…53/90

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