0.567567567… as a Fraction

0.567567567… (0.567 repeating) as a fraction is 21/37.

How to convert 0.567567567… to a fraction

  1. Let x = 0.567567567... (the underlined part, 567, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 567.567567567...
  3. Subtract to cancel the repeating tail: 1000x − x = 567 − 0, so 999x = 567.
  4. Solve: x = 567/999. The greatest common divisor is 27, so x = 21/37.

Check

Divide 21 by 37 on a calculator: 21 ÷ 37 = 0.5675675676… which matches 0.567567567….

Similar repeating decimals

DecimalFraction
0.555…5/9
0.565656…56/99
0.5666…17/30
0.571571571…571/999
0.575757…19/33
0.5777…26/45
0.58333…7/12
0.585858…58/99

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