0.5666… as a Fraction

0.5666… (0.56 repeating) as a fraction is 17/30.

How to convert 0.5666… to a fraction

  1. Let x = 0.5666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 56.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 56 − 5, so 90x = 51.
  5. Solve: x = 51/90. The greatest common divisor is 3, so x = 17/30.

Check

Divide 17 by 30 on a calculator: 17 ÷ 30 = 0.5666666667… which matches 0.5666….

Similar repeating decimals

DecimalFraction
0.555…5/9
0.565656…56/99
0.567567567…21/37
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.