0.565656… as a Fraction

0.565656… (0.56 repeating) as a fraction is 56/99.

How to convert 0.565656… to a fraction

  1. Let x = 0.565656... (the underlined part, 56, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 56.565656...
  3. Subtract to cancel the repeating tail: 100x − x = 56 − 0, so 99x = 56.
  4. Solve: x = 56/99. The greatest common divisor is 1, so x = 56/99 (already in lowest terms).

Check

Divide 56 by 99 on a calculator: 56 ÷ 99 = 0.5656565657… which matches 0.565656….

Similar repeating decimals

DecimalFraction
0.545454…6/11
0.555…5/9
0.5666…17/30
0.567567567…21/37
0.571571571…571/999
0.575757…19/33
0.5777…26/45
0.58333…7/12

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