5.666… as a Fraction

5.666… (5.6 repeating) as a fraction is 17/3. As a mixed number that is 5 2/3.

How to convert 5.666… to a fraction

  1. Let x = 5.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 56.666...
  3. Subtract to cancel the repeating tail: 10x − x = 56 − 5, so 9x = 51.
  4. Solve: x = 51/9. The greatest common divisor is 3, so x = 17/3.

Since 17 is larger than 3, it can also be written as the mixed number 5 2/3.

Check

Divide 17 by 3 on a calculator: 17 ÷ 3 = 5.6666666667… which matches 5.666….

Similar repeating decimals

DecimalFraction
5.222…47/9
5.333…16/3
5.444…49/9
5.555…50/9
5.777…52/9
5.888…53/9
6.111…55/9
6.222…56/9

See also: 17/3 as a mixed number.

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