6.666… as a Fraction

6.666… (6.6 repeating) as a fraction is 20/3. As a mixed number that is 6 2/3.

How to convert 6.666… to a fraction

  1. Let x = 6.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 66.666...
  3. Subtract to cancel the repeating tail: 10x − x = 66 − 6, so 9x = 60.
  4. Solve: x = 60/9. The greatest common divisor is 3, so x = 20/3.

Since 20 is larger than 3, it can also be written as the mixed number 6 2/3.

Check

Divide 20 by 3 on a calculator: 20 ÷ 3 = 6.6666666667… which matches 6.666….

Similar repeating decimals

DecimalFraction
6.222…56/9
6.333…19/3
6.444…58/9
6.555…59/9
6.777…61/9
6.888…62/9
7.111…64/9
7.222…65/9

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