0.666… as a Fraction

0.666… (0.6 repeating) as a fraction is 2/3.

How to convert 0.666… to a fraction

  1. Let x = 0.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 6.666...
  3. Subtract to cancel the repeating tail: 10x − x = 6 − 0, so 9x = 6.
  4. Solve: x = 6/9. The greatest common divisor is 3, so x = 2/3.

Check

Divide 2 by 3 on a calculator: 2 ÷ 3 = 0.6666666667… which matches 0.666….

Similar repeating decimals

DecimalFraction
0.6444…29/45
0.646464…64/99
0.6555…59/90
0.656565…65/99
0.676767…67/99
0.6777…61/90
0.678678678…226/333
0.686868…68/99

See also: 2/3 as a decimal.

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