2.666… as a Fraction

2.666… (2.6 repeating) as a fraction is 8/3. As a mixed number that is 2 2/3.

How to convert 2.666… to a fraction

  1. Let x = 2.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 26.666...
  3. Subtract to cancel the repeating tail: 10x − x = 26 − 2, so 9x = 24.
  4. Solve: x = 24/9. The greatest common divisor is 3, so x = 8/3.

Since 8 is larger than 3, it can also be written as the mixed number 2 2/3.

Check

Divide 8 by 3 on a calculator: 8 ÷ 3 = 2.6666666667… which matches 2.666….

Similar repeating decimals

DecimalFraction
2.222…20/9
2.333…7/3
2.444…22/9
2.5333…38/15
2.555…23/9
2.777…25/9
2.888…26/9
3.111…28/9

See also: 8/3 as a mixed number.

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