8.666… as a Fraction

8.666… (8.6 repeating) as a fraction is 26/3. As a mixed number that is 8 2/3.

How to convert 8.666… to a fraction

  1. Let x = 8.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 86.666...
  3. Subtract to cancel the repeating tail: 10x − x = 86 − 8, so 9x = 78.
  4. Solve: x = 78/9. The greatest common divisor is 3, so x = 26/3.

Since 26 is larger than 3, it can also be written as the mixed number 8 2/3.

Check

Divide 26 by 3 on a calculator: 26 ÷ 3 = 8.6666666667… which matches 8.666….

Similar repeating decimals

DecimalFraction
8.111…73/9
8.222…74/9
8.333…25/3
8.444…76/9
8.555…77/9
8.777…79/9
8.888…80/9
9.111…82/9

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