7.666… as a Fraction

7.666… (7.6 repeating) as a fraction is 23/3. As a mixed number that is 7 2/3.

How to convert 7.666… to a fraction

  1. Let x = 7.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 76.666...
  3. Subtract to cancel the repeating tail: 10x − x = 76 − 7, so 9x = 69.
  4. Solve: x = 69/9. The greatest common divisor is 3, so x = 23/3.

Since 23 is larger than 3, it can also be written as the mixed number 7 2/3.

Check

Divide 23 by 3 on a calculator: 23 ÷ 3 = 7.6666666667… which matches 7.666….

Similar repeating decimals

DecimalFraction
7.222…65/9
7.333…22/3
7.444…67/9
7.555…68/9
7.777…70/9
7.888…71/9
8.111…73/9
8.222…74/9

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