9.666… as a Fraction

9.666… (9.6 repeating) as a fraction is 29/3. As a mixed number that is 9 2/3.

How to convert 9.666… to a fraction

  1. Let x = 9.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 96.666...
  3. Subtract to cancel the repeating tail: 10x − x = 96 − 9, so 9x = 87.
  4. Solve: x = 87/9. The greatest common divisor is 3, so x = 29/3.

Since 29 is larger than 3, it can also be written as the mixed number 9 2/3.

Check

Divide 29 by 3 on a calculator: 29 ÷ 3 = 9.6666666667… which matches 9.666….

Similar repeating decimals

DecimalFraction
8.888…80/9
9.111…82/9
9.222…83/9
9.333…28/3
9.444…85/9
9.555…86/9
9.777…88/9
9.888…89/9

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