3.666… as a Fraction

3.666… (3.6 repeating) as a fraction is 11/3. As a mixed number that is 3 2/3.

How to convert 3.666… to a fraction

  1. Let x = 3.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 36.666...
  3. Subtract to cancel the repeating tail: 10x − x = 36 − 3, so 9x = 33.
  4. Solve: x = 33/9. The greatest common divisor is 3, so x = 11/3.

Since 11 is larger than 3, it can also be written as the mixed number 3 2/3.

Check

Divide 11 by 3 on a calculator: 11 ÷ 3 = 3.6666666667… which matches 3.666….

Similar repeating decimals

DecimalFraction
3.222…29/9
3.333…10/3
3.444…31/9
3.555…32/9
3.777…34/9
3.8333…23/6
3.888…35/9
4.111…37/9

See also: 11/3 as a mixed number.

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