4.666… as a Fraction

4.666… (4.6 repeating) as a fraction is 14/3. As a mixed number that is 4 2/3.

How to convert 4.666… to a fraction

  1. Let x = 4.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 46.666...
  3. Subtract to cancel the repeating tail: 10x − x = 46 − 4, so 9x = 42.
  4. Solve: x = 42/9. The greatest common divisor is 3, so x = 14/3.

Since 14 is larger than 3, it can also be written as the mixed number 4 2/3.

Check

Divide 14 by 3 on a calculator: 14 ÷ 3 = 4.6666666667… which matches 4.666….

Similar repeating decimals

DecimalFraction
4.222…38/9
4.333…13/3
4.444…40/9
4.555…41/9
4.777…43/9
4.888…44/9
5.111…46/9
5.222…47/9

See also: 14/3 as a mixed number.

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