4.444… as a Fraction

4.444… (4.4 repeating) as a fraction is 40/9. As a mixed number that is 4 4/9.

How to convert 4.444… to a fraction

  1. Let x = 4.444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 44.444...
  3. Subtract to cancel the repeating tail: 10x − x = 44 − 4, so 9x = 40.
  4. Solve: x = 40/9. The greatest common divisor is 1, so x = 40/9 (already in lowest terms).

Since 40 is larger than 9, it can also be written as the mixed number 4 4/9.

Check

Divide 40 by 9 on a calculator: 40 ÷ 9 = 4.4444444444… which matches 4.444….

Similar repeating decimals

DecimalFraction
3.888…35/9
4.111…37/9
4.222…38/9
4.333…13/3
4.555…41/9
4.666…14/3
4.777…43/9
4.888…44/9

See also: 40/9 as a mixed number.

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