0.444… as a Fraction

0.444… (0.4 repeating) as a fraction is 4/9.

How to convert 0.444… to a fraction

  1. Let x = 0.444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 4.444...
  3. Subtract to cancel the repeating tail: 10x − x = 4 − 0, so 9x = 4.
  4. Solve: x = 4/9. The greatest common divisor is 1, so x = 4/9 (already in lowest terms).

Check

Divide 4 by 9 on a calculator: 4 ÷ 9 = 0.4444444444… which matches 0.444….

Similar repeating decimals

DecimalFraction
0.424242…14/33
0.428428428…428/999
0.4333…13/30
0.434343…43/99
0.454545…5/11
0.4555…41/90
0.456456456…152/333
0.461461461…461/999

See also: 4/9 as a decimal.

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