3.444… as a Fraction

3.444… (3.4 repeating) as a fraction is 31/9. As a mixed number that is 3 4/9.

How to convert 3.444… to a fraction

  1. Let x = 3.444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 34.444...
  3. Subtract to cancel the repeating tail: 10x − x = 34 − 3, so 9x = 31.
  4. Solve: x = 31/9. The greatest common divisor is 1, so x = 31/9 (already in lowest terms).

Since 31 is larger than 9, it can also be written as the mixed number 3 4/9.

Check

Divide 31 by 9 on a calculator: 31 ÷ 9 = 3.4444444444… which matches 3.444….

Similar repeating decimals

DecimalFraction
3.111…28/9
3.222…29/9
3.333…10/3
3.555…32/9
3.666…11/3
3.777…34/9
3.8333…23/6
3.888…35/9

See also: 31/9 as a mixed number.

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