0.3444… as a Fraction

0.3444… (0.34 repeating) as a fraction is 31/90.

How to convert 0.3444… to a fraction

  1. Let x = 0.3444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 34.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 3.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 34 − 3, so 90x = 31.
  5. Solve: x = 31/90. The greatest common divisor is 1, so x = 31/90 (already in lowest terms).

Check

Divide 31 by 90 on a calculator: 31 ÷ 90 = 0.3444444444… which matches 0.3444….

Similar repeating decimals

DecimalFraction
0.3222…29/90
0.323232…32/99
0.333…1/3
0.343434…34/99
0.345345345…115/333
0.353535…35/99
0.3555…16/45
0.363636…4/11

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