0.2444… as a Fraction

0.2444… (0.24 repeating) as a fraction is 11/45.

How to convert 0.2444… to a fraction

  1. Let x = 0.2444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 24.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 24 − 2, so 90x = 22.
  5. Solve: x = 22/90. The greatest common divisor is 2, so x = 11/45.

Check

Divide 11 by 45 on a calculator: 11 ÷ 45 = 0.2444444444… which matches 0.2444….

Similar repeating decimals

DecimalFraction
0.230230230…230/999
0.232323…23/99
0.2333…7/30
0.234234234…26/111
0.242424…8/33
0.252525…25/99
0.2555…23/90
0.262626…26/99

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