0.5444… as a Fraction

0.5444… (0.54 repeating) as a fraction is 49/90.

How to convert 0.5444… to a fraction

  1. Let x = 0.5444... (the underlined part, 4, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 54.444...
  3. Move the decimal point past the non-repeating digits too: 10x = 5.4444...
  4. Subtract to cancel the repeating tail: 100x − 10x = 54 − 5, so 90x = 49.
  5. Solve: x = 49/90. The greatest common divisor is 1, so x = 49/90 (already in lowest terms).

Check

Divide 49 by 90 on a calculator: 49 ÷ 90 = 0.5444444444… which matches 0.5444….

Similar repeating decimals

DecimalFraction
0.5222…47/90
0.525252…52/99
0.5333…8/15
0.535353…53/99
0.538538538…538/999
0.545454…6/11
0.555…5/9
0.565656…56/99

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