0.404040… as a Fraction

0.404040… (0.40 repeating) as a fraction is 40/99.

How to convert 0.404040… to a fraction

  1. Let x = 0.404040... (the underlined part, 40, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 40.404040...
  3. Subtract to cancel the repeating tail: 100x − x = 40 − 0, so 99x = 40.
  4. Solve: x = 40/99. The greatest common divisor is 1, so x = 40/99 (already in lowest terms).

Check

Divide 40 by 99 on a calculator: 40 ÷ 99 = 0.404040404… which matches 0.404040….

Similar repeating decimals

DecimalFraction
0.384384384…128/333
0.3888…7/18
0.393939…13/33
0.4111…37/90
0.41333…31/75
0.414141…41/99
0.41666…5/12
0.4222…19/45

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