0.040404… as a Fraction

0.040404… (0.04 repeating) as a fraction is 4/99.

How to convert 0.040404… to a fraction

  1. Let x = 0.040404... (the underlined part, 04, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 4.040404...
  3. Subtract to cancel the repeating tail: 100x − x = 4 − 0, so 99x = 4.
  4. Solve: x = 4/99. The greatest common divisor is 1, so x = 4/99 (already in lowest terms).

Check

Divide 4 by 99 on a calculator: 4 ÷ 99 = 0.0404040404… which matches 0.040404….

Similar repeating decimals

DecimalFraction
0.027027027…1/37
0.030303…1/33
0.0333…1/30
0.037037037…1/27
0.0444…2/45
0.050505…5/99
0.054054054…2/37
0.0555…1/18

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