0.424242… as a Fraction

0.424242… (0.42 repeating) as a fraction is 14/33.

How to convert 0.424242… to a fraction

  1. Let x = 0.424242... (the underlined part, 42, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 42.424242...
  3. Subtract to cancel the repeating tail: 100x − x = 42 − 0, so 99x = 42.
  4. Solve: x = 42/99. The greatest common divisor is 3, so x = 14/33.

Check

Divide 14 by 33 on a calculator: 14 ÷ 33 = 0.4242424242… which matches 0.424242….

Similar repeating decimals

DecimalFraction
0.4111…37/90
0.41333…31/75
0.414141…41/99
0.41666…5/12
0.4222…19/45
0.428428428…428/999
0.4333…13/30
0.434343…43/99

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