0.4222… as a Fraction

0.4222… (0.42 repeating) as a fraction is 19/45.

How to convert 0.4222… to a fraction

  1. Let x = 0.4222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 42.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 4.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 42 − 4, so 90x = 38.
  5. Solve: x = 38/90. The greatest common divisor is 2, so x = 19/45.

Check

Divide 19 by 45 on a calculator: 19 ÷ 45 = 0.4222222222… which matches 0.4222….

Similar repeating decimals

DecimalFraction
0.4111…37/90
0.41333…31/75
0.414141…41/99
0.41666…5/12
0.424242…14/33
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.