4.222… as a Fraction

4.222… (4.2 repeating) as a fraction is 38/9. As a mixed number that is 4 2/9.

How to convert 4.222… to a fraction

  1. Let x = 4.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 42.222...
  3. Subtract to cancel the repeating tail: 10x − x = 42 − 4, so 9x = 38.
  4. Solve: x = 38/9. The greatest common divisor is 1, so x = 38/9 (already in lowest terms).

Since 38 is larger than 9, it can also be written as the mixed number 4 2/9.

Check

Divide 38 by 9 on a calculator: 38 ÷ 9 = 4.2222222222… which matches 4.222….

Similar repeating decimals

DecimalFraction
3.777…34/9
3.8333…23/6
3.888…35/9
4.111…37/9
4.333…13/3
4.444…40/9
4.555…41/9
4.666…14/3

See also: 38/9 as a mixed number.

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