5.222… as a Fraction

5.222… (5.2 repeating) as a fraction is 47/9. As a mixed number that is 5 2/9.

How to convert 5.222… to a fraction

  1. Let x = 5.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 52.222...
  3. Subtract to cancel the repeating tail: 10x − x = 52 − 5, so 9x = 47.
  4. Solve: x = 47/9. The greatest common divisor is 1, so x = 47/9 (already in lowest terms).

Since 47 is larger than 9, it can also be written as the mixed number 5 2/9.

Check

Divide 47 by 9 on a calculator: 47 ÷ 9 = 5.2222222222… which matches 5.222….

Similar repeating decimals

DecimalFraction
4.666…14/3
4.777…43/9
4.888…44/9
5.111…46/9
5.333…16/3
5.444…49/9
5.555…50/9
5.666…17/3

See also: 47/9 as a mixed number.

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