1.222… as a Fraction

1.222… (1.2 repeating) as a fraction is 11/9. As a mixed number that is 1 2/9.

How to convert 1.222… to a fraction

  1. Let x = 1.222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 12.222...
  3. Subtract to cancel the repeating tail: 10x − x = 12 − 1, so 9x = 11.
  4. Solve: x = 11/9. The greatest common divisor is 1, so x = 11/9 (already in lowest terms).

Since 11 is larger than 9, it can also be written as the mixed number 1 2/9.

Check

Divide 11 by 9 on a calculator: 11 ÷ 9 = 1.2222222222… which matches 1.222….

Similar repeating decimals

DecimalFraction
0.9777…44/45
0.979797…97/99
0.9888…89/90
0.989898…98/99
1.111…10/9
1.1666…7/6
1.333…4/3
1.444…13/9

See also: 11/9 as a mixed number.

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