0.1222… as a Fraction

0.1222… (0.12 repeating) as a fraction is 11/90.

How to convert 0.1222… to a fraction

  1. Let x = 0.1222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 12.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 12 − 1, so 90x = 11.
  5. Solve: x = 11/90. The greatest common divisor is 1, so x = 11/90 (already in lowest terms).

Check

Divide 11 by 90 on a calculator: 11 ÷ 90 = 0.1222222222… which matches 0.1222….

Similar repeating decimals

DecimalFraction
0.111…1/9
0.121212…4/33
0.123123123…41/333
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.141414…14/99
0.142142142…142/999

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