0.121212… as a Fraction

0.121212… (0.12 repeating) as a fraction is 4/33.

How to convert 0.121212… to a fraction

  1. Let x = 0.121212... (the underlined part, 12, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 12.121212...
  3. Subtract to cancel the repeating tail: 100x − x = 12 − 0, so 99x = 12.
  4. Solve: x = 12/99. The greatest common divisor is 3, so x = 4/33.

Check

Divide 4 by 33 on a calculator: 4 ÷ 33 = 0.1212121212… which matches 0.121212….

Similar repeating decimals

DecimalFraction
0.101010…10/99
0.111…1/9
0.1222…11/90
0.123123123…41/333
0.131313…13/99
0.1333…2/15
0.135135135…5/37
0.141414…14/99

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