0.212121… as a Fraction

0.212121… (0.21 repeating) as a fraction is 7/33.

How to convert 0.212121… to a fraction

  1. Let x = 0.212121... (the underlined part, 21, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 21.212121...
  3. Subtract to cancel the repeating tail: 100x − x = 21 − 0, so 99x = 21.
  4. Solve: x = 21/99. The greatest common divisor is 3, so x = 7/33.

Check

Divide 7 by 33 on a calculator: 7 ÷ 33 = 0.2121212121… which matches 0.212121….

Similar repeating decimals

DecimalFraction
0.191919…19/99
0.202020…20/99
0.2111…19/90
0.222…2/9
0.230230230…230/999
0.232323…23/99
0.2333…7/30
0.234234234…26/111

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