0.2111… as a Fraction

0.2111… (0.21 repeating) as a fraction is 19/90.

How to convert 0.2111… to a fraction

  1. Let x = 0.2111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 21.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 2.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 21 − 2, so 90x = 19.
  5. Solve: x = 19/90. The greatest common divisor is 1, so x = 19/90 (already in lowest terms).

Check

Divide 19 by 90 on a calculator: 19 ÷ 90 = 0.2111111111… which matches 0.2111….

Similar repeating decimals

DecimalFraction
0.1888…17/90
0.191919…19/99
0.202020…20/99
0.212121…7/33
0.222…2/9
0.230230230…230/999
0.232323…23/99
0.2333…7/30

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