0.202020… as a Fraction

0.202020… (0.20 repeating) as a fraction is 20/99.

How to convert 0.202020… to a fraction

  1. Let x = 0.202020... (the underlined part, 20, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 20.202020...
  3. Subtract to cancel the repeating tail: 100x − x = 20 − 0, so 99x = 20.
  4. Solve: x = 20/99. The greatest common divisor is 1, so x = 20/99 (already in lowest terms).

Check

Divide 20 by 99 on a calculator: 20 ÷ 99 = 0.202020202… which matches 0.202020….

Similar repeating decimals

DecimalFraction
0.1777…8/45
0.181818…2/11
0.185185185…5/27
0.1888…17/90
0.191919…19/99
0.2111…19/90
0.212121…7/33
0.222…2/9

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