0.020202… as a Fraction

0.020202… (0.02 repeating) as a fraction is 2/99.

How to convert 0.020202… to a fraction

  1. Let x = 0.020202... (the underlined part, 02, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 2.020202...
  3. Subtract to cancel the repeating tail: 100x − x = 2 − 0, so 99x = 2.
  4. Solve: x = 2/99. The greatest common divisor is 1, so x = 2/99 (already in lowest terms).

Check

Divide 2 by 99 on a calculator: 2 ÷ 99 = 0.0202020202… which matches 0.020202….

Similar repeating decimals

DecimalFraction
0.009009009…1/111
0.010101…1/99
0.0111…1/90
0.012012012…4/333
0.012345012345012345…4115/333333
0.0222…1/45
0.027027027…1/37
0.030303…1/33

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