0.0222… as a Fraction

0.0222… (0.02 repeating) as a fraction is 1/45.

How to convert 0.0222… to a fraction

  1. Let x = 0.0222... (the underlined part, 2, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 2.222...
  3. Move the decimal point past the non-repeating digits too: 10x = 0.2222...
  4. Subtract to cancel the repeating tail: 100x − 10x = 2 − 0, so 90x = 2.
  5. Solve: x = 2/90. The greatest common divisor is 2, so x = 1/45.

Check

Divide 1 by 45 on a calculator: 1 ÷ 45 = 0.0222222222… which matches 0.0222….

Similar repeating decimals

DecimalFraction
0.010101…1/99
0.0111…1/90
0.012012012…4/333
0.012345012345012345…4115/333333
0.020202…2/99
0.027027027…1/37
0.030303…1/33
0.0333…1/30

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