0.010101… as a Fraction

0.010101… (0.01 repeating) as a fraction is 1/99.

How to convert 0.010101… to a fraction

  1. Let x = 0.010101... (the underlined part, 01, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 1.010101...
  3. Subtract to cancel the repeating tail: 100x − x = 1 − 0, so 99x = 1.
  4. Solve: x = 1/99. The greatest common divisor is 1, so x = 1/99 (already in lowest terms).

Check

Divide 1 by 99 on a calculator: 1 ÷ 99 = 0.0101010101… which matches 0.010101….

Similar repeating decimals

DecimalFraction
0.005005005…5/999
0.006006006…2/333
0.007007007…7/999
0.008008008…8/999
0.009009009…1/111
0.0111…1/90
0.012012012…4/333
0.012345012345012345…4115/333333

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