0.101010… as a Fraction

0.101010… (0.10 repeating) as a fraction is 10/99.

How to convert 0.101010… to a fraction

  1. Let x = 0.101010... (the underlined part, 10, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 10.101010...
  3. Subtract to cancel the repeating tail: 100x − x = 10 − 0, so 99x = 10.
  4. Solve: x = 10/99. The greatest common divisor is 1, so x = 10/99 (already in lowest terms).

Check

Divide 10 by 99 on a calculator: 10 ÷ 99 = 0.101010101… which matches 0.101010….

Similar repeating decimals

DecimalFraction
0.080808…8/99
0.081081081…3/37
0.08333…1/12
0.08666…13/150
0.0888…4/45
0.090909…1/11
0.111…1/9
0.121212…4/33

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