0.181818… as a Fraction

0.181818… (0.18 repeating) as a fraction is 2/11.

How to convert 0.181818… to a fraction

  1. Let x = 0.181818... (the underlined part, 18, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 18.181818...
  3. Subtract to cancel the repeating tail: 100x − x = 18 − 0, so 99x = 18.
  4. Solve: x = 18/99. The greatest common divisor is 9, so x = 2/11.

Check

Divide 2 by 11 on a calculator: 2 ÷ 11 = 0.1818181818… which matches 0.181818….

Similar repeating decimals

DecimalFraction
0.16333…49/300
0.1666…1/6
0.16666…1/6
0.171717…17/99
0.1777…8/45
0.185185185…5/27
0.1888…17/90
0.191919…19/99

See also: 2/11 as a decimal.

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