0.185185185… as a Fraction

0.185185185… (0.185 repeating) as a fraction is 5/27.

How to convert 0.185185185… to a fraction

  1. Let x = 0.185185185... (the underlined part, 185, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 185.185185185...
  3. Subtract to cancel the repeating tail: 1000x − x = 185 − 0, so 999x = 185.
  4. Solve: x = 185/999. The greatest common divisor is 37, so x = 5/27.

Check

Divide 5 by 27 on a calculator: 5 ÷ 27 = 0.1851851852… which matches 0.185185185….

Similar repeating decimals

DecimalFraction
0.1666…1/6
0.16666…1/6
0.171717…17/99
0.1777…8/45
0.181818…2/11
0.1888…17/90
0.191919…19/99
0.202020…20/99

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