0.1888… as a Fraction

0.1888… (0.18 repeating) as a fraction is 17/90.

How to convert 0.1888… to a fraction

  1. Let x = 0.1888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 18.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 1.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 18 − 1, so 90x = 17.
  5. Solve: x = 17/90. The greatest common divisor is 1, so x = 17/90 (already in lowest terms).

Check

Divide 17 by 90 on a calculator: 17 ÷ 90 = 0.1888888889… which matches 0.1888….

Similar repeating decimals

DecimalFraction
0.1666…1/6
0.16666…1/6
0.171717…17/99
0.1777…8/45
0.181818…2/11
0.185185185…5/27
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.