0.888… as a Fraction

0.888… (0.8 repeating) as a fraction is 8/9.

How to convert 0.888… to a fraction

  1. Let x = 0.888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 8.888...
  3. Subtract to cancel the repeating tail: 10x − x = 8 − 0, so 9x = 8.
  4. Solve: x = 8/9. The greatest common divisor is 1, so x = 8/9 (already in lowest terms).

Check

Divide 8 by 9 on a calculator: 8 ÷ 9 = 0.8888888889… which matches 0.888….

Similar repeating decimals

DecimalFraction
0.8666…13/15
0.868686…86/99
0.8777…79/90
0.878787…29/33
0.898989…89/99
0.909090…10/11
0.9111…41/45
0.91333…137/150

See also: 8/9 as a decimal.

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