0.898989… as a Fraction

0.898989… (0.89 repeating) as a fraction is 89/99.

How to convert 0.898989… to a fraction

  1. Let x = 0.898989... (the underlined part, 89, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 89.898989...
  3. Subtract to cancel the repeating tail: 100x − x = 89 − 0, so 99x = 89.
  4. Solve: x = 89/99. The greatest common divisor is 1, so x = 89/99 (already in lowest terms).

Check

Divide 89 by 99 on a calculator: 89 ÷ 99 = 0.898989899… which matches 0.898989….

Similar repeating decimals

DecimalFraction
0.8777…79/90
0.878787…29/33
0.888…8/9
0.909090…10/11
0.9111…41/45
0.91333…137/150
0.91666…11/12
0.919191…91/99

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