0.989898… as a Fraction

0.989898… (0.98 repeating) as a fraction is 98/99.

How to convert 0.989898… to a fraction

  1. Let x = 0.989898... (the underlined part, 98, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 98.989898...
  3. Subtract to cancel the repeating tail: 100x − x = 98 − 0, so 99x = 98.
  4. Solve: x = 98/99. The greatest common divisor is 1, so x = 98/99 (already in lowest terms).

Check

Divide 98 by 99 on a calculator: 98 ÷ 99 = 0.9898989899… which matches 0.989898….

Similar repeating decimals

DecimalFraction
0.949494…94/99
0.9555…43/45
0.959595…95/99
0.9666…29/30
0.969696…32/33
0.9777…44/45
0.979797…97/99
0.9888…89/90

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