0.9888… as a Fraction

0.9888… (0.98 repeating) as a fraction is 89/90.

How to convert 0.9888… to a fraction

  1. Let x = 0.9888... (the underlined part, 8, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 98.888...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.8888...
  4. Subtract to cancel the repeating tail: 100x − 10x = 98 − 9, so 90x = 89.
  5. Solve: x = 89/90. The greatest common divisor is 1, so x = 89/90 (already in lowest terms).

Check

Divide 89 by 90 on a calculator: 89 ÷ 90 = 0.9888888889… which matches 0.9888….

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
0.989898…98/99

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