0.969696… as a Fraction

0.969696… (0.96 repeating) as a fraction is 32/33.

How to convert 0.969696… to a fraction

  1. Let x = 0.969696... (the underlined part, 96, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 96.969696...
  3. Subtract to cancel the repeating tail: 100x − x = 96 − 0, so 99x = 96.
  4. Solve: x = 96/99. The greatest common divisor is 3, so x = 32/33.

Check

Divide 32 by 33 on a calculator: 32 ÷ 33 = 0.9696969697… which matches 0.969696….

Similar repeating decimals

DecimalFraction
0.949494…94/99
0.9555…43/45
0.959595…95/99
0.9666…29/30
0.9777…44/45
0.979797…97/99
0.9888…89/90
0.989898…98/99

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