0.9666… as a Fraction

0.9666… (0.96 repeating) as a fraction is 29/30.

How to convert 0.9666… to a fraction

  1. Let x = 0.9666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 96.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 96 − 9, so 90x = 87.
  5. Solve: x = 87/90. The greatest common divisor is 3, so x = 29/30.

Check

Divide 29 by 30 on a calculator: 29 ÷ 30 = 0.9666666667… which matches 0.9666….

Similar repeating decimals

DecimalFraction
0.9444…17/18
0.949494…94/99
0.9555…43/45
0.959595…95/99
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.