0.8666… as a Fraction

0.8666… (0.86 repeating) as a fraction is 13/15.

How to convert 0.8666… to a fraction

  1. Let x = 0.8666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 86.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 86 − 8, so 90x = 78.
  5. Solve: x = 78/90. The greatest common divisor is 6, so x = 13/15.

Check

Divide 13 by 15 on a calculator: 13 ÷ 15 = 0.8666666667… which matches 0.8666….

Similar repeating decimals

DecimalFraction
0.846846846…94/111
0.848484…28/33
0.8555…77/90
0.857857857…857/999
0.858585…85/99
0.868686…86/99
0.8777…79/90
0.878787…29/33

See also: 13/15 as a decimal.

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