0.868686… as a Fraction

0.868686… (0.86 repeating) as a fraction is 86/99.

How to convert 0.868686… to a fraction

  1. Let x = 0.868686... (the underlined part, 86, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 86.868686...
  3. Subtract to cancel the repeating tail: 100x − x = 86 − 0, so 99x = 86.
  4. Solve: x = 86/99. The greatest common divisor is 1, so x = 86/99 (already in lowest terms).

Check

Divide 86 by 99 on a calculator: 86 ÷ 99 = 0.8686868687… which matches 0.868686….

Similar repeating decimals

DecimalFraction
0.848484…28/33
0.8555…77/90
0.857857857…857/999
0.858585…85/99
0.8666…13/15
0.8777…79/90
0.878787…29/33
0.888…8/9

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