0.858585… as a Fraction

0.858585… (0.85 repeating) as a fraction is 85/99.

How to convert 0.858585… to a fraction

  1. Let x = 0.858585... (the underlined part, 85, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 85.858585...
  3. Subtract to cancel the repeating tail: 100x − x = 85 − 0, so 99x = 85.
  4. Solve: x = 85/99. The greatest common divisor is 1, so x = 85/99 (already in lowest terms).

Check

Divide 85 by 99 on a calculator: 85 ÷ 99 = 0.8585858586… which matches 0.858585….

Similar repeating decimals

DecimalFraction
0.8444…38/45
0.846846846…94/111
0.848484…28/33
0.8555…77/90
0.857857857…857/999
0.8666…13/15
0.868686…86/99
0.8777…79/90

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