0.8555… as a Fraction

0.8555… (0.85 repeating) as a fraction is 77/90.

How to convert 0.8555… to a fraction

  1. Let x = 0.8555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 85.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 85 − 8, so 90x = 77.
  5. Solve: x = 77/90. The greatest common divisor is 1, so x = 77/90 (already in lowest terms).

Check

Divide 77 by 90 on a calculator: 77 ÷ 90 = 0.8555555556… which matches 0.8555….

Similar repeating decimals

DecimalFraction
0.838383…83/99
0.8444…38/45
0.846846846…94/111
0.848484…28/33
0.857857857…857/999
0.858585…85/99
0.8666…13/15
0.868686…86/99

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