0.878787… as a Fraction

0.878787… (0.87 repeating) as a fraction is 29/33.

How to convert 0.878787… to a fraction

  1. Let x = 0.878787... (the underlined part, 87, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 87.878787...
  3. Subtract to cancel the repeating tail: 100x − x = 87 − 0, so 99x = 87.
  4. Solve: x = 87/99. The greatest common divisor is 3, so x = 29/33.

Check

Divide 29 by 33 on a calculator: 29 ÷ 33 = 0.8787878788… which matches 0.878787….

Similar repeating decimals

DecimalFraction
0.8555…77/90
0.857857857…857/999
0.858585…85/99
0.8666…13/15
0.868686…86/99
0.8777…79/90
0.888…8/9
0.898989…89/99

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