0.8777… as a Fraction

0.8777… (0.87 repeating) as a fraction is 79/90.

How to convert 0.8777… to a fraction

  1. Let x = 0.8777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 87.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 8.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 87 − 8, so 90x = 79.
  5. Solve: x = 79/90. The greatest common divisor is 1, so x = 79/90 (already in lowest terms).

Check

Divide 79 by 90 on a calculator: 79 ÷ 90 = 0.8777777778… which matches 0.8777….

Similar repeating decimals

DecimalFraction
0.8555…77/90
0.857857857…857/999
0.858585…85/99
0.8666…13/15
0.868686…86/99
0.878787…29/33
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.