0.9777… as a Fraction

0.9777… (0.97 repeating) as a fraction is 44/45.

How to convert 0.9777… to a fraction

  1. Let x = 0.9777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 97.777...
  3. Move the decimal point past the non-repeating digits too: 10x = 9.7777...
  4. Subtract to cancel the repeating tail: 100x − 10x = 97 − 9, so 90x = 88.
  5. Solve: x = 88/90. The greatest common divisor is 2, so x = 44/45.

Check

Divide 44 by 45 on a calculator: 44 ÷ 45 = 0.9777777778… which matches 0.9777….

Similar repeating decimals

DecimalFraction
0.949494…94/99
0.9555…43/45
0.959595…95/99
0.9666…29/30
0.969696…32/33
0.979797…97/99
0.9888…89/90
0.989898…98/99

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