0.769769769… as a Fraction

0.769769769… (0.769 repeating) as a fraction is 769/999.

How to convert 0.769769769… to a fraction

  1. Let x = 0.769769769... (the underlined part, 769, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 769.769769769...
  3. Subtract to cancel the repeating tail: 1000x − x = 769 − 0, so 999x = 769.
  4. Solve: x = 769/999. The greatest common divisor is 1, so x = 769/999 (already in lowest terms).

Check

Divide 769 by 999 on a calculator: 769 ÷ 999 = 0.7697697698… which matches 0.769769769….

Similar repeating decimals

DecimalFraction
0.75333…113/150
0.7555…34/45
0.75666…227/300
0.757575…25/33
0.7666…23/30
0.767676…76/99
0.777…7/9
0.787878…26/33

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