0.7666… as a Fraction

0.7666… (0.76 repeating) as a fraction is 23/30.

How to convert 0.7666… to a fraction

  1. Let x = 0.7666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 76.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 76 − 7, so 90x = 69.
  5. Solve: x = 69/90. The greatest common divisor is 3, so x = 23/30.

Check

Divide 23 by 30 on a calculator: 23 ÷ 30 = 0.7666666667… which matches 0.7666….

Similar repeating decimals

DecimalFraction
0.747474…74/99
0.75333…113/150
0.7555…34/45
0.75666…227/300
0.757575…25/33
0.767676…76/99
0.769769769…769/999
0.777…7/9

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