0.75666… as a Fraction

0.75666… (0.756 repeating) as a fraction is 227/300.

How to convert 0.75666… to a fraction

  1. Let x = 0.75666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 1000x = 756.666...
  3. Move the decimal point past the non-repeating digits too: 100x = 75.6666...
  4. Subtract to cancel the repeating tail: 1000x − 100x = 756 − 75, so 900x = 681.
  5. Solve: x = 681/900. The greatest common divisor is 3, so x = 227/300.

Check

Divide 227 by 300 on a calculator: 227 ÷ 300 = 0.7566666667… which matches 0.75666….

Similar repeating decimals

DecimalFraction
0.7444…67/90
0.747474…74/99
0.75333…113/150
0.7555…34/45
0.757575…25/33
0.7666…23/30
0.767676…76/99
0.769769769…769/999

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