0.757575… as a Fraction

0.757575… (0.75 repeating) as a fraction is 25/33.

How to convert 0.757575… to a fraction

  1. Let x = 0.757575... (the underlined part, 75, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 75.757575...
  3. Subtract to cancel the repeating tail: 100x − x = 75 − 0, so 99x = 75.
  4. Solve: x = 75/99. The greatest common divisor is 3, so x = 25/33.

Check

Divide 25 by 33 on a calculator: 25 ÷ 33 = 0.7575757576… which matches 0.757575….

Similar repeating decimals

DecimalFraction
0.7444…67/90
0.747474…74/99
0.75333…113/150
0.7555…34/45
0.75666…227/300
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.