0.7555… as a Fraction

0.7555… (0.75 repeating) as a fraction is 34/45.

How to convert 0.7555… to a fraction

  1. Let x = 0.7555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 75.555...
  3. Move the decimal point past the non-repeating digits too: 10x = 7.5555...
  4. Subtract to cancel the repeating tail: 100x − 10x = 75 − 7, so 90x = 68.
  5. Solve: x = 68/90. The greatest common divisor is 2, so x = 34/45.

Check

Divide 34 by 45 on a calculator: 34 ÷ 45 = 0.7555555556… which matches 0.7555….

Similar repeating decimals

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