7.555… as a Fraction

7.555… (7.5 repeating) as a fraction is 68/9. As a mixed number that is 7 5/9.

How to convert 7.555… to a fraction

  1. Let x = 7.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 75.555...
  3. Subtract to cancel the repeating tail: 10x − x = 75 − 7, so 9x = 68.
  4. Solve: x = 68/9. The greatest common divisor is 1, so x = 68/9 (already in lowest terms).

Since 68 is larger than 9, it can also be written as the mixed number 7 5/9.

Check

Divide 68 by 9 on a calculator: 68 ÷ 9 = 7.5555555556… which matches 7.555….

Similar repeating decimals

DecimalFraction
7.111…64/9
7.222…65/9
7.333…22/3
7.444…67/9
7.666…23/3
7.777…70/9
7.888…71/9
8.111…73/9

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