3.555… as a Fraction

3.555… (3.5 repeating) as a fraction is 32/9. As a mixed number that is 3 5/9.

How to convert 3.555… to a fraction

  1. Let x = 3.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 35.555...
  3. Subtract to cancel the repeating tail: 10x − x = 35 − 3, so 9x = 32.
  4. Solve: x = 32/9. The greatest common divisor is 1, so x = 32/9 (already in lowest terms).

Since 32 is larger than 9, it can also be written as the mixed number 3 5/9.

Check

Divide 32 by 9 on a calculator: 32 ÷ 9 = 3.5555555556… which matches 3.555….

Similar repeating decimals

DecimalFraction
3.111…28/9
3.222…29/9
3.333…10/3
3.444…31/9
3.666…11/3
3.777…34/9
3.8333…23/6
3.888…35/9

See also: 32/9 as a mixed number.

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