4.555… as a Fraction

4.555… (4.5 repeating) as a fraction is 41/9. As a mixed number that is 4 5/9.

How to convert 4.555… to a fraction

  1. Let x = 4.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 45.555...
  3. Subtract to cancel the repeating tail: 10x − x = 45 − 4, so 9x = 41.
  4. Solve: x = 41/9. The greatest common divisor is 1, so x = 41/9 (already in lowest terms).

Since 41 is larger than 9, it can also be written as the mixed number 4 5/9.

Check

Divide 41 by 9 on a calculator: 41 ÷ 9 = 4.5555555556… which matches 4.555….

Similar repeating decimals

DecimalFraction
4.111…37/9
4.222…38/9
4.333…13/3
4.444…40/9
4.666…14/3
4.777…43/9
4.888…44/9
5.111…46/9

See also: 41/9 as a mixed number.

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