5.111… as a Fraction

5.111… (5.1 repeating) as a fraction is 46/9. As a mixed number that is 5 1/9.

How to convert 5.111… to a fraction

  1. Let x = 5.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 51.111...
  3. Subtract to cancel the repeating tail: 10x − x = 51 − 5, so 9x = 46.
  4. Solve: x = 46/9. The greatest common divisor is 1, so x = 46/9 (already in lowest terms).

Since 46 is larger than 9, it can also be written as the mixed number 5 1/9.

Check

Divide 46 by 9 on a calculator: 46 ÷ 9 = 5.1111111111… which matches 5.111….

Similar repeating decimals

DecimalFraction
4.555…41/9
4.666…14/3
4.777…43/9
4.888…44/9
5.222…47/9
5.333…16/3
5.444…49/9
5.555…50/9

See also: 46/9 as a mixed number.

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