3.111… as a Fraction

3.111… (3.1 repeating) as a fraction is 28/9. As a mixed number that is 3 1/9.

How to convert 3.111… to a fraction

  1. Let x = 3.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 31.111...
  3. Subtract to cancel the repeating tail: 10x − x = 31 − 3, so 9x = 28.
  4. Solve: x = 28/9. The greatest common divisor is 1, so x = 28/9 (already in lowest terms).

Since 28 is larger than 9, it can also be written as the mixed number 3 1/9.

Check

Divide 28 by 9 on a calculator: 28 ÷ 9 = 3.1111111111… which matches 3.111….

Similar repeating decimals

DecimalFraction
2.666…8/3
2.777…25/9
2.888…26/9
3.222…29/9
3.333…10/3
3.444…31/9
3.555…32/9
3.666…11/3

See also: 28/9 as a mixed number.

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