6.111… as a Fraction

6.111… (6.1 repeating) as a fraction is 55/9. As a mixed number that is 6 1/9.

How to convert 6.111… to a fraction

  1. Let x = 6.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 61.111...
  3. Subtract to cancel the repeating tail: 10x − x = 61 − 6, so 9x = 55.
  4. Solve: x = 55/9. The greatest common divisor is 1, so x = 55/9 (already in lowest terms).

Since 55 is larger than 9, it can also be written as the mixed number 6 1/9.

Check

Divide 55 by 9 on a calculator: 55 ÷ 9 = 6.1111111111… which matches 6.111….

Similar repeating decimals

DecimalFraction
5.555…50/9
5.666…17/3
5.777…52/9
5.888…53/9
6.222…56/9
6.333…19/3
6.444…58/9
6.555…59/9

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