2.111… as a Fraction

2.111… (2.1 repeating) as a fraction is 19/9. As a mixed number that is 2 1/9.

How to convert 2.111… to a fraction

  1. Let x = 2.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 21.111...
  3. Subtract to cancel the repeating tail: 10x − x = 21 − 2, so 9x = 19.
  4. Solve: x = 19/9. The greatest common divisor is 1, so x = 19/9 (already in lowest terms).

Since 19 is larger than 9, it can also be written as the mixed number 2 1/9.

Check

Divide 19 by 9 on a calculator: 19 ÷ 9 = 2.1111111111… which matches 2.111….

Similar repeating decimals

DecimalFraction
1.777…16/9
1.8333…11/6
1.888…17/9
2.1666…13/6
2.222…20/9
2.333…7/3
2.444…22/9
2.5333…38/15

See also: 19/9 as a mixed number.

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