1.111… as a Fraction

1.111… (1.1 repeating) as a fraction is 10/9. As a mixed number that is 1 1/9.

How to convert 1.111… to a fraction

  1. Let x = 1.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 11.111...
  3. Subtract to cancel the repeating tail: 10x − x = 11 − 1, so 9x = 10.
  4. Solve: x = 10/9. The greatest common divisor is 1, so x = 10/9 (already in lowest terms).

Since 10 is larger than 9, it can also be written as the mixed number 1 1/9.

Check

Divide 10 by 9 on a calculator: 10 ÷ 9 = 1.1111111111… which matches 1.111….

Similar repeating decimals

DecimalFraction
0.9666…29/30
0.969696…32/33
0.9777…44/45
0.979797…97/99
0.9888…89/90
0.989898…98/99
1.1666…7/6
1.222…11/9

See also: 10/9 as a mixed number.

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