7.111… as a Fraction

7.111… (7.1 repeating) as a fraction is 64/9. As a mixed number that is 7 1/9.

How to convert 7.111… to a fraction

  1. Let x = 7.111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 71.111...
  3. Subtract to cancel the repeating tail: 10x − x = 71 − 7, so 9x = 64.
  4. Solve: x = 64/9. The greatest common divisor is 1, so x = 64/9 (already in lowest terms).

Since 64 is larger than 9, it can also be written as the mixed number 7 1/9.

Check

Divide 64 by 9 on a calculator: 64 ÷ 9 = 7.1111111111… which matches 7.111….

Similar repeating decimals

DecimalFraction
6.555…59/9
6.666…20/3
6.777…61/9
6.888…62/9
7.222…65/9
7.333…22/3
7.444…67/9
7.555…68/9

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