2.777… as a Fraction

2.777… (2.7 repeating) as a fraction is 25/9. As a mixed number that is 2 7/9.

How to convert 2.777… to a fraction

  1. Let x = 2.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 27.777...
  3. Subtract to cancel the repeating tail: 10x − x = 27 − 2, so 9x = 25.
  4. Solve: x = 25/9. The greatest common divisor is 1, so x = 25/9 (already in lowest terms).

Since 25 is larger than 9, it can also be written as the mixed number 2 7/9.

Check

Divide 25 by 9 on a calculator: 25 ÷ 9 = 2.7777777778… which matches 2.777….

Similar repeating decimals

DecimalFraction
2.333…7/3
2.444…22/9
2.5333…38/15
2.555…23/9
2.666…8/3
2.888…26/9
3.111…28/9
3.222…29/9

See also: 25/9 as a mixed number.

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