3.777… as a Fraction

3.777… (3.7 repeating) as a fraction is 34/9. As a mixed number that is 3 7/9.

How to convert 3.777… to a fraction

  1. Let x = 3.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 37.777...
  3. Subtract to cancel the repeating tail: 10x − x = 37 − 3, so 9x = 34.
  4. Solve: x = 34/9. The greatest common divisor is 1, so x = 34/9 (already in lowest terms).

Since 34 is larger than 9, it can also be written as the mixed number 3 7/9.

Check

Divide 34 by 9 on a calculator: 34 ÷ 9 = 3.7777777778… which matches 3.777….

Similar repeating decimals

DecimalFraction
3.333…10/3
3.444…31/9
3.555…32/9
3.666…11/3
3.8333…23/6
3.888…35/9
4.111…37/9
4.222…38/9

See also: 34/9 as a mixed number.

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