1.777… as a Fraction

1.777… (1.7 repeating) as a fraction is 16/9. As a mixed number that is 1 7/9.

How to convert 1.777… to a fraction

  1. Let x = 1.777... (the underlined part, 7, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 17.777...
  3. Subtract to cancel the repeating tail: 10x − x = 17 − 1, so 9x = 16.
  4. Solve: x = 16/9. The greatest common divisor is 1, so x = 16/9 (already in lowest terms).

Since 16 is larger than 9, it can also be written as the mixed number 1 7/9.

Check

Divide 16 by 9 on a calculator: 16 ÷ 9 = 1.7777777778… which matches 1.777….

Similar repeating decimals

DecimalFraction
1.333…4/3
1.444…13/9
1.555…14/9
1.666…5/3
1.8333…11/6
1.888…17/9
2.111…19/9
2.1666…13/6

See also: 16/9 as a mixed number.

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