1.555… as a Fraction

1.555… (1.5 repeating) as a fraction is 14/9. As a mixed number that is 1 5/9.

How to convert 1.555… to a fraction

  1. Let x = 1.555... (the underlined part, 5, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 15.555...
  3. Subtract to cancel the repeating tail: 10x − x = 15 − 1, so 9x = 14.
  4. Solve: x = 14/9. The greatest common divisor is 1, so x = 14/9 (already in lowest terms).

Since 14 is larger than 9, it can also be written as the mixed number 1 5/9.

Check

Divide 14 by 9 on a calculator: 14 ÷ 9 = 1.5555555556… which matches 1.555….

Similar repeating decimals

DecimalFraction
1.1666…7/6
1.222…11/9
1.333…4/3
1.444…13/9
1.666…5/3
1.777…16/9
1.8333…11/6
1.888…17/9

See also: 14/9 as a mixed number.

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