1.666… as a Fraction

1.666… (1.6 repeating) as a fraction is 5/3. As a mixed number that is 1 2/3.

How to convert 1.666… to a fraction

  1. Let x = 1.666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 10x = 16.666...
  3. Subtract to cancel the repeating tail: 10x − x = 16 − 1, so 9x = 15.
  4. Solve: x = 15/9. The greatest common divisor is 3, so x = 5/3.

Since 5 is larger than 3, it can also be written as the mixed number 1 2/3.

Check

Divide 5 by 3 on a calculator: 5 ÷ 3 = 1.6666666667… which matches 1.666….

Similar repeating decimals

DecimalFraction
1.222…11/9
1.333…4/3
1.444…13/9
1.555…14/9
1.777…16/9
1.8333…11/6
1.888…17/9
2.111…19/9

See also: 5/3 as a mixed number.

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