2.1666… as a Fraction

2.1666… (2.16 repeating) as a fraction is 13/6. As a mixed number that is 2 1/6.

How to convert 2.1666… to a fraction

  1. Let x = 2.1666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 216.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 21.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 216 − 21, so 90x = 195.
  5. Solve: x = 195/90. The greatest common divisor is 15, so x = 13/6.

Since 13 is larger than 6, it can also be written as the mixed number 2 1/6.

Check

Divide 13 by 6 on a calculator: 13 ÷ 6 = 2.1666666667… which matches 2.1666….

Similar repeating decimals

DecimalFraction
1.777…16/9
1.8333…11/6
1.888…17/9
2.111…19/9
2.222…20/9
2.333…7/3
2.444…22/9
2.5333…38/15

See also: 13/6 as a mixed number.

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