1.1666… as a Fraction

1.1666… (1.16 repeating) as a fraction is 7/6. As a mixed number that is 1 1/6.

How to convert 1.1666… to a fraction

  1. Let x = 1.1666... (the underlined part, 6, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 116.666...
  3. Move the decimal point past the non-repeating digits too: 10x = 11.6666...
  4. Subtract to cancel the repeating tail: 100x − 10x = 116 − 11, so 90x = 105.
  5. Solve: x = 105/90. The greatest common divisor is 15, so x = 7/6.

Since 7 is larger than 6, it can also be written as the mixed number 1 1/6.

Check

Divide 7 by 6 on a calculator: 7 ÷ 6 = 1.1666666667… which matches 1.1666….

Similar repeating decimals

DecimalFraction
0.969696…32/33
0.9777…44/45
0.979797…97/99
0.9888…89/90
0.989898…98/99
1.111…10/9
1.222…11/9
1.333…4/3

See also: 7/6 as a mixed number.

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