0.6111… as a Fraction

0.6111… (0.61 repeating) as a fraction is 11/18.

How to convert 0.6111… to a fraction

  1. Let x = 0.6111... (the underlined part, 1, repeats forever).
  2. Move the decimal point past one full repeating block: 100x = 61.111...
  3. Move the decimal point past the non-repeating digits too: 10x = 6.1111...
  4. Subtract to cancel the repeating tail: 100x − 10x = 61 − 6, so 90x = 55.
  5. Solve: x = 55/90. The greatest common divisor is 5, so x = 11/18.

Check

Divide 11 by 18 on a calculator: 11 ÷ 18 = 0.6111111111… which matches 0.6111….

Similar repeating decimals

DecimalFraction
0.5888…53/90
0.595959…59/99
0.606060…20/33
0.615615615…205/333
0.616161…61/99
0.6222…28/45
0.626262…62/99
0.6333…19/30

See also: 11/18 as a decimal.

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