3/11 as a decimal

How to convert this fraction

Divide 3 by 11 using integer long division. The whole-number part is 0; the remaining fraction is 3/11.

1. Bring down a zero: remainder × 10 gives the next decimal digit 2; the new remainder is 8.
2. Bring down a zero: remainder × 10 gives the next decimal digit 7; the new remainder is 3.

The remainder repeats, so the decimal repeats with 27 as the repeating cycle. The displayed value 0.272727272727 is rounded; the exact value remains 3/11.

Check: 0 × 11 + 3 = 3, so the quotient and remainder reconstruct the original fraction.