9/11 as a decimal

How to convert this fraction

Divide 9 by 11 using integer long division. The whole-number part is 0; the remaining fraction is 9/11.

1. Bring down a zero: remainder × 10 gives the next decimal digit 8; the new remainder is 2.
2. Bring down a zero: remainder × 10 gives the next decimal digit 1; the new remainder is 9.

The remainder repeats, so the decimal repeats with 81 as the repeating cycle. The displayed value 0.818181818182 is rounded; the exact value remains 9/11.

Check: 0 × 11 + 9 = 9, so the quotient and remainder reconstruct the original fraction.