10/11 as a decimal

How to convert this fraction

Divide 10 by 11 using integer long division. The whole-number part is 0; the remaining fraction is 10/11.

1. Bring down a zero: remainder × 10 gives the next decimal digit 9; the new remainder is 1.
2. Bring down a zero: remainder × 10 gives the next decimal digit 0; the new remainder is 10.

The remainder repeats, so the decimal repeats with 90 as the repeating cycle. The displayed value 0.909090909091 is rounded; the exact value remains 10/11.

Check: 0 × 11 + 10 = 10, so the quotient and remainder reconstruct the original fraction.