1/11 as a decimal

How to convert this fraction

Divide 1 by 11 using integer long division. The whole-number part is 0; the remaining fraction is 1/11.

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

The remainder repeats, so the decimal repeats with 09 as the repeating cycle. The displayed value 0.090909090909 is rounded; the exact value remains 1/11.

Check: 0 × 11 + 1 = 1, so the quotient and remainder reconstruct the original fraction.