Reciprocal of 11

Theorem
The decimal expansion of the reciprocal of $11$ is as follows:
 * $\dfrac 1 {11} = 0 \cdotp \dot 0 \dot 9$

and hence has a period of $2$.

Proof
Performing the calculation using long division:

0.0909... 11)1.000000000    99      100       99      ---      ...