Reciprocal of 13

Theorem
The decimal expansion of the reciprocal of $13$ is as follows:
 * $\dfrac 1 {13} = 0 \cdotp \dot 07692 \dot 3 \ldots$

Proof
Performing the calculation using long division:

0.07692307... - 13)1.00000000...     91                  90      78      --      120      117      ---        30        26        --         40         39         --          100           91          ---          ...