Reciprocal of 9091

Theorem
The reciprocal of $9091$ is:
 * $\dfrac 1 {9091} = 0 \cdotp \dot 00010 \, 9998 \dot 9$

Proof
Performing the calculation using long division:

0.00010999890001... 9091)1.00000000000000...      9091        90900        81819        -         90810         81819         -          89910          81819          -           80910           72728           -            81820            81819            -                10000                 9091                -                  ...