Reciprocal of 909,091

Theorem
The reciprocal of $909 \, 091$ is:
 * $\dfrac 1 {909 \, 091} = 0 \cdotp \dot 00000 \, 10999 \, 998 \dot 9$

Proof
Performing the calculation using long division:

0.00000109999989000001... 909091)1.00000000000000000000...        909091         --          9090900          8181819          ---           9090810           8181819           ---            9089910            8181819            ---             9080910             8181819             ---              8990910              8181819              ---               8090910               7272728               ---                8181820                8181819                ---                      1000000                       909091                      ---                       ......