Reciprocal of 1089

Theorem
The reciprocal of $1089$ is:
 * $\dfrac 1 {1089} = 0 \cdotp \dot 00091 \, 82736 \, 45546 \, 37281 \, 9 \dot 1$

Note that it consists mainly of the unit multiples of $9$ from $1$ to $9$ concatenated.

Proof
Performing the calculation using long division:

0.00091827364554637281910009... 1089)1.00000000000000000000000000...      9801    5445    1089        1990    5950    9910        1089    5445    9801         9010    5050    1090         8712    4356    1089          2980    6940      10000          2178    6534       9801           8020    4060      ....           7623    3267            3970    7930            3267    7623             7030    3070             6534    2178              4960    8920              4356    8712               6040    2080               5445    1089