Reciprocal of 81

Theorem
The decimal expansion of the reciprocal of $81$ has a particularly interesting pattern:
 * $\dfrac 1 {81} = 0 \cdotp \dot 01234 \, 567 \dot 9$

Proof
Performing the calculation using long division:

0.0123456790... 81)1.0000000000000    81     --     190     162     ---      280      243      ---       370       324       ---        460        405        ---         550         486         ---          640          567           --           730           729           ---             100              81             ---             ...

Also see

 * Reciprocal of Square of 1 Less than Number Base