Reciprocal of 101

Theorem

The decimal expansion of the reciprocal of $101$ is as follows:

$\dfrac 1 {101} = 0 \cdotp \dot 009 \dot 9$

This sequence is A021105 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

    0.00990099...
   --------------
101)1.00000000...
      909
      ---
       910
       909
       ---
         1000
          909
         ----
           910
           909
           ---
           ...

$\blacksquare$