Reciprocal of 11

Theorem

The decimal expansion of the reciprocal of $11$ is as follows:

$\dfrac 1 {11} = 0 \cdotp \dot 0 \dot 9$

This sequence is A010680 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof

Performing the calculation using long division: 

   0.0909...
  ------------
11)1.000000000
     99
   ----
      100
       99
      ---
      ...

$\blacksquare$

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