Reciprocal of 3

Theorem

The decimal expansion of the reciprocal of $3$ is as follows:

$\dfrac 1 3 = 0 \cdotp \dot 3$

This sequence is A010701 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof

Performing the calculation using long division: 

   0.33...
  --------
 3)1.00...
     9
   ---
     10
      9
     --
     ..

$\blacksquare$

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