Reciprocal of 73

Theorem

The decimal expansion of the reciprocal of $73$ is as follows:

$\dfrac 1 {73} = 0 \cdotp \dot 01369 \, 86 \dot 3$

This sequence is A021077 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Proof

Performing the calculation using long division: 

   0.0136986301...
  -------------
73)1.0000000000...
     73
   ----
     270
     219
     ---
      510
      438
      ---
       720
       657
       ---
        630
        584
        ---
         460
         438
         ---
          220
          219
          ---
            100
             73
            ---
            ...

$\blacksquare$

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