Reciprocal of 79

Theorem

The decimal expansion of the reciprocal of $79$ is as follows:

$\dfrac 1 {79} = 0 \cdotp \dot 01265 \, 82278 \, 48 \dot 1$

This sequence is A021083 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

   0.012658227848101...
  ---------------------
79)1.000000000000000...
     79
   ----
     210    670
     158    632
     ---    ---
      520    380
      474    316
      ---    ---
       460    640
       395    632
       ---    ---
        650     80
        632     79
        ---     --
         180     100
         158      79
         ---     ---
          220    ...
          158
          ---
           620
           553
           ---
            670

$\blacksquare$