Reciprocal of 103

Theorem

The decimal expansion of the reciprocal of $103$ is as follows:

$\dfrac 1 {103} = 0 \cdotp \dot 00970 \, 87378 \, 64077 \, 66990 \, 29126 \, 21359 \, 223 \dot 3$

This sequence is A021107 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Proof

Performing the calculation using long division:

    0.0097087378640776699029126213592233009...
  --------------------------------------------
103)1.0000000000000000000000000000000000000...
      927     618     927     103    309
      ---     ---     ---     ---    ---
       730     420      300    370     1000
       721     412      206    309      927
       ---     ---      ---    ---     ----
         900     800     940    610    ....
         824     721     927    515
         ---     ---     ---    ---
          760     790     130    950
          721     721     103    927
          ---     ---     ---    ---
           390     690     270    230
           309     618     206    206
           ---     ---     ---    ---
            810     720     640    240
            721     618     618    206
            ---     ---     ---    ---
             890    1020     220    340
             824     927     206    309
             ---    ----     ---    ---
              660     930     140    310
              618     927     103    309

$\blacksquare$