Reciprocal of 9901

Theorem

The reciprocal of $9901$ is:

$\dfrac 1 {9901} = 0 \cdotp \dot 00010 \, 09998 \, 9 \dot 9$


Proof

Performing the calculation using long division: 

     0.0001009998990001...
    --------------------------------------------
9901)1.0000000000000000...
       9901
       ----
         99000
         89109
         -----
          98910
          89109
          -----
           98010
           89109
           -----
            89010
            79208
            -----
             98020
             89109
             -----
               89110
               89109
               -----
                   10000
                    9901
                   -----
                    ....

$\blacksquare$

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