Reciprocal of 909,091

Theorem

The reciprocal of $909 \, 091$ is:

$\dfrac 1 {909 \, 091} = 0 \cdotp \dot 00000 \, 10999 \, 998 \dot 9$

Proof

Performing the calculation using long division:

       0.00000109999989000001...
      --------------------------------------------
909091)1.00000000000000000000...
         909091
         ------
          9090900
          8181819
          -------
           9090810
           8181819
           -------
            9089910
            8181819
            -------
             9080910
             8181819
             -------
              8990910
              8181819
              -------
               8090910
               7272728
               -------
                8181820
                8181819
                -------
                      1000000
                       909091
                      -------
                       ......

$\blacksquare$