Long Period Prime/Examples/19

Theorem
The decimal expansion of the reciprocal of $19$ has the maximum period, that is: $18$:
 * $\dfrac 1 {19} = 0 \cdotp \dot 05263 \, 15789 \, 47368 \, 42 \dot 1$

Proof
Performing the calculation using long division:

0.05263157894736842105... 19)1.00000000000000000000000    95     --      50      38     ---      120      114      ---        60        57        --         30         19         --         110          95          --          150          133           --           170           152           ---            180            171             --              90              76              --              140              133               --                70                57                --                130                114                ---                 160                 152                  --                   80                   76                   --                    40                    38                    --                     20                     19                     --                      100                       95                       --                       ....