Reciprocal of 99,990,001

Theorem
The reciprocal of $99 \, 990 \, 001$ is:
 * $\dfrac 1 {99 \, 990 \, 001} = 0 \cdotp \dot 00000 \, 00100 \, 00999 \, 99998 \, 999 \dot 9$

Proof
Performing the calculation using long division:

0.00000001000099999998999900000001... 99990001)1.00000000000000000000000000000000...          99990001               999900000               899910009               -                999899910                899910009                -                 999899010                 899910009                 -                  999890010                  899910009                  -                   999800010                   899910009                   -                    998900010                    899910009                    -                     989900010                     899910009                     -                      899900010                      799920008                      -                       999800020                       899910009                       -                        998900110                        899910009                        -                         988801010                         899910009                         -                          899910010                          899910009                          -                                  100000000                                   99990001                                  -                                   ........