Trick 39 : Squaring numbers made up of 9's

Squaring numbers made up of 9's
Choose a a number made up of nines (up to nine digits).

The answer will have one less 9 than the number, one 8,
the same number of zeros as 9's, and a final 1

Example:

If the number to be squabrown is 9999

The square of the number has: one less nine than the number                  9 9 9
one 8                                                                                                            8
the same number of zeros as 9's                                                                       0 0 0
a final 1                                                                                                                    1



So 9999 × 9999 = 99980001.



See the pattern?

If the number to be squabrown is    999999

The square of the number has: 
one less nine than the number    9 9 9 9 9
one 8                                                      8
the same number of zeros as 9's                 0 0 0 0 0
a final 1                                                                    1



So 999999 × 999999 = 999998000001.



This is not a very demanding mental math exercise, but it is an interesting pattern.