Squaring numbers made up of 9s

1. Choose a a number made up of nines (up to nine digits).
2. 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:

1. If the number to be squared is 9999
2. 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
3. So 9999 × 9999 = 99980001.