Surprising Number Patterns IV

Now the logical thing to inspect would be the pattern of these strange
products.
1 x 8 = 8
11 x 88 = 968
111 x 888 = 98568
1111 x 8888 = 9874568
11111 x 88888 = 987634568
111111 x 888888 = 98765234568
1111111 x 8888888 = 9876541234568
11111111 x 88888888 = 987654301234568
111111111 x 888888888 = 98765431901234568
1111111111 x 8888888888 = 987654321791234568

Here are some more charmers of mathematics that depend on the surprising
nature of its number system. Again, not many words are needed
to demonstrate the charm, for it is obvious at first sight. These depend
on the property described in Unit 1.4 and the unusual property of the
number 9.
999 999 x 1 = 0 999 999
999 999 x 2 = 1 999 998
999 999 x 3 = 2 999 997
999 999 x 4 = 3 999 996
999 999 x 5 = 4 999 995
999 999 x 6 = 5 999 994
999 999 x 7 = 6 999 993
999 999 x 8 = 7 999 992
999 999 x 9 = 8 999 991
999 999 x 10 = 9 999 990

Again, the number 9, which owes some of its unique properties to the fact
that it is 1 less than the base 10, presents some nice peculiarities.
9 x 9 = 81
99 x 99 = 9 801
999 x 999 = 998 001
9 999 x 9 999 = 99 980 001
99 999 x 99 999 = 9 999 800 001
999 999 x 999 999 = 999 998 000 001
9 999 999 x 9 999 999 = 99 999 980 000 001