(i) Greatest number of three digits = 999
and Smallest number of five digits = 10000
Required product = 999 x 10000 = 9990000
(ii) Greatest number of four digits = 9999
and Greatest number of three digits = 999
Required product = 9999 x 999
= 9999 x (1000 – 1)
= 9999 x 1000 – 9999 x 1 (using distributivity)
= (10000- 1) x 1000 – (10000- 1) x 1
= 10000 x 1000 – 1 x 1000 – 10000 + 1
= 10000000 – 1000 – 10000 + 1
= 10000001 – 11000
= 9989001