Question

Sum of the greatest 8-digit number and the smallest 9-digit number is
A. 19999999
B. 199999999
C. 999999999
D. 10000999

Answer 1

Hint: The greatest n digit number is obtained by placing n number of 9’s. Similarly, the smallest n digital number is obtained by placing one as the leftmost digit and other n-1 digits as 0.

“Complete step-by-step answer:”
In the problem we have to find the sum of the greatest 8-digit number and the smallest 9-digit number.
First, we need to find the greatest 8- digit number.
The number has maximum value when the individual digits on each place have the maximum value. Therefore, the greatest n digit number is obtained by placing n numbers of 9’s.
By using the above rule, the greatest 8-digit number is 99999999.
Similarly, we have to obtain the smallest 9-digit number.
The number has the minimum value when the individual digits on each place have the minimum value. But the leftmost or the first digit in the number has to be 1 for the number to be a valid n number digit.
Therefore, the smallest n digital number is obtained by placing one as the leftmost digit and other n-1 digits as 0.
By using the above rule, the smallest 9-digit number is 100000000.
Now we have obtained the greatest 8-digit number and the smallest 9-digit number, so we can find their sum.
Sum of the greatest 8-digit number and the smallest 9-digit number $ = 99999999 + 100000000 = 199999999$
Hence the correct option is (B). 199999999.

Note: The greatest and the smallest n digit number is to be obtained by using the above-mentioned rules. The above rules are valid for decimal number systems and may be modified for other number systems. The place value of the digits is needed to be kept in mind in problems like above.