Question

Find the smallest 7-digit number.
(a) 10,00,000
(b) 1 + greatest 6-digit number
(c) Either a or b
(d) None of these

Answer 1

Hint: The smallest n-digit number will be of the form ${{10}^{n-1}}$ .The greatest n-digit number will be of the form ${{10}^{n}}-1$ . The smallest n-digit number and the largest (n-1)-digit number are consecutive numbers.

Complete step-by-step solution -
We have to find the smallest 7-digit number. We know that the smallest 1-digit number is 1 and the smallest 2-digit number is 10. Similarly, the smallest 3-digit number is 100 and the smallest 4-digit number is 1000.
This suggests to us that the smallest n-digit number will be of the form ${{10}^{n-1}}$ .
Hence, for n = 7, the smallest 7-digit number will be ${{10}^{7-1}}={{10}^{6}}=10,00,000$ .
We know that the largest 1-digit number is 9. 1 + 9 = 10, which is the smallest 2-digit number.
Similarly, the largest 2-digit number is 99, and 1 + 99 = 100, which is the smallest 3-digit number.
The largest 3-digit number is 999, and 1 + 999 = 1000, which is the smallest 4-digit number.
Thus, we observe that 1 + largest n-digit number = smallest (n+1) - digit number.
Hence, 1 + largest 6-digit number = smallest 7-digit number.
Thus, the correct option is option (c).

Note: Students in a hurry, may often see only the first option and mark it as the correct one, forgetting to see that the other options may also be valid. Thus, they may mark only option (a). Hence, students should always check all the options before submitting the final solution as other options may also be correct.