Question

The smallest 7-digit number is
(A) 1000000
(B) 1 + greatest 6-digit number
(C) Both A and B
(D) 999999

Answer 1

Hint: We know that every number is composed of numbers from 0 to 9 and zero is the smallest number among the numbers from 0 to 9. For the smallest number of 7-digit, every digit should be equal to zero except the \[{{7}^{th}}\] digit. The \[{{7}^{th}}\] digit should be equal to 1. But the seventh digit of the 7-digit number should not be equal to zero because if the seventh digit is zero then the number will not be a 7-digit number. Now, get the smallest 7-digit number. Also, use that the greatest 6-digit number is 999999.

Complete step by step answer:
According to the question, we are asked to find out the smallest 7-digit number.
We know that every number is composed of numbers from 0 to 9 and zero is the smallest number among the numbers from 0 to 9.
Here, we can think of a logic. Since we are asked to find the smallest 7-digit number, the unit place of the 7-digit number should be equal to zero.
Similarly, using the same logic we can say that the tenth place, hundredth place up to the sixth digit of the 7-digit number should be equal to zero …………………………………………(1)
But the seventh digit of the 7-digit number should not be equal to zero because if the seventh digit is zero then the number will not be a 7-digit number. Other than 0, the smallest number from 0 to 9 is 1.
So, the seventh digit of the 7-digit number should be equal to 1 ………………………………………(2)
Now, from equation (1) and equation (2), we get
The smallest 7-digit number = 1000000 …………………………………………….(3)
Now, on modifying equation (3), we get
The smallest 7-digit number = \[1000000=1+999999\] ……………………………………(4)
We also know that every digit of greatest 6-digit number is equal to 9 i.e., 999999 ……………………………………………..(5)
Now, from equation (4) and equation (5), we get
The smallest 7-digit number = 1+ greatest 6-digit number ………………………………….(5)
Now, from equation (3) and equation (5), we have
The smallest 7-digit number = 1000000 = 1 + greatest 6-digit number.
Hence, the correct option is (C).

Note:
For this type of question use the logic that every digit of n-digit number must be equal to zero except the \[{{n}^{th}}\] digit. The \[{{n}^{th}}\] digit of the n-digit number should be equal to 1. We can also use the formula, the smallest number of n-digit = 1 + greatest number of (n-1) digit numbers.