Question

Write the smallest and the largest six-digit numbers. How many numbers are between these two values?

Answer 1

Hint: We need to find the smallest and largest six-digit number and the difference between them. We will start by writing the smallest and largest 6-digit number. As we know that 0 is the smallest digit but 0 cannot be used in the highest place value. So, we will go to the second smallest digit that is 1. From this, we will form the smallest 6-digit number. Now, we will find the largest 6-digit number, as we know that 9 is the largest digit which can be used in any place. With this, we will find the 6-digit number and we can determine the number lies between these two values by subtracting the highest from the lowest.

Complete step-by-step answer:
The aim is to find the smallest and largest 6-digit number and after that, we need to find how many numbers are between these two values.
We will start by finding the smallest 6-digit number.
As we know that 0 is the smallest digit which can not be used in the highest place value so, we will consider the next smallest digit that is 1 and 1 can be used in the highest place value.
Thus, we can form the required 6-digit smallest number with 0 and 1.
Hence, the smallest 6-digit number is 100000.
Now, we will find the largest 6-digit number.
As we know that the largest digit is 9 which can be used in any place. So, we will form the largest 6-digit number with digit 9.
Thus, the largest 6-digit number is 999999.
Next, we need to find how many numbers lie between these two values.
So, we can determine how many numbers lie between the smallest 6-digit number and the largest 6-digit number by subtracting the smallest from the largest.
Thus, we get,
\[ \Rightarrow 999999 - 100000 = 899999\]
Hence, 899999 numbers are there between the smallest 6-digit number and the largest 6-digit number.
Therefore, the smallest 6-digit number is 100000, the largest 6-digit number is 999999 and 899999 numbers lie between these two numbers.

Note: We know that there are a total 10 digits which can be used to form any number, so, to form the smallest number we need to use smallest digits 0 and 1 and to form the largest number we need to use the largest digit 9. 0 can never be used in the highest place value as the result will be 0 only so, we always choose 1 on the highest place and 9 for the largest number on the highest place.