Question

Now make the greatest and the smallest 4-digit number by using any one digit twice. The given digits are 3, 8, 7.

Answer 1

Hint: Now we have 3 digits and we can only repeat 1 digit among those 3 to create a number. Hence to create the largest number we will repeat the largest digit and arrange the digits in descending order. Similarly when we are creating the smallest number we will repeat the smallest digit and arrange the digits in ascending order.

Complete step-by-step answer:
Now let us first learn how to compare numbers. We first start by counting the number of digits.
The number with the highest number of digits is the greater one.
Now if in this step we get the number of digits is the same then we compare the first digit from the left.
Hence the number with greater digit on the left is the greater one.
Now again if in this step we get that the first digits from the left in both numbers are the same then we check the second digit from the left and so on.
For example consider the number 789 and 778.
Here the number of digits of both numbers are 3.
Now if we check the first digit from the left in 789 we get 7.
Similarly the first digit from the left im 778 is 7.
Hence we get the first digit from the left in both numbers is the same.
Now we will check the second digit from left
For number 789 we get the second digit from the left is 8 and similarly in 778 it is 7.
Now we know that 8 > 7. Hence we have 789 > 778.
Hence we know that the leftmost digit must be greater to be the largest number.
Now the given digits are 3, 8, 7.
We want to create the largest 4 digit number here the largest digit is 8 hence 8 will be repeated.
Now we have 3, 8, 7, 8.
We will place the digits in descending order to create the largest number.
Hence the largest number is 8873.
Now again consider the three digits. 3, 8, 7
Here the smallest digit is 3. Hence to create the smallest number we will repeat 3.
Now we have 4 digits 3, 3, 8, 7
Now we will arrange the digits in ascending order to create the smallest number
Hence the smallest number is 3378.

Note: Note that while creating the largest number we place all the digits in descending order and if we want to create the smallest number we place the digits in ascending order. It is not just to take care about the leftmost term the order is also equally important.