In examples on the formation of greatest and the smallest number we know that the procedure of arranging the numbers in ascending and descending order. The position of the digit at the extreme left of a number increases its place value. So the greatest digit should be placed at the extreme left side of the number to enhance its value.
Consider the following:
1. Form the greatest and the smallest number using the digits 6, 3, 8, 7, 1
We may say the procedure of forming the greatest number is as follows:
(a) The smallest digit is placed at one’s place.
(b) The next greater digit is placed at ten's place.
(c) The next greater digit is placed at hundred's place and so on.
(d) The greatest digit is placed at the highest place of the number.
The smallest number is formed by the following the reverse procedure.
(a) The greatest digit is placed at one's place.
(b) The next smaller digit at ten’s place and so on till all the given digits are finished.
(c) The smallest digit is placed at the highest place of the number.
2. Write the greatest and smallest number with the given 5 digits (2, 0, 5, 3, 9) without repeating any digit.
Solution:Tth Th H T O
(Whenever one of the given digits is 0, it is not written at the extreme left for the smallest number. It is written in the second place from the left)
Worked-out examples on the formation of greatest and the smallest numbers:
1. Write the greatest 4 digit number using the digit 7 5 2 8.
Using the same digits, write the smallest number.
To get the greatest number, we arrange the digits in descending order.
8 > 7 > 5 > 2. The greatest number using the digits 7 5 2 8 is 8752.
To get the smallest number, we arrange the digits in ascending order.
2 < 5 < 7 < 8. The smallest number using the digits 7 5 2 8 is 2578.
2. Write the greatest and smallest 5 digit number using the digits 9 0 1 5 4.
Descending order 9 > 5 > 4 > 1 > 0
The greatest number formed is 95410.
Ascending order 0 < 1 < 5 < 5 < 9.
A number cannot begin with 0, so we will put it in the second place.
The smallest digit (other than 0) is 1.
The number will begin with 1.
The smallest number formed is 10459.
3. Write the smallest 5 digit number using the following digits, (digits may be repeated). 2 1 3 7
Arrange in ascending order. 1 < 2 < 3 < 7
Since we have to make the smallest 5 digit number using 4 given digits, we will repeat the smallest digit 1
The smallest 5 digit number is 11237.
4. Write the greatest 5 digit number using 1 2 5. The digit may be repeated.
Arrange in descending order. 5 > 2 > 1
Since we have to make the greatest 5 digit number using 3 digits, we will repeat the greatest digit required number of times.
The greatest 5 digit number is 55521.