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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

Among the 8-digit numbers: C tL L TTh Th H t O Example 1: Form the smallest number using the following digits:

27504545 < 51889620 < 53072249 < 86121450. 5 3 0 7 2 2 4 9 8-digit ( a) 4, 5, 6, 8, 3, 7 (b) 2, 5, 3, 0, 1, 9
5 1 8 8 9 6 2 0 8-digit
So, the ascending order of the numbers is: 8 6 1 2 1 4 5 0 8-digit Solution: (a) The smallest digit is 3.

983250 < 27504545 < 51889620 < 53072249 2 7 5 0 4 5 4 5 8-digit The other digits in ascending order are 4, 5, 6, 7 and 8.
< 86121450 9 8 3 2 5 0 6-digit So, the smallest number formed by the given digits is 345678.
( b) The smallest digit is 1 (other than 0). Be Aware
Example 5: Arrange the following numbers in descending order:
The other digits in ascending order are 0, 2, 3, 5 0 at the leftmost
83672906, 74635618, 83910257, 9876879, 74613898 and 9. place has no meaning.

Solution: Let us arrange the given numbers in the place value chart. So, the smallest number formed by the given digits is 102359.
Clearly, 83672906 and 83910257, both have C tL L TTh Th H t O To form the greatest number using the given digits, write the greatest digit at the leftmost
the same digits in the two leftmost places, 8 3 6 7 2 9 0 6 8-digit place and then write the other digits in their descending order.

i.e., 8 and 3, and the digits in the next place 7 4 6 3 5 6 1 8 8-digit Example 2: Form the greatest number using the following digits:
from the left (lakhs place) are 6 and 9. 8 3 9 1 0 2 5 7 8-digit ( a) 8, 5, 9, 6, 3, 2 (b) 4, 0, 3, 5, 6, 7
9 8 7 6 8 7 9 7-digit
9 > 6 7 4 6 1 3 8 9 8 8-digit Solution: ( a) Here, the greatest digit among the given digits is 9.

So, 83910257 > 83672906. The other digits in descending order are 8, 6, 5, 3 and 2.
So, the greatest number formed by the given digits is 986532.
Now, 74635618 and 74613898, both have the same digits in the three leftmost ( b) Here, the greatest digit among the given digits is 7.

places, i.e., 7, 4 and 6, and the digits in the next place from the left (ten
thousands place) are 3 and 1. The other digits in descending order are 6, 5, 4, 3 and 0.
So, the greatest number formed by the given digits is 765430.
3 > 1 with repetition of Digits
So, 74635618 > 74613898.
To form the smallest number, we repeat the smallest digit.
9876879 is a 7-digit number. Hence, it is the smallest number.
Example 3: Form the smallest 8-digit number using the digits 2, 3, 1, 4, 5 and 0.
So, the given numbers in descending order are: Solution: To form the smallest 8-digit number using the given digits, repeat the smallest

83910257 > 83672906 > 74635618 > 74613898 > 9876879 digit 0 thrice. Thus, the smallest 8-digit number formed using the given digits
is 10002345.
Think Tank Critical Thinking To form the greatest number, we repeat the greatest digit.

Write your mother's and father's date of birth in the form of ddmmyyyy and Example 4: Form the greatest 7-digit number using the digits 5, 1, 4, 3 and 2.
compare both the numbers thus formed.
Solution: To form the greatest 7-digit number using the given digits, repeat the greatest
digit 5 thrice. Thus, the greatest 7-digit number formed using the given digits
Forming numbers is 5554321.

without repetition of Digits Practice time 1c

Many numbers can be formed with given digits. We know the method of forming the

smallest and the greatest numbers using given digits. 1. Fill in the blanks using <, > or = .
( a) 805637 707656 (b) 2056953 206075
To form the smallest number using the given digits, write the smallest digit other than zero
(0) at the leftmost place and then write zero (0) if given, otherwise write the other digits ( c) 8670757 8670954 (d) 44524017 44324017
in their ascending order. ( e) 42003600 42003600 (f) 79000000 79999999

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