Formation of Numbers
with the Given Digits
In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits. Let us observe some of the formation of numbers without the repetition of digits.
Some 2-digit numbers formed by given digits are shown below:
(i) with digits 2 and 3 the formed numbers are 23, 32
(ii) with digits 4 and 7 we may form the numbers 47, 74
(iii) with digits 5 and 9 we may form the numbers 59, 95
But with the digit 0 and the digit 6, only the number 60 is formed. The number 06 is not a two-digit number.
Accordingly, 3-digit numbers are also formed.
Look at the numbers 123, 231 and 312.
Which digits are used here?
The digits used here are 1, 2 and 3.
Try making more 3-digit numbers using these digits and write on the blanks.
123, 231, 312, ___, ___, ___
Some numbers formed by 3 digits are given below:
(a) The numbers by 2, 3, and 4 are:
234, 243, 324, 342, 423, 432 (6 numbers each of 3 digits)
(b) The numbers by 4, 6 and 9 are:
469, 496, 649, 694, 946, 964 (6 numbers each of 3 digits)
(c) The numbers by 3, 7 and 8 are:
378, 387, 738, 783, 837, 873 (6 numbers each of 3 digits)
(d) The numbers by 0, 1 and 5 are
105, 150, 501, 510 (only 4 numbers of 3 digits)
Some numbers formed by 4 digits are given below:
(a) The numbers formed by 1, 2, 3 and 4 are:
1234, 1243, 1324, 1342, 1423, 1432
2134, 2143, 2314, 2341, 2413, 2431
3124, 3142, 3421, 3412, 3214, 3241
4123, 4132, 4213, 4231, 4312, 4321
(b) Similarly, other 4-digit numbers may be formed.
We observe that, when the numbers of digits are increased, more and more
numbers are formed. We are familiar with the formation of numbers with 2
or 3 digits. We should know the procedure of forming the greatest and
smallest numbers having definite digits.
Making the Greatest Number with the given Digits:
To make the greatest number, we start from left and write the greatest digit first. Then, we write the greatest of the remaining digits and so on.
For example:
• the greatest number made using the digits 3, 6 and 8 will be 863.
• the greatest number made using the digits 7, 0 and 9 will be 970.
Note: We can also say that to make the greatest number, we write the given digits in descending order.
Making the Smallest Number with the given Digits:
To make the smallest number, we start from left and write the smallest digit first. Then we write the smallest of the remaining digits and so on.
For example:
• the smallest number made using the digits 3, 6 and 8 will be 368.
• the smallest number made using the digits 4, 1 and 9 will be 149.
Note: We can also say that to make the smallest number, we write the given digits in ascending order.
Examples on Formation of Numbers with the Given Digits:
1. How many 3 digit numbers can be formed by using the digits 0, 3 and 7 without repeating any digit.
Solution:
Placing 0 at one's place, we can have two natural numbers 730 and 370.
While placing 0 at tens place we can have two natural numbers 307 and 703.
Zero cannot be placed at hundreds place. Hence, the numbers are 370, 730, 307 and 703.
2. The greatest 6-digit number formed by using the digits 9, 7, 0, 5 (where two of the four digits are allowed to repeat twice only) is
(a) 779950
(b) 999750
(c) 997750
(d) 997500
Answer: (c) 997750
3. Form the greatest 9-digit number having six different digits is __________.
(a) 999998656
(b) 999999999
(c) 998877663
(d) 999987654
Answer: (d) 999987654
4. Without repeating any digit, write the smallest and largest possible 4-digit numbers having 6 in tens place.
Answer:
Smallest possible 4-digit numbers having 6 in tens place is 1062
Largest possible 4-digit numbers having 6 in tens place is 9867
Worksheet on Formation of Numbers with the Given Digits:
1. Write all the 3-digit numbers that can be made using the given digits once.
(i) 4, 5, 6: ___, ___, ___, ___, ___, ___
(ii) 3, 4, 2: ___, ___, ___, ___, ___, ___
(iii) 8, 9, 1: ___, ___, ___, ___, ___, ___
(iv) 4, 5, 7: ___, ___, ___, ___, ___, ___
(v) 6, 9, 4: ___, ___, ___, ___, ___, ___
2. Write the greatest and the smallest 3-digit numbers using the given digits once.
Note: The smallest number made using the digits 6, 0 and 8 will be 608 and not 068 because we cannot start a number with 0.
|
Greatest Smallest |
Number Number | |
|
(i) 2, 9, 1 |
_____ |
_____ |
|
(ii) 4, 8, 3 |
_____ |
_____ |
|
(iii) 7, 6, 8 |
_____ |
_____ |
|
(iv) 5, 2, 3 |
_____ |
_____ |
|
(v) 4, 2, 7 |
_____ |
_____ |
|
(vi) 9, 0, 2 |
_____ |
_____ |
|
(vii) 8, 1, 6 |
_____ |
_____ |
|
(viii) 4, 9, 1 |
_____ |
_____ |
|
(ix) 8, 0, 2 |
_____ |
_____ |
|
(x) 9, 1, 3 |
_____ |
_____ |
|
(xi) 5, 8, 0 |
_____ |
_____ |
Answer:
2. (i) Greatest Number: 921
Smallest Number: 129
(ii) Greatest Number: 843
Smallest Number: 348
(iii) Greatest Number: 876
Smallest Number: 678
(iv) Greatest Number: 532
Smallest Number: 235
(v) Greatest Number: 247
Smallest Number: 742
(vi) Greatest Number: 920
Smallest Number: 209
(vii) Greatest Number: 861
Smallest Number: 168
(viii) Greatest Number: 941
Smallest Number: 149
(ix) Greatest Number: 820
Smallest Number: 208
(x) Greatest Number: 931
Smallest Number: 139
(xi) Greatest Number: 850
Smallest Number: 508
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● Numbers Showing on Spike Abacus.
● 1 Digit Number on Spike Abacus.
● 2 Digits Number on Spike Abacus.
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● 5 Digits Number on Spike Abacus.
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● Formation of Numbers with the Given Digits.
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