ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 1 Knowing Our Numbers Ex 1.2
Question 1.
Use the appropriate symbol < or > to fill in the blanks:
(i) 173 … 189
(ii) 1058 … 1074
(iii) 8315 … 8037
Solution:
(i) 173 
189
(ii) 1058 1074
(iii) 8315 
8037
Question 2.
In each of the following pairs of numbers, state which number is smaller:
(i) 553,503
(ii) 41338,1139
(iii) 25431,24531
Solution:
(i) 503 number is smaller.
(ii) 1139 number is smaller.
(iii) 24531 number is smaller.
Question 3.
Find the greatest and the smallest numbers in each row:
(i) 71834, 75284, 571, 2333, 594
(ii) 9853, 7691, 9999, 12002.
Solution:
(i) 571 is the smallest number and
75284 is the greatest number.
(ii) 7691 is the smallest number and
12002 is the greatest number.
Question 4.
Arrange the following numbers in ascending order:
304, 340, 34, 43, 430
Solution:
Arranging the following numbers in Ascending order.
34, 43, 304, 340,430
Question 5.
Arrange the following numbers in descending order:
53, 7333, 553, 7529, 335.
Solution:
Arranging the following numbers in Descending order:
7529, 7333, 553, 335, 53
Question 6.
Write all possible 2-digits numbers that can be formed by using the digits 2, 3 and 4. Repetition of digits is not allowed. Also find their sum.
Solution:
The given digits are 2,3,4 and repetition of digits is not allowed.
Out of the given digits, the possible ways of choosing the two digits are
2, 3; 2, 4; 3, 4
Using the digits 2 and 3, the numbers are 23 and 32
Similarily, Using the digits 2 and 4, the numbers are 24 and 42
Using the digits 3 and 4, the numbers are 34 and 43
Hence, all possible 2-digit numbers are 23, 32, 24, 42, 34, 43
∴ Sum of above numbers
= 23 + 34 + 32 + 24 + 43 + 42 = 198.
Question 7.
Write all possible 3-digits numbers using the digits 3, 1 and 5. Repetition of digits is not allowed.
Solution:
We are required to write 3-digit numbers using the digits 1, 3, 5 and the repetition of the digits is not allowed.
Keeping 1 at unit’s place, 3-digit number obtained are 351 and 531.
Keeping 3 at unit’s place, 3-digit number obtained are 153 and 513.
Keeping 5 at unit’s place, 3-digit number obtained are 315 and 135.
Hence, all possible 3-digit numbers are : 315, 351, 153, 135, 531, 513
Question 8.
Write all possible 3-digits numbers using the digits 7, 0 and 6. Repetition of digits is not allowed. Also, find their sum.
Solution:
We are required to write 3-digit numbers using the digits 0, 6, 7 and the repetition of the digits is not allowed.
Keeping 0 at unit’s place, 3-digit number obtained are 670 and 760.
Keeping 6 at unit’s place, 3-digit number obtained are 706.
Keeping 7 at unit’s place, 3-digit number obtained are 607.
Hence, all possible 3-digit numbers are : 670, 760, 607, 706.
∴ Sum of above numbers
= 670 + 760 + 607 + 706 = 2743
Question 9.
Write all possible 2-digit numbers using the digits 4, 0 and 9. Repetition of digits is not allowed. Also find their sum.
Solution:
The given digits are 0,4, 9 and repetition of digits is not allowed.
Out of the given digits, the possible ways of choosing the two digits are
4, 0; 4, 9; 9, 0
Using the digits 4 and 0, the number are 40.
Similarily, Using the digits 4 and 9, the numbers are 49 and 94.
Using the digits 9Hence, all possible 2-digit numbers are 40, 49, 90, 94
∴ Sum of above numbers = 40 + 49 + 90 + 94 = 273
Question 10.
Write all possible 2-digit numbers that can be formed by using the digit 3, 7 and 9. Repetition of digits is allowed.
Solution:
The given digits are 3, 7, 9 and repetition of digits is not allowed.
Out of the given digits, the possible ways of choosing the two digits are
3, 7; 3, 9; 7, 9
Using the digits 3 and 7, the numbers are
37, 73, 33 and 77.
Similarity, Using the digits 3 and 9, the numbers are 39, 93, and 99.
Using the digits 7 and 9, the numbers are 79 and 97.
Hence, all possible 2-digit numbers are
37, 73, 33, 77, 39, 93, 99, 79, 97
Question 11.
Write all possible numbers using the digits 3,1 and 5. Repetition of digits is not allowed.
Solution:
The given digits are 1, 3, 5 and repetition of digits is not allowed.
The one- digit numbers that can be formed are 1, 3 and 5.
We are required to write 2-digit numbers.
Out of the given digits, the possible ways of choosing the two digits are
1, 3; 1, 5; 3, 5
Using the digits 1 and 3, the numbers are 13 and 31.
Similarity, Using the digits 1 and 5, the numbers are 15 and 51.
Using the digits 3 and 5, the numbers are 35 and 53.
Hence, all possible 2-digit numbers are
13, 31, 15.51, 35, 53
Now, We are required to write 3-digit numbers using the digits 1, 3, 5 and the
repetition of the digits is not allowed. Keeping 1 at unit’s place, 3-digit number obtained are 351 and 531.
Keeping 3 at unit’s place, 3-digit number obtained are 153 and 513.
Keeping 5 at unit’s place, 3-digit number obtained are 315 and 135.
Hence, all possible 3-digit numbers are : 315, 351, 153, 135, 531, 513
All possible numbers using the digits 3, 1 and 5 are :
1, 3, 5, 31, 13, 35, 53, 15, 51, 315, 153, 351, 531, 513, 135.
Question 12.
How many 6-digit numbers are there in all ?
Solution:
The greatest 6-digit numbers = 999999
The greatest 5-digit numbers = 99999 The total number of 6-digit numbers
= 999999 – 99999 = 900000
Question 13.
Write down the greatest number and the smallest number of 4-digits that can be formed by the digits 7, 5,0 and 4 using each digit only once.
Solution:
We are required to write 4-digit numbers using the digits 7, 5, 0, 4 and the repetition of the digits is not allowed.
Keeping 0 at unit’s place, 4-digit number obtained are 4570,4750, 5470, 5740, 7450, and 7540.
Keeping 4 at unit’s place, 4-digit number obtained are 5074, 5704, 7054 and 7504. Keeping 5 at unit’s place, 4-digit number obtained are
Keeping 7 at unit’s place, 4-digit number obtained are 4057, 4507, 5047 and 5407.
Hence, all possible 4-digit numbers are : 4570, 4750, 5470, 5740, 7450, 7540, 5074, 5704, 7054, 7504, 4075, 4705, 7045, 7405, 4057, 4507, 5047, 5407
Hence, The Greatest number = 7540 and The smallest number = 4057
Question 14.
Rearrange the digits of the number 5701024 to get the largest number and the smallest number of 7 digits.
Solution:
Largest number =7542100
[Method used : Firstly, write largest to smallest number in descending order.] Smallest number = 1002457.
[Method used : Firstly, write smallest to largest number in ascending order. (Start from 1 then 0 then next digits)]
Question 15.
Keeping the place value of digit 3 in the number 730265 same, rearrange the digits of the given number to get the largest number and smallest number of 6 digits.
Solution:
Keeping the same place value of digit 3 in the number 730265 and rearranging the digits of the given number,
Greatest number of 6 digits = 736520 Smallest number of 6 digits = 230567
Question 16.
Form the smallest and greatest 4-digit numbers by using any one digit twice from the digits:
(i) 5, 2, 3, 9
(ii) 6, 0, 1, 4
(iii) 4, 6, 1, 5, 8.
Solution:
(i) The smallest 4-digit numbers = 2235
and the greatest 4-digit numbers = 9935
(ii) The smallest 4-digit numbers = 1004
The greatest 4-digit numbers = 6641
(iii) The smallest 4-digit numbers =1145
The greatest 4-digit numbers = 8865
Question 17.
Write
(i) the greatest number of 6 digits
(ii) the smallest number of 7 digits. Also find their difference.
Solution:
(i) Greatest 6 digit number = 999999
(ii) Smallest 7 digit number =1000000
Question 18.
Write the greatest 4-digit number of distinct digits.
Solution:
Greatest 4-digit number of four different digit = 9876
Question 19.
Write the smallest 4-digit number of distinct digits.
Solution:
Smallest 4-digit number of four digit = 1023
Question 20.
Write the greatest 6-digit number using three different digits.
Solution:
Greatest 6 digit number using three different digits = 999987.
Question 21.
Write the smallest 7-digit number using four different digits.
Solution:
Smallest 7 digit number by using four different digit = 1000023
Question 22.
Write the greatest and the smallest 4-digit numbers using four different digits with the conditions as given:
(i) Digit 7 is always at units place.
(ii) Digit 4 is always at tens place.
(iii) Digit 9 is always at hundreds place.
(iv) Digit 2 is always at thousands place.
Solution:
(i) 9867; 1027
(ii) 9847; 1042
(iii) 8976; 1902
(iv) 2987; 2013