Number system grade 9 RD SHARMA

Class IX Chapter 1 – Number System Maths
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Exercise -1.1
𝑝
1. Is zero a rational number? Can you write it in the form 𝑞, where p and q are integers and
𝑞 ≠ 0?
Sol:
p
Yes, zero is a rotational number. It can be written in the form of where q to as such as
q
0 0 0
, , , etc.........
3 5 11

2. Find five rational numbers between 1 and 2.
Sol:
Given to find five rotational numbers between 1 and 2
A rotational number lying between 1 and 2 is
3 3
1  2   2  3  2  i.e.,1   2
2 2
3
Now, a rotational number lying between 1 and is
2
 3  23 5 5 1 5
1    2   2  2   
 2  2  2 2 2 4
5 3
i.e., 1  
4 2
5
Similarly, a rotational number lying between 1 and is
4
 5  45 9 9 1 9
1    2   2  2   
 4  2  4 4 2 8
9 5
i.e., 1  
8 4
3
Now, a rotational number lying between and 2 is
2
 5  45 9 9 1 9
1    2   2  2   
 4  4  4 4 2 8
9 5
i.e., 1  
8 4
3
Now, a rotational number lying between and 2 is
2
3   3 4  7 1 7
  2  2   2   
2   2  2 2 4

,Class IX Chapter 1 – Number System Maths
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3 7
i.e.,  2
2 4
7
Similarly, a rotational number lying between and 2 is
4
7   78 15 1 15
  2  2   2   
4   4  4 2 8
7 15
i.e.,   2
4 8
9 5 3 7 15
1      2
8 4 2 4 8
Recall that to find a rational number between r and s, you can add r and s and divide the
rs 3
sum by 2, that is lies between r and s So, is a number between 1 and 2. you can
2 2
proceed in this manner to find four more rational numbers between 1 and 2, These four
5 11 13 7
numbers are, , , and
4 8 8 4

3. Find six rational numbers between 3 and 4.
Sol:
Given to find six rotational number between 3 and 4
We have,
7 21 7 28
3  and 4  
7 7 7 7
We know that
21  22  23  24  25  26  27  28
21 22 23 24 25 26 27 28
       
7 7 7 7 7 7 7 7
22 23 24 25 26 27
3      4
7 7 7 7 7 7
Hence, 6 rotational number between 3 and 4 are
22 23 24 25 26 27
, , , , ,
7 7 7 7 7 7

3 4
4. Find five rational numbers between 4 𝑎𝑛𝑑 5
Sol:
3 4
Given to find 5 rotational numbers lying between and .
5 5
We have,

, Class IX Chapter 1 – Number System Maths
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3 6 18 4 6 24
  and  
5 6 100 5 6 30
We know that
18  19  20  21  22  23  24
18 19 20 21 22 23 24
      
30 30 30 30 30 30 30
3 19 20 21 22 23 4
     , ,
5 30 30 30 30 30 5
3 19 2 7 11 23 4
      
5 30 3 10 15 30 5
3 4
Hence, 5 rotational number between and are
5 5
19 2 7 11 23
, , , , .
30 3 10 15 30

5. Are the following statements true or false? Give reasons for your answer.
(i) Every whole number is a rational number.
(ii) Every integer is a rational number.
(iii) Every rational number is a integer.
(iv) Every natural number is a whole number.
(v) Every integer is a whole number.
(vi) Evert rational number is a whole number.
Sol:
(i) False. As whole numbers include zero, whereas natural number does not include zero
(ii) True. As integers are a part of rotational numbers.
(iii) False. As integers are a part of rotational numbers.
(iv) True. As whole numbers include all the natural numbers.
(v) False. As whole numbers are a part of integers
(vi) False. As rotational numbers includes all the whole numbers.