9Maths 1 Number Systems Class 9 Notes | EduRev

Class 9 : 9Maths 1 Number Systems Class 9 Notes | EduRev

 Page 1


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Class IX  Chapter 1 –   
Number Sustems   Maths    
   
Exercise 1.1 Question    
Is zero a rational number? Can you write it in the form , where p and q are integers   ? 
0?   
and q     
Answer:    
Yes. Zero is a rational number as it can be represented as etc.    
Question 2:    
 
Find six rational numbers between 3 and 4.     
  
Answer:      
    
There are infinite rational numbers in between 3 an     d 4.      
3     and 4 can be represented as     respectively.      
Therefore, rational numbers between 3 and 4 are      
      
Question 3:      
Page 2


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Class IX  Chapter 1 –   
Number Sustems   Maths    
   
Exercise 1.1 Question    
Is zero a rational number? Can you write it in the form , where p and q are integers   ? 
0?   
and q     
Answer:    
Yes. Zero is a rational number as it can be represented as etc.    
Question 2:    
 
Find six rational numbers between 3 and 4.     
  
Answer:      
    
There are infinite rational numbers in between 3 an     d 4.      
3     and 4 can be represented as     respectively.      
Therefore, rational numbers between 3 and 4 are      
      
Question 3:      
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Find  five  rational  numbers 
 between Answer:    
There   are   infinite   rational numbers 
between .    
    
Therefore,   rational  are    
    
Question 4:    
State whether the following statements are true or false. Give reasons for your answers.    
(i) Every natural number is a whole number.    
(ii) Every integer is a whole number.    
(iii) Every rational number is a whole number.    
Answer:    
(i) True; since the collection of whole numbers contains all natural numbers.    
(ii) False; as integers may be negative but whole numbers are positive. For example: -3 
is an integer but not a whole number.    
(iii) False; as rational numbers may be fractional but whole numbers may not be. For    
example: is a rational number but not a whole number.    
    
    
    
    
    
    
numbers    between 
.      
Page 3


NCRTSOLUTIONS.BLOGSPOT.COM    
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Class IX  Chapter 1 –   
Number Sustems   Maths    
   
Exercise 1.1 Question    
Is zero a rational number? Can you write it in the form , where p and q are integers   ? 
0?   
and q     
Answer:    
Yes. Zero is a rational number as it can be represented as etc.    
Question 2:    
 
Find six rational numbers between 3 and 4.     
  
Answer:      
    
There are infinite rational numbers in between 3 an     d 4.      
3     and 4 can be represented as     respectively.      
Therefore, rational numbers between 3 and 4 are      
      
Question 3:      
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NCRTSOLUTIONS.BLOGSPOT.COM       
Find  five  rational  numbers 
 between Answer:    
There   are   infinite   rational numbers 
between .    
    
Therefore,   rational  are    
    
Question 4:    
State whether the following statements are true or false. Give reasons for your answers.    
(i) Every natural number is a whole number.    
(ii) Every integer is a whole number.    
(iii) Every rational number is a whole number.    
Answer:    
(i) True; since the collection of whole numbers contains all natural numbers.    
(ii) False; as integers may be negative but whole numbers are positive. For example: -3 
is an integer but not a whole number.    
(iii) False; as rational numbers may be fractional but whole numbers may not be. For    
example: is a rational number but not a whole number.    
    
    
    
    
    
    
numbers    between 
.      
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Exercise 1.2 Question 1:    
State whether the following statements are true or false. Justify your answers.    
(i) Every irrational number is a real number.    
(ii) Every point on the number line is of the form , where m is a natural number.    
(iii) Every real number is an irrational number.    
Answer:    
(i) True; since the collection of real numbers is made up of rational and irrational numbers.    
(ii) False; as negative numbers cannot be expressed as the square root of any other 
number.    
(iii) False; as real numbers include both rational and irrational numbers. Therefore, every 
real number cannot be an irrational number.    
Question 2:    
Are the square roots of all positive integers irrational? If not, give an example of the square 
root of a number that is a rational number.    
Answer:    
If numbers such as are considered,    
Page 4


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Class IX  Chapter 1 –   
Number Sustems   Maths    
   
Exercise 1.1 Question    
Is zero a rational number? Can you write it in the form , where p and q are integers   ? 
0?   
and q     
Answer:    
Yes. Zero is a rational number as it can be represented as etc.    
Question 2:    
 
Find six rational numbers between 3 and 4.     
  
Answer:      
    
There are infinite rational numbers in between 3 an     d 4.      
3     and 4 can be represented as     respectively.      
Therefore, rational numbers between 3 and 4 are      
      
Question 3:      
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NCRTSOLUTIONS.BLOGSPOT.COM       
Find  five  rational  numbers 
 between Answer:    
There   are   infinite   rational numbers 
between .    
    
Therefore,   rational  are    
    
Question 4:    
State whether the following statements are true or false. Give reasons for your answers.    
(i) Every natural number is a whole number.    
(ii) Every integer is a whole number.    
(iii) Every rational number is a whole number.    
Answer:    
(i) True; since the collection of whole numbers contains all natural numbers.    
(ii) False; as integers may be negative but whole numbers are positive. For example: -3 
is an integer but not a whole number.    
(iii) False; as rational numbers may be fractional but whole numbers may not be. For    
example: is a rational number but not a whole number.    
    
    
    
    
    
    
numbers    between 
.      
NCRTSOLUTIONS.BLOGSPOT.COM    
NCRTSOLUTIONS.BLOGSPOT.COM       
    
    
    
    
    
    
    
    
    
Exercise 1.2 Question 1:    
State whether the following statements are true or false. Justify your answers.    
(i) Every irrational number is a real number.    
(ii) Every point on the number line is of the form , where m is a natural number.    
(iii) Every real number is an irrational number.    
Answer:    
(i) True; since the collection of real numbers is made up of rational and irrational numbers.    
(ii) False; as negative numbers cannot be expressed as the square root of any other 
number.    
(iii) False; as real numbers include both rational and irrational numbers. Therefore, every 
real number cannot be an irrational number.    
Question 2:    
Are the square roots of all positive integers irrational? If not, give an example of the square 
root of a number that is a rational number.    
Answer:    
If numbers such as are considered,    
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NCRTSOLUTIONS.BLOGSPOT.COM       
Then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers 
are not irrational.    
intersecting number line at C.    
C is representing .    
    
  
perpendicular to OA. Then, taking O as centre and OB as radius, draw an arc    
Show how   can be represented on the number line.      
      
Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length    
Question 3:      
Answer:      
We know that,           
And,            
Page 5


NCRTSOLUTIONS.BLOGSPOT.COM    
NCRTSOLUTIONS.BLOGSPOT.COM       
   
Class IX  Chapter 1 –   
Number Sustems   Maths    
   
Exercise 1.1 Question    
Is zero a rational number? Can you write it in the form , where p and q are integers   ? 
0?   
and q     
Answer:    
Yes. Zero is a rational number as it can be represented as etc.    
Question 2:    
 
Find six rational numbers between 3 and 4.     
  
Answer:      
    
There are infinite rational numbers in between 3 an     d 4.      
3     and 4 can be represented as     respectively.      
Therefore, rational numbers between 3 and 4 are      
      
Question 3:      
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NCRTSOLUTIONS.BLOGSPOT.COM       
Find  five  rational  numbers 
 between Answer:    
There   are   infinite   rational numbers 
between .    
    
Therefore,   rational  are    
    
Question 4:    
State whether the following statements are true or false. Give reasons for your answers.    
(i) Every natural number is a whole number.    
(ii) Every integer is a whole number.    
(iii) Every rational number is a whole number.    
Answer:    
(i) True; since the collection of whole numbers contains all natural numbers.    
(ii) False; as integers may be negative but whole numbers are positive. For example: -3 
is an integer but not a whole number.    
(iii) False; as rational numbers may be fractional but whole numbers may not be. For    
example: is a rational number but not a whole number.    
    
    
    
    
    
    
numbers    between 
.      
NCRTSOLUTIONS.BLOGSPOT.COM    
NCRTSOLUTIONS.BLOGSPOT.COM       
    
    
    
    
    
    
    
    
    
Exercise 1.2 Question 1:    
State whether the following statements are true or false. Justify your answers.    
(i) Every irrational number is a real number.    
(ii) Every point on the number line is of the form , where m is a natural number.    
(iii) Every real number is an irrational number.    
Answer:    
(i) True; since the collection of real numbers is made up of rational and irrational numbers.    
(ii) False; as negative numbers cannot be expressed as the square root of any other 
number.    
(iii) False; as real numbers include both rational and irrational numbers. Therefore, every 
real number cannot be an irrational number.    
Question 2:    
Are the square roots of all positive integers irrational? If not, give an example of the square 
root of a number that is a rational number.    
Answer:    
If numbers such as are considered,    
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NCRTSOLUTIONS.BLOGSPOT.COM       
Then here, 2 and 3 are rational numbers. Thus, the square roots of all positive integers 
are not irrational.    
intersecting number line at C.    
C is representing .    
    
  
perpendicular to OA. Then, taking O as centre and OB as radius, draw an arc    
Show how   can be represented on the number line.      
      
Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length    
Question 3:      
Answer:      
We know that,           
And,            
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Exercise 1.3 Question 1:    
Write the following in decimal form and say what kind of decimal expansion each  . Can 
you predict what the decimal expansion of    
are, without actually doing the long division? If so, how?    
[Hint: Study the remainders while finding the value of carefully.] Answer:    
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