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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 . .
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.
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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,
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 . .
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.
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, 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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