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# 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
Yes. Zero is a rational number as it can be represented as etc.
Question 2:

Find six rational numbers between 3 and 4.

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

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
Yes. Zero is a rational number as it can be represented as etc.
Question 2:

Find six rational numbers between 3 and 4.

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
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.
(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
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
Yes. Zero is a rational number as it can be represented as etc.
Question 2:

Find six rational numbers between 3 and 4.

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:
NCRTSOLUTIONS.BLOGSPOT.COM
NCRTSOLUTIONS.BLOGSPOT.COM
Find  five  rational  numbers
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.
(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.
(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.
If numbers such as are considered,
Page 4

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
Yes. Zero is a rational number as it can be represented as etc.
Question 2:

Find six rational numbers between 3 and 4.

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:
NCRTSOLUTIONS.BLOGSPOT.COM
NCRTSOLUTIONS.BLOGSPOT.COM
Find  five  rational  numbers
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.
(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.
(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.
If numbers such as are considered,
NCRTSOLUTIONS.BLOGSPOT.COM
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:
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
Yes. Zero is a rational number as it can be represented as etc.
Question 2:

Find six rational numbers between 3 and 4.

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:
NCRTSOLUTIONS.BLOGSPOT.COM
NCRTSOLUTIONS.BLOGSPOT.COM
Find  five  rational  numbers
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.
(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.
(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.
If numbers such as are considered,
NCRTSOLUTIONS.BLOGSPOT.COM
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:
We know that,
And,
NCRTSOLUTIONS.BLOGSPOT.COM
NCRTSOLUTIONS.BLOGSPOT.COM

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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