Table of Contents

9th Maths New Book Exercise 1.1 notes

Introduction to 9th Maths New Book Exercise 1.1

9th Maths New Book Exercise 1.1 focuses on the basic concepts of real numbers. It introduces the classification of numbers, including natural, whole, integers, rational, and irrational numbers, and explores their properties. Students will learn about real numbers’ placement on the number line and their density property. This exercise lays the groundwork for understanding the real number system, a key part of the 9th Math New Book Federal Board syllabus.

Question 1:- Identify each of the following as a rational or irrational number.

Question	Rational / Irrational
2.353535	Rational
0.666666…..	Rational
2.236067….	Irrational
√7	Irrational
e	Irrational
π	Irrational
5 + `√`11	Irrational
√3 +√13	Irrational
15/4	Rational
(2-√2)(2+√2)	Rational

For complete solution watch the following video https://youtu.be/vNvXKxkv5wU?si=PVUtBQmQBWYx7joY

New Book Math Class 9 Exercise 1.1 Question 1 video lecture

Question 2:- Represent the following on number Line.

For Solution watch the video below. https://youtu.be/RuU-hqCLfLc?si=LGqJ4rWVcRrD55Bn

New Book Math Class 9 Exercise 1.1 Question 2 video lecture

Question 3:- Express the following as rational number p/q where p and q are integers and q ≠ 0

(i):- 0.44444……..

Let x = 0.4444…..

Multiplying both sides by 10

10x = 10(0.4444……..)

10x = 4.4444…….

subtracting x on both sides

10x – x = 4.4444…… – x

9x = 4.4444…….. – 0.444……

9x = 4

Dividing both sides by 9

x = 4/9

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(ii):- 0.373737………

Let x = 0.373737……

Multiplying both sides by 100

100x = 100(0.373737….)

100x = 37.3737……

Subtracting x on both the sides

100x – x = 37.373737……. – x

99x = 37.373737…….. – 0.373737……..

99x = 37

dividing both sides by 99

x = 37/99

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(iii):- 0.212121……

Let x = 0.212121…..

100x = 100(0.212121….)

100x = 21.212121……

Subtracting x on both the sides

100x – x = 21.212121….. – x

99x = 21.212121…….. – 0.212121…….

99x = 21

dividing both sides by 99

x = 21/99

For solution watch the following video https://youtu.be/qdd3ebzcRFM?si=d3_Trp9WItz95udB

New Book Math Class 9 Exercise 1.1 Question 3

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Question 4:- Name the property used in the following.

(a+4)+b = a+(4+b)	Associative law of addition
√2 +√3 = √3+√2	Commutative law of addition
x – x = 0	Additive inverse
a(b+c) = ab+ac	Left distributive law of multiplication w.r.t. addition
16+0=16	additive identity
100×1 = 100	Multiplicative identity
4x(5×8) = (4×5)x8	Associative law of multiplication
ab = ba	Commutative law of multiplication

For Solution watch the video below. https://youtu.be/arMI_ykTqLo?si=KcEpjCU7D2j2_lQt

New Book Math Class 9 Exercise 1.1 Question 4

Question 5:- Name the property used in the following

-3<-1 `→` 0<2	Additive
If a<b then 1/a>1/b	Reciprocal
if a<b then a+c<b+c	Additive
if ac<bc and c>0 then a<b	Multiplicative
if ac<bc and c<0 then a>b	Multiplicative
Either a > b or a=b or a < b	Trichotomy