Introduction to Exercise 1.1
9th Math New Book Federal Board
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
Question 2:- Represent the following on number Line.
For Solution watch the video below.
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
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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.
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 |
For complete solution watch the following video
Question 6:- Insert two rational numbers between
(i):- 1/3 and 1/4
Average of 1/3 and 1/4 = 7/24
Average of 7/24 and 1/4= 13/24
7/24 and 13/24 are the required rational numbers
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(ii):- 3 and 4
Average of 3 and 4 = 7/2
Average of 7/2 and 4 = 15/2
7/2 and 15/2 are the required rational numbers
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(iii):- 3/5 and 4/5
Average of 3/5 and 4/5 = 7/10
Average of 7/10 and 4/5 = 15/10 = 3/2
7/10 and 3/2 are the required rational numbers
for complete solution watch the following video
New Book Math Class 9 Exercise 1.1 Question 5
For complete solution exercise 1.1 math class 9 new book watch the following video
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