Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers

Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers

APlusTopper.com provides step by step solutions for Selina Concise Mathematics Class 9 ICSE Solutions Chapter 1 Rational and Irrational Numbers. You can download the Selina Concise Mathematics ICSE Solutions for Class 9 with Free PDF download option. Selina Publishers Concise Mathematics for Class 9 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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Exercise 1(A)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 1
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 2
Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 2a

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 3

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 4

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 5
Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 6

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 7

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 8

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 9

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 10

Exercise 1(B)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 11

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 12

Solution 3(i):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 13

Solution 3(ii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 14

Solution 3(iii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 15

Solution 3(iv):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 16

Solution 3(v):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 17

Solution 3(vi):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 18

Solution 3(vii):
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Solution 3(viii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 20

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 21

Solution 5(i):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 22

Solution 5(ii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 23

Solution 5(iii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 24

Solution 5(iv):

Solution 5(v):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 26

Solution 5(vi):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 27

Solution 5(vii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 28

Solution 5(viii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 29

Exercise 1(C)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 30

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 31

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 32

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 33
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 34

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 35

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 36

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 37

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 38

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 39

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 40

Solution 11:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 41

Solution 12:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 42

Solution 13:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 43

Solution 14:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 44

Solution 15:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 45

Solution 16:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 46

Solution 17:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 47

Solution 18:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 48

Solution 19:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 49

Exercise 1(D)

Solution 1:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 50

Solution 2:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 51
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 52

Solution 3:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 53
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 54

Solution 4:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 55
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 56

Solution 5:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 57

Solution 6:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 58

Solution 7:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 59

Solution 8:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 60

Solution 9:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 61

Solution 10:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 62
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 63

Solution 11:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 64

Solution 12:
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 65

Solution 13(i):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 66

Solution 13(ii):
Selina Concise Mathematics Class 9 ICSE Solutions Rational and Irrational Numbers 67
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Rational and Irrational Numbers

Rational and Irrational Numbers

Both rational and irrational numbers are real numbers.

Rational and Irrational Numbers 1
This Venn Diagram shows the relationships between sets of numbers. Notice that rational and irrational numbers are contained in the large blue rectangle representing the set of Real Numbers.

Rational Numbers

A rational number is a number that can be expressed as a fraction or ratio.
The numerator and the denominator of the fraction are both integers.
Examples of rational numbers are:
Rational and Irrational Numbers 2

A rational number can be expressed as a ratio (fraction) with integers in both the top and the bottom of the fraction.
When the fraction is divided out, it becomes a terminating or repeating decimal. (The repeating decimal portion may be one number or a billion numbers.)
Rational and Irrational Numbers 3

Rational numbers on  number line:
A number line is a straight line diagram on which every point corresponds to a real number.
Since rational numbers are real numbers, they have a specific location on a number line.
Rational and Irrational Numbers 6

To convert a repeating decimal to a fraction:
Rational and Irrational Numbers 4

To show that the rational numbers are “dense”:
(The term “dense” means that between any two rational numbers there is another rational number.)
Rational and Irrational Numbers 5

Irrational Numbers

An irrational number cannot be expressed as a fraction.

  1. Irrational numbers cannot be represented as terminating or repeating decimals.
  2. Irrational numbers are non-terminating, non-repeating decimals.
  3. Examples of irrational numbers are:
    Rational and Irrational Numbers 7

Note: Many students think that π is the terminating decimal, 3.14, but it is not. Yes, certain math problems ask you to use π as 3.14, but that problem is rounding the value of to make your calculations easier. π is actually a non-ending decimal and is an irrational number.

There are certain radical values which fall into the irrational number category.
For example, √2 cannot be written as a “simple fraction”
which has integers in the numerator and the denominator.
As a decimal, √2 = 1.414213562373095048801688624 …
which is a non-ending and non-repeating decimal, making √2 irrational.

Irrational Numbers on a Number Line:
By definition, a number line is a straight line diagram on which every point corresponds to a real number.
Since irrational numbers are a subset of the real numbers, and real numbers can be represented on a number line, one might assume that each irrational number has a “specific” location on the number line.
“Estimates” of the locations of irrational numbers on number line:
Rational and Irrational Numbers 8
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