OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1. We Provide Step by Step Answer of Exe-1(a), Exe-1(b), Exe-1(c) with Chapter Test of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-9.

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1


-: Select Topics :-

Exercise-1(a)

Exercise-1(b)

Exercise-1(c)

Chapter Test


Exercise-1

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1

Introduction to Number Systems :

Numbers :

Number: Arithmetical value representing a particular quantity. The various types of numbers are Natural Numbers, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers etc.

Natural Numbers :

Natural numbers(N) are positive numbers i.e. 1, 2, 3 ..and so on.

Whole Numbers :

Whole numbers (W) are 0, 1, 2,..and so on. Whole numbers are all Natural Numbers including ‘0’. Whole numbers do not include any fractions, negative numbers or decimals.

Integers :

Integers are the numbers that includes whole numbers along with the negative numbers.

Rational Numbers :

A number ‘r’ is called a rational number if it can be written in the form p/q, where p and q are integers and q ≠ 0.

Irrational Numbers :

Any number that cannot be expressed in the form of p/q, where p and q are integers and q≠0, is an irrational number. Examples: √2, 1.010024563…, e, π

Real Numbers :

Any number which can be represented on the number line is a Real Number(R). It includes both rational and irrational numbers. Every point on the number line represents a unique real number.

Identities for Irrational Numbers :

Arithmetic operations between:

  • rational and irrational will give an irrational number.
  • irrational and irrational will give a rational or irrational number.

Example : 2 × √3 = 2√3 i.e. irrational. √3 × √3 = 3 which is rational.

Decimal expansion of Rational and Irrational Numbers :

The decimal expansion of a rational number is either terminating or non- terminating and recurring.

Example: 1/2 = 0.5 , 1/3 = 3.33…….
The decimal expansion of an irrational number is non terminating and non-recurring.
Examples: √2 = 1.41421356..

Some Special Characteristics of Rational Numbers :

  • Every Rational number is expressible either as a terminating decimal or as a repeating decimal.
  • Every terminating decimal is a rational number.
  • Every repeating decimal is a rational number.

Irrational Numbers :

  • The non-terminating, non-repeating decimals are irrational numbers.

Example: 0.0100100001001…

  • Similarly, if m is a positive number which is not a perfect square, then √m is irrational.

Example: √3

  • If m is a positive integer which is not a perfect cube, then 3√m is irrational.

Example: 3√2

Properties of Irrational Numbers :

  • These satisfy the commutative, associative and distributive laws for addition and multiplication.
  • Sum of two irrationals need not be irrational.

Example: (2 + √3) + (4 – √3) = 6

  • Difference of two irrationals need not be irrational.

Example: (5 + √2) – (3 + √2) = 2

  • Product of two irrationals need not be irrational.

Example: √3 x √3 = 3

  • The quotient of two irrationals need not be irrational.

2√3/√3 = 2

  • Sum of rational and irrational is irrational.
  • The difference of rational and irrational number is irrational.
  • Product of rational and irrational is irrational.
  • Quotient of rational and irrational is irrational.

Question 1 :-

(i) Find a rational number between 1/2 AND 3/4.

(ii) Find two rational …………. 0.2

(iii) Howe many rational …………  numbers?

to 

Question 11 :-

Write the repeating decimal for each of the following and use a bar to show the repetend.

(i) 1/19   

(ii) -4/3

Exercise-1.(a)

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1


Question 1 :- Look at the following real numbers :

to

Question 6 :- Is √100 + √36 the same as √100 + 36 ?

Give reasons.

 

Exercise-1.(b)

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1


Question 1 :- Simplify :

Question 15 :- If x= ……..

Exercise-1.(c)

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1


Chapter Test

OP Malhotra Rational and Irrational Number Class-9 S.Chand ICSE Maths Ch-1

 

— : End of Rational and Irrational Number OP Malhotra S Chand Solutions :–


Return to :–  OP Malhotra S Chand Solutions for ICSE Class-9 Maths

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