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
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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
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