CBSE Class 9 Maths Chapter 3: The World of Numbers — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 3: The World of Numbers from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Every natural number is an integer.
Reason (R): The integers extend the natural numbers by including zero and negative whole numbers.
Reason (R): The integers extend the natural numbers by including zero and negative whole numbers.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Natural numbers form a subset of the larger integer set.
2
Assertion (A): Integers are closed under addition.
Reason (R): Natural numbers are not closed under subtraction.
Reason (R): Natural numbers are not closed under subtraction.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but failure of closure for natural-number subtraction does not explain integer closure under addition.
3
Assertion (A): The product of two negative integers is positive.
Reason (R): Division by zero is defined and produces zero.
Reason (R): Division by zero is defined and produces zero.
Answer: (c)
A is true, but R is false. Division by zero is undefined.
4
Assertion (A): Negative numbers belong to the set of natural numbers.
Reason (R): The set of integers includes negative numbers, zero, and positive whole numbers.
Reason (R): The set of integers includes negative numbers, zero, and positive whole numbers.
Answer: (d)
A is false, but R is true. Natural numbers are counting numbers, whereas integers extend the system to include zero and negatives.
5
Assertion (A): A rational number can be written as p/q, where p and q are integers and q is non-zero.
Reason (R): The non-zero denominator condition prevents division by zero.
Reason (R): The non-zero denominator condition prevents division by zero.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This is the defining representation of rational numbers.
6
Assertion (A): Zero is an integer and acts as the additive identity.
Reason (R): Every integer can also be expressed as a rational number.
Reason (R): Every integer can also be expressed as a rational number.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are correct, but the rational representation of integers does not explain the additive-identity property.
7
Assertion (A): Rational numbers are closed under division by a non-zero rational number.
Reason (R): In the representation p/q of a rational number, q may equal zero.
Reason (R): In the representation p/q of a rational number, q may equal zero.
Answer: (c)
A is true, but R is false. The denominator must be non-zero, including after taking a quotient.
8
Assertion (A): There is no rational number between two distinct rational numbers.
Reason (R): Infinitely many rational numbers lie between any two distinct rational numbers.
Reason (R): Infinitely many rational numbers lie between any two distinct rational numbers.
Answer: (d)
A is false, but R is true. This property is called the density of rational numbers.
9
Assertion (A): The arithmetic mean of two distinct rational numbers lies between them.
Reason (R): The mean is rational because rational numbers are closed under addition and division by 2.
Reason (R): The mean is rational because rational numbers are closed under addition and division by 2.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This construction provides one rational number between any given pair.
10
Assertion (A): A rational number has either a terminating or a non-terminating repeating decimal expansion.
Reason (R): The decimal expansion of 1/7 contains the repeating cyclic block 142857.
Reason (R): The decimal expansion of 1/7 contains the repeating cyclic block 142857.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but one cyclic example does not explain the complete decimal classification.
11
Assertion (A): The arithmetic mean of two rational numbers is rational.
Reason (R): Rational numbers occur as isolated consecutive points with no rational number between them.
Reason (R): Rational numbers occur as isolated consecutive points with no rational number between them.
Answer: (c)
A is true, but R is false. Rational numbers are dense, so they do not have consecutive members on the number line.
12
Assertion (A): A rational number in lowest terms can terminate even when its denominator contains a prime factor other than 2 or 5.
Reason (R): A terminating decimal in lowest terms has a denominator whose prime factors are only 2 and/or 5.
Reason (R): A terminating decimal in lowest terms has a denominator whose prime factors are only 2 and/or 5.
Answer: (d)
A is false, but R is true. Other prime factors produce a non-terminating repeating decimal.
13
Assertion (A): A rational number whose lowest-form denominator is 2^m x 5^n has a terminating decimal expansion.
Reason (R): A suitable power of 10 can be made a multiple of such a denominator.
Reason (R): A suitable power of 10 can be made a multiple of such a denominator.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Multiplying numerator and denominator appropriately converts the fraction to a denominator 10^k.
14
Assertion (A): An irrational number has a non-terminating, non-repeating decimal expansion.
Reason (R): The irrationality of sqrt(2) can be established by a proof by contradiction.
Reason (R): The irrationality of sqrt(2) can be established by a proof by contradiction.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the proof method for one number does not explain the general decimal definition.
15
Assertion (A): The number sqrt(5) is irrational.
Reason (R): It is irrational because its decimal expansion terminates after finitely many places.
Reason (R): It is irrational because its decimal expansion terminates after finitely many places.
Answer: (c)
A is true, but R is false. A terminating decimal is rational; sqrt(5) has a non-terminating, non-repeating expansion.
16
Assertion (A): An irrational number can be expressed exactly as p/q for integers p and non-zero q.
Reason (R): An irrational number cannot be represented as a ratio of two integers.
Reason (R): An irrational number cannot be represented as a ratio of two integers.
Answer: (d)
A is false, but R is true. The impossibility of a fractional representation distinguishes irrational numbers from rational numbers.
17
Assertion (A): The real numbers are the union of rational and irrational numbers.
Reason (R): Together they fill the real number line without gaps.
Reason (R): Together they fill the real number line without gaps.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Every point on the real line corresponds to one of these two types.
18
Assertion (A): Pi is an irrational real number.
Reason (R): The real number line also contains all rational numbers.
Reason (R): The real number line also contains all rational numbers.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are correct, but inclusion of rational numbers does not explain the irrationality of pi.
19
Assertion (A): No real number has a square equal to -1.
Reason (R): The square of every real number is negative.
Reason (R): The square of every real number is negative.
Answer: (c)
A is true, but R is false. Squares of real numbers are non-negative.
20
Assertion (A): The sum of a rational number and an irrational number is always rational.
Reason (R): Adding a rational number to an irrational number gives an irrational number.
Reason (R): Adding a rational number to an irrational number gives an irrational number.
Answer: (d)
A is false, but R is true. If the sum were rational, subtracting the rational addend would make the irrational number rational, a contradiction.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 3 The World of Numbers?
This chapter covers all key topics from The World of Numbers as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study The World of Numbers online for free?
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