CBSE Class 8 Maths Chapter 3: A Story of Numbers — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 3: A Story of Numbers from the NCERT Class 8 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): A positional numeral system assigns value according to both digit and position.
Reason (R): Place values are powers of the chosen base.
Reason (R): Place values are powers of the chosen base.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The position determines which base power multiplies the digit.
2
Assertion (A): The decimal system has base 10.
Reason (R): The binary system has base 2.
Reason (R): The binary system has base 2.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but binary's base does not explain decimal notation.
3
Assertion (A): In base 10, 407 represents 4 x 100 + 0 x 10 + 7.
Reason (R): The zero in 407 has no placeholding role.
Reason (R): The zero in 407 has no placeholding role.
Answer: (c)
A is true, but R is false. Zero preserves the tens position even though its contribution is zero.
4
Assertion (A): The digit 5 has the same value in 50 and 500.
Reason (R): A digit's place changes its value in a positional system.
Reason (R): A digit's place changes its value in a positional system.
Answer: (d)
A is false, but R is true. The values are 50 and 500 respectively.
5
Assertion (A): A base-b numeral uses place values 1, b, b squared, b cubed and so on.
Reason (R): Moving one place left multiplies place value by b.
Reason (R): Moving one place left multiplies place value by b.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Successive powers of the base define the positions.
6
Assertion (A): Binary numerals use only digits 0 and 1.
Reason (R): Roman numerals are not a pure positional base-10 system.
Reason (R): Roman numerals are not a pure positional base-10 system.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but Roman notation does not explain the allowed binary digits.
7
Assertion (A): The binary numeral 101 equals decimal 5.
Reason (R): Its place-value expansion equals decimal 6.
Reason (R): Its place-value expansion equals decimal 6.
Answer: (c)
A is true, but R is false. The expansion is 4 + 0 + 1 = 5.
8
Assertion (A): The decimal number 8 is written as 100 in binary.
Reason (R): The binary numeral 100 represents 4.
Reason (R): The binary numeral 100 represents 4.
Answer: (d)
A is false, but R is true. Eight is 1000 in binary.
9
Assertion (A): Grouping and bundling support the development of base systems.
Reason (R): A fixed number of units can be exchanged for one unit of the next place.
Reason (R): A fixed number of units can be exchanged for one unit of the next place.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Repeated bundling creates positional place values.
10
Assertion (A): A base can be any integer greater than 1 for a standard positional system.
Reason (R): The symbols needed usually represent values from 0 to one less than the base.
Reason (R): The symbols needed usually represent values from 0 to one less than the base.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the digit range describes rather than explains the choice of every base.
11
Assertion (A): A base-5 numeral cannot use the digit 7.
Reason (R): Base 5 allows every decimal digit from 0 to 9.
Reason (R): Base 5 allows every decimal digit from 0 to 9.
Answer: (c)
A is true, but R is false. Only digits 0 through 4 are permitted.
12
Assertion (A): The base-5 numeral 23 equals decimal 23.
Reason (R): Its value is 2 x 5 + 3.
Reason (R): Its value is 2 x 5 + 3.
Answer: (d)
A is false, but R is true. It equals decimal 13.
13
Assertion (A): Zero is essential as a placeholder in positional notation.
Reason (R): It distinguishes numerals such as 24, 204 and 240.
Reason (R): It distinguishes numerals such as 24, 204 and 240.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Without a placeholder, empty positions would be ambiguous.
14
Assertion (A): Ancient numeral systems developed in response to counting and record-keeping needs.
Reason (R): Different civilisations sometimes represented numbers in different ways.
Reason (R): Different civilisations sometimes represented numbers in different ways.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but diversity of systems does not explain every original practical need.
15
Assertion (A): Ancient number systems used varied symbols and rules.
Reason (R): Every civilisation used modern Hindu-Arabic digits from the beginning.
Reason (R): Every civilisation used modern Hindu-Arabic digits from the beginning.
Answer: (c)
A is true, but R is false. Numeral systems developed differently across time and place.
16
Assertion (A): A non-positional numeral gives each symbol a value determined entirely by its position.
Reason (R): In non-positional systems, symbols may retain fixed values and combine by other rules.
Reason (R): In non-positional systems, symbols may retain fixed values and combine by other rules.
Answer: (d)
A is false, but R is true. The assertion describes positional notation.
17
Assertion (A): The decimal expansion of a numeral can be written as a sum of digit times powers of 10.
Reason (R): For 352, this is 3 x 10 squared + 5 x 10 + 2.
Reason (R): For 352, this is 3 x 10 squared + 5 x 10 + 2.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The expansion follows its hundreds, tens and units positions.
18
Assertion (A): Changing a numeral's base changes its written form while the represented quantity may remain the same.
Reason (R): Decimal 5 is binary 101.
Reason (R): Decimal 5 is binary 101.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the example illustrates rather than explains the general principle.
19
Assertion (A): The numeral 10 can represent different quantities in different bases.
Reason (R): It always represents decimal ten regardless of base.
Reason (R): It always represents decimal ten regardless of base.
Answer: (c)
A is true, but R is false. In base b, the numeral 10 has value b.
20
Assertion (A): Place value is unnecessary for performing arithmetic efficiently.
Reason (R): A systematic positional representation supports algorithms for calculation.
Reason (R): A systematic positional representation supports algorithms for calculation.
Answer: (d)
A is false, but R is true. Place value makes regrouping and computation practical.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 3 A Story of Numbers?
This chapter covers all key topics from A Story of Numbers as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 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 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study A Story of Numbers online for free?
Yes, complete Assertion & Reason for A Story of Numbers is available free at eBookPublisher. Study online directly — no download needed.
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