NCERT Solutions For Class 8 Maths Chapter 3 A Story Of Numbers

NCERT Solutions for Class 8 Maths Chapter 3 A Story Of Numbers helps students understand numbers in a deeper and more practical way. This chapter focuses on rational numbers, properties of numbers, number patterns, operations, and their applications in daily life. Students learn how to compare, arrange, simplify, and solve mathematical problems using different types of numbers. Strong understanding of this chapter helps in algebra, higher arithmetic, and logical reasoning. Regular practice improves problem-solving skills and builds confidence in mathematics.

Important Concepts Covered

  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational Numbers
  • Number Line Representation
  • Properties of Numbers
  • Operations on Numbers
  • Comparing and Ordering Numbers

Formula Revision

  • a + b = b + a (Commutative Property)
  • a × b = b × a
  • (a + b) + c = a + (b + c)
  • (a × b) × c = a × (b × c)
  • a × (b + c) = ab + ac

Question & Answers

Q1. Classify the following numbers:

(i) 7

Answer: Natural Number

NCERT Solutions For Class 8 Maths Chapter 3 A Story Of Numbers

A Story of Numbers (New NCERT)
Medium
Q.
12 = 1
112 = 121
212 = 441
22 = 4
122 = 144
222 = 484
32 = 9
132 = 169
232 = 529
42 = 16
142 = 196
242 = 576
52 = 25
152 = 225
252 = 625
62 = 36
162 = 256
262 = 676
72 = 49
172 = 289
272 = 729
82 = 64
182 = 324
282 = 784
92 = 81
192 = 361
292 = 841
102 = 100
202 = 400
302 = 900
​Find more such patterns by observing the numbers and their squares from the table you filled earlier.​
A Story of Numbers (New NCERT)
Medium
Q.
​Compute the landmark numbers of a base-7 system. In general, what are the landmark numbers of a base-n system?​
A Story of Numbers (New NCERT)
Medium
Q.
Where in your daily lives, and in which professions, do the Hindu numerals, and 0, play an important role? How might our lives have been different if our number system and 0 hadn’t been invented or conceived of?
A Story of Numbers (New NCERT)
Medium
Q.
​Form a base-2 place value system using ‘ukasar’ and ‘urapon’ as the digits. Compare this system with that of the Gumulgal’s.​
A Story of Numbers (New NCERT)
Medium
Q.
​Why do you think the Chinese alternated between the Zong and Heng symbols? If only the Zong symbols were to be used, how would 41 be represented? Could this numeral be interpreted in any other way if there is no significant space between two successive positions?​
A Story of Numbers (New NCERT)
Medium
Q.
Represent the following numbers in the Mesopotamian system:
(i) 63
(ii) 132
(iii) 200
(iv) 60
(v) 3605
A Story of Numbers (New NCERT)
Medium
Q.
​Give a simple rule to multiply a given number by 5 in the base-5 system that we created.​
A Story of Numbers (New NCERT)
Medium
Q.
​Can there be a number whose representation in Egyptian numerals has one of the symbols occurring 10 or more times? Why not?​
A Story of Numbers (New NCERT)
Medium
Q.
​Add the following numerals that are in the base-5 system that we created:
Remember that in this system, 5 times a landmark number gives the next one!
A Story of Numbers (New NCERT)
Medium
Q.
​Add the following Egyptian numerals:

A Story of Numbers (New NCERT)
Medium
Q.
Is there a number that cannot be represented in our base-5 system below ? Why or why not?
A Story of Numbers (New NCERT)
Medium
Q.
​Suppose you are using the number system that uses sticks to represent numbers. Without using either the number names or the numerals of the Hindu number system, give a method for adding, subtracting, multiplying, and dividing two numbers or two collections of sticks.​
A Story of Numbers (New NCERT)
Medium
Q.
Write the following numbers in the below base-5 system using the symbols in Table: 15, 50, 137, 293, 651.
A Story of Numbers (New NCERT)
Medium
Q.
What numbers do these numerals stand for?
A Story of Numbers (New NCERT)
Medium
Q.
Represent the following numbers in the Egyptian system:
10458, 1023, 2660, 784, 1111, 70707
A Story of Numbers (New NCERT)
Medium
Q.
​Identify the features of the Hindu number system that make it efficient when compared to the Roman number system.​
A Story of Numbers (New NCERT)
Medium
Q.
Consider the extension of the Gumulgal number system beyond 6 in the same way of counting by 2s. Come up with ways of performing the different arithmetic operations (+, -, ×, ÷) for numbers occurring in this system, without using Hindu numerals. Use this to evaluate the following:
(i) (ukasar-ukasar-ukasar-ukasar-urapon) + (ukasar-ukasar-ukasar-urapon)
(ii) (ukasar-ukasar-ukasar-ukasar-urapon) – (ukasar-ukasar-ukasar)
(iii) (ukasar-ukasar-ukasar-ukasar-urapon) × (ukasar-ukasar)
(iv) (ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar) ÷ (ukasar-ukasar)
A Story of Numbers (New NCERT)
Medium
Q.
​A group of indigenous people in a Pacific island uses different sequences of number names to count different objects. Why do you think they do this?​
A Story of Numbers (New NCERT)
Medium
Q.
Represent the following numbers in the Roman system.
(i) 1222
(ii) 2999
(iii) 302
(iv) 715
A Story of Numbers (New NCERT)
Medium
Q.
Try making your own number system.
A Story of Numbers (New NCERT)
Medium
Q.
Method 2: Instead of objects, we could use a standard sequence of sounds or names. For example, we could use the sounds of the letters of any language. While counting, we could make a one-to-one mapping between the objects and the letters: that is, associate each object to be counted with a letter, following the letter-order. This mapping can then be used to come up with a way of verbally representing numbers.
One way of extending the number system in Method 2 is by using strings with more than one letter — for example, we could use ‘aa’ for 27. How can you extend this system to represent all the numbers? There are many ways of doing it!
A Story of Numbers (New NCERT)
Medium
Q.
The ancient Indians likely used base 10 for the Hindu number system because humans have 10 fingers, and so we can use our fingers to count. But what if we had only 8 fingers? How would we be writing numbers then? What would the Hindu numerals look like if we were using base 8 instead? Base 5? Try writing the base-10 Hindu numeral 25 as base-8 and base-5 Hindu numerals, respectively. Can you write it in base-2?

NCERT Solutions For Class 8 Maths Chapter 3 A Story Of Numbers

(ii) 0

Answer: Whole Number

(iii) -9

Answer: Integer

(iv) 3/5

Answer: Rational Number

Q2. Represent on number line:

(i) -2

Answer: Point lies 2 units left of 0.

(ii) 4

Answer: Point lies 4 units right of 0.

Q3. Solve:

(i) 5 + (-3)

Answer: 2

(ii) -6 + 10

Answer: 4

(iii) 3/4 + 1/4

Answer: 1

Q4. Arrange in ascending order:

(i) 5, -2, 0, 9, -7

Answer: -7, -2, 0, 5, 9

FAQs

1. What is Chapter 3 of Class 8 Maths?

Chapter 3 of Class 8 Maths is A Story Of Numbers, based on different types of numbers and operations.

2. Why is this chapter important?

It builds the base for algebra, arithmetic, and logical reasoning.

3. What are rational numbers?

Numbers written in p/q form where q ≠ 0 are rational numbers.

Example: 3/5, -7/2

4. What is an integer?

Positive numbers, negative numbers, and zero together are called integers.