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MathematicsClass 8Numbers

Numbers | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 3 min read

Numbers – this guide gives you a concise, exam-ready overview of Numbers from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Introduction

The chapter 'Numbers' in Class 8 Mathematics introduces students to the concept of rational and irrational numbers, building upon their prior knowledge of natural numbers, whole numbers, integers, and rational numbers from earlier classes. This chapter aims to deepen the understanding of numbers and their properties, focusing on the classification of numbers, decimal expansions, and the representation of numbers on the number line. It begins by revisiting rational numbers, emphasizing their decimal expansions which either terminate or repeat, and then introduces irrational numbers, whose decimal expansions neither terminate nor repeat. The chapter also discusses the importance of irrational numbers in completing the number line, ensuring that every point on the line corresponds to a unique number. Through this chapter, students learn to distinguish between rational and irrational numbers, understand their properties, and represent them graphically. The chapter also includes activities to help students visualize these concepts practically, such as locating irrational numbers on the number line using geometric methods. This foundational knowledge is crucial for higher mathematics, including algebra and geometry, as it provides a complete understanding of the number system used in various mathematical contexts.

📊 Diagram: The introductory section includes a diagram of the number line showing points representing rational numbers like 1/2, 3/4, and irrational numbers like √2 placed approximately between integers.

🧪 Activity: Activity 3.1: Locating rational and irrational numbers on the number line using geometric constructions.

🔗 Connection: This introduction sets the stage for the next section, which delves deeper into the properties and decimal expansions of rational numbers.

Frequently asked questions

1. 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? 2. Form a base-2 place value system using ‘ukasar’ and ‘urapon’ as the digits. Compare this system with that of the Gumulgal’s. 3. 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? 4. 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?

1. The Chinese alternated between the Zong and Heng symbols likely to avoid confusion and to clearly distinguish between different place values. If only the Zong symbols were used, the numeral 41 would be represented by four Zong symbols followed by one Zong symbol for the units place. Without significant spacing, this could be misinterpreted as 11 or 14, causing ambiguity.

2. Using ‘ukasar’ and ‘urapon’ as digits for base-2, 'ukasar' can represent 0 and 'urapon' can represent 1. Numbers would

Which of the following statements correctly describes a rational number?

A number that can be expressed as a ratio of two integers, where the denominator is not zero

What is the decimal expansion of the rational number $\frac{1}{3}$?

0.333... (repeating)

Which of the following decimal expansions represents an irrational number?

3.1415926535... (non-terminating, non-repeating)

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