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.
Rational Numbers and Their Decimal Expansions
This section focuses on the detailed properties of rational numbers, particularly their decimal expansions. A rational number is defined as any number that can be expressed in the form p/q, where p and q are integers and q ≠ 0. The decimal expansion of rational numbers is either terminating or non-terminating repeating. Terminating decimals are those which have a finite number of digits after the decimal point, such as 0.25 or 0.5. Non-terminating repeating decimals have infinite digits after the decimal point but the digits repeat in a pattern, such as 0.333... or 0.142857142857... The section explains the process of converting fractions into decimals by long division and illustrates how the remainder repeats to create the repeating decimal pattern. It also discusses the converse, showing that any terminating or repeating decimal can be expressed as a rational number. The section includes examples and exercises to reinforce these concepts and helps students understand the importance of recognizing patterns in decimals to identify rational numbers.
📊 Diagram: Diagrams include the long division process showing how remainders repeat leading to repeating decimals, and number line segments marking terminating and repeating decimals.
🧪 Activity: Activity 3.2: Converting given rational numbers into decimals and identifying if they terminate or repeat.
🔗 Connection: This section leads to the next, which introduces irrational numbers and their decimal expansions that neither terminate nor repeat.
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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