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Rational and Irrational Numbers

ICSE · Class 9 · Mathematics

Complete topic list for Rational and Irrational Numbers in ICSE Class 9 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

35 questions30 flashcards5 concepts

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A nested Venn diagram illustrating the relationships between natural numbers (N), integers (Z), rational numbers (Q), and real numbers (R) as subsets of each other.
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4 Topics · ICSE Class 9 Mathematics

Topics in Rational and Irrational Numbers

1

Number System and Basic Classification

  • The complete number system is divided into imaginary numbers and real numbers.
  • If x = 4, then √-4 is imaginary and √4 = 2 is real.
  • Square root of every negative number is an imaginary number; if the number is not imaginary, it is a real number.
2

Rational Numbers, Comparison, and Between Them

  • Two rational numbers a/b and c/d are equal if and only if a × d = b × c.
  • For comparison, a/b > c/d if a × d > b × c.
  • The average of two rational numbers lies between them.
3

Decimal Representation of Rational Numbers

  • Every rational number can be expressed either as a terminating decimal or a non-terminating recurring decimal.
  • Terminating decimals end exactly after a finite number of digits.
  • Recurring decimals have a repeating digit or repeating block.
4

Irrational Numbers and Their Properties

  • The square roots, cube roots, and higher roots of natural numbers are irrational if their exact values cannot be obtained.
  • A non-terminating and non-recurring decimal is irrational.
  • π is irrational and is defined as circumference of a circle divided by diameter of the circle.

Key Concepts

Central concept: Real Numbers

Imaginary NumbersRational NumbersIrrational NumbersSurdsDecimal RepresentationBetween Two Rational NumbersRationalisationComparison of Surds

Frequently Asked Questions

What are the important topics in Rational and Irrational Numbers for ICSE Class 9 Mathematics?
Rational and Irrational Numbers covers several key topics that are frequently asked in ICSE Class 9 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Rational and Irrational Numbers — ICSE Class 9 Mathematics?
Understand the core concepts first, then work through the 35 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All 28 chapters — ICSE Class 9 Mathematics Syllabus

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