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Rational and Irrational Numbers

ICSE · Class 9 · Mathematics

Practice quiz for Rational and Irrational Numbers — ICSE Class 9 Mathematics. MCQs and questions with answers to test your preparation.

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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Quick Quiz: Rational and Irrational Numbers

0/4

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1

Convert the decimal 0.75 to a rational number in its simplest form.

2

Find three rational numbers between 1/4 and 1/2.

3

Rationalize the denominator: 1/(3 + √2)

4

Arrange these numbers in ascending order: √8, 2.5, 22/9, √10

35 Questions·
multiple choicemultiple correcttext answertrue falsematchingordering

Sample Questions

1multiple correct

Which of the following numbers are rational?

Show answer

0.333..., √16, 22/7

Step 1: Check each number. 0.333... = 1/3 (recurring decimal = rational). √16 = 4 (perfect square = rational). √7 is non-terminating non-recurring (irrational). 22/7 is already in p/q form (rational). π = 3.14159... is non-terminating non-recurring (irrational).

2text answer

Calculate: 2√3 × 3√3

3true false

The sum of a rational number and an irrational number is always irrational.

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True

Step 1: Let r be rational and i be irrational. Step 2: Assume r + i = q (rational). Step 3: Then i = q - r. Since q and r are both rational, q - r is rational. Step 4: This contradicts that i is irrational. Therefore, r + i must be irrational.

4multiple correct

Which of the following are properties of irrational numbers?

Show answer

Non-terminating, non-recurring decimals, Cannot be expressed as p/q, Product with non-zero rational is irrational

Step 1: Check each property. Non-terminating, non-recurring decimals ✓. Cannot be expressed as p/q ✓. Sum of two irrationals: (2+√3) + (2-√3) = 4 (rational) ✗. Product with non-zero rational: 2×√3 = 2√3 (irrational) ✓.

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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.

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