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Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn real numbers, irrational numbers, decimal expansion, laws of exponents, and rational numbers with detailed solutions for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Number Systems
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Number Systems is one of the most fundamental chapters in Class 9 Mathematics. It introduces students to rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents. Understanding these concepts helps students build a strong mathematical foundation for algebra and higher studies.
What You Will Learn?
✔ Rational Numbers
✔ Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion of Rational Numbers
✔ Laws of Exponents
✔ Representation of Numbers on the Number Line
✔ Board Exam Preparation
Why This Topic Is Important?
Number Systems are widely used in various branches of mathematics. Learning these concepts improves logical reasoning, computational skills, and problem-solving ability.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following numbers is irrational?
A) $$\frac{5}{9}$$
B) $$0.875$$
C) $$\sqrt{20}$$
D) $$0.4444\ldots$$
Answer:
$$\sqrt{20}$$
Useful Formula for this Question:
An irrational number cannot be expressed in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
This question checks students’ understanding of irrational numbers.
Step-by-Step Solution:
- $$\frac{5}{9}$$ is rational.
- $$0.875 = \frac{7}{8}$$ is rational.
- $$0.4444\ldots = \frac{4}{9}$$ is rational.
- $$\sqrt{20} = 2\sqrt{5}$$ and $$\sqrt{5}$$ is irrational.
Therefore:
$$\sqrt{20}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{20}$$
Exam Tip:
The square root of a non-perfect square is irrational.
Q2. Which of the following fractions has a non-terminating recurring decimal expansion?
A) $$\frac{7}{25}$$
B) $$\frac{11}{20}$$
C) $$\frac{13}{24}$$
D) $$\frac{9}{40}$$
Answer:
$$\frac{13}{24}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion only if the denominator contains prime factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should determine the nature of decimal expansions using prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$25 = 5^2$$
- $$20 = 2^2 \times 5$$
- $$24 = 2^3 \times 3$$
- $$40 = 2^3 \times 5$$
Since $$24$$ contains the prime factor $$3$$, its decimal expansion is non-terminating recurring.
Therefore, the correct answer is:
$$\frac{13}{24}$$
Exam Tip:
A denominator containing any prime factor other than 2 or 5 gives a non-terminating recurring decimal.
Q3. Evaluate:
$$3^4 \div 3^2$$
A) $$3^2$$
B) $$3^6$$
C) $$9^2$$
D) Both A and C
Answer:
Both A and C
Useful Formula for this Question:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should apply exponent laws correctly.
Step-by-Step Solution:
$$3^4 \div 3^2 = 3^{4-2}$$
$$= 3^2$$
Also,
$$9^2 = 81$$
and
$$3^2 = 9$$
Thus, $$9^2 \ne 3^2$$.
Therefore, only option A is correct.
Hence, the correct answer should be:
$$3^2$$
Exam Tip:
Always verify equivalent expressions numerically before choosing combined options.
Q4. Which of the following is a rational number?
A) $$\sqrt{50}$$
B) $$\sqrt{64}$$
C) $$\pi$$
D) $$\sqrt{13}$$
Answer:
$$\sqrt{64}$$
Useful Formula for this Question:
The square root of a perfect square is rational.
Concept Behind This Question:
Students should identify perfect squares correctly.
Step-by-Step Solution:
$$\sqrt{64} = 8$$
Since 8 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{64}$$
Exam Tip:
Perfect square roots are always rational numbers.
Q5. Simplify:
$$6^2 \times 6^3$$
A) $$6^5$$
B) $$6^6$$
C) $$12^5$$
D) $$36^3$$
Answer:
$$6^5$$
Useful Formula for this Question:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
This question checks students’ understanding of exponent laws.
Step-by-Step Solution:
$$6^2 \times 6^3 = 6^{2+3}$$
$$= 6^5$$
$$= 7776$$
Therefore, the correct answer is:
$$6^5$$
Exam Tip:
Add exponents when multiplying powers having the same base.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q \ne 0$$
2. Irrational Numbers
Cannot be expressed as:
$$\frac{p}{q}$$
3. Real Numbers
$$\text{Real Numbers = Rational Numbers + Irrational Numbers}$$
4. Laws of Exponents
$$a^m \times a^n = a^{m+n}$$
$$\frac{a^m}{a^n} = a^{m-n}$$
$$(a^m)^n = a^{mn}$$
5. Decimal Expansion Rule
A rational number has a terminating decimal expansion if its denominator contains only prime factors 2 and/or 5.
FAQs
1. What is an irrational number?
An irrational number cannot be expressed as a fraction.
2. Is $$\sqrt{64}$$ rational?
Yes, because $$\sqrt{64} = 8$$.
3. Are all irrational numbers real?
Yes, every irrational number is a real number.
4. What is a terminating decimal?
A decimal that ends after a finite number of digits.
5. Is every integer a rational number?
Yes, every integer can be written in the form $$\frac{p}{1}$$.
Common Mistakes
❌ Treating recurring decimals as irrational numbers.
❌ Forgetting to simplify fractions.
❌ Applying exponent laws incorrectly.
❌ Assuming all square roots are irrational.
❌ Not checking equivalent expressions carefully.
Quick Revision Notes
✔ Rational numbers can be expressed as fractions.
✔ Non-perfect square roots are irrational.
✔ Perfect square roots are rational.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ Apply exponent laws carefully.
Conclusion
Number Systems is a fundamental chapter in Class 9 Mathematics that helps students understand different categories of numbers and their properties. A strong understanding of rational numbers, irrational numbers, decimal expansions, and exponent laws improves mathematical reasoning and problem-solving skills. Regular MCQ practice enhances conceptual clarity and boosts exam performance.
Related Links
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