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Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn rational numbers, irrational numbers, decimal expansion, real numbers, and laws of exponents 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 important chapters in Class 9 Mathematics. It introduces students to rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents. These concepts form the basis of higher mathematics and help students solve mathematical problems efficiently.
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 used extensively in algebra, geometry, and arithmetic. A strong understanding of this chapter improves logical reasoning and prepares students for advanced mathematical concepts.
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) $$\frac{11}{18}$$
B) $$0.4$$
C) $$\sqrt{6}$$
D) $$0.999\ldots$$
Answer:
$$\sqrt{6}$$
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’ ability to distinguish between rational and irrational numbers.
Step-by-Step Solution:
- $$\frac{11}{18}$$ is rational.
- $$0.4 = \frac{2}{5}$$ is rational.
- $$0.999\ldots = 1$$ is rational.
- $$6$$ is not a perfect square.
Therefore:
$$\sqrt{6}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{6}$$
Exam Tip:
Recurring decimals are always rational numbers.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{13}{40}$$
B) $$\frac{7}{18}$$
C) $$\frac{11}{21}$$
D) $$\frac{5}{12}$$
Answer:
$$\frac{13}{40}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion if the denominator contains only prime factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should determine the nature of decimal expansion through prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$40 = 2^3 \times 5$$
- $$18 = 2 \times 3^2$$
- $$21 = 3 \times 7$$
- $$12 = 2^2 \times 3$$
Only $$40$$ contains prime factors 2 and 5 only.
Therefore:
$$\frac{13}{40}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{13}{40}$$
Exam Tip:
Check the denominator after simplification.
Q3. Evaluate:
$$3^5 \div 3^2$$
A) $$3^3$$
B) $$3^7$$
C) $$9^3$$
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 division laws of exponents correctly.
Step-by-Step Solution:
$$3^5 \div 3^2 = 3^{5-2}$$
$$= 3^3$$
$$= 27$$
Also,
$$9^3 = 729$$
Since:
$$9^3 \ne 3^3$$
Only option A is correct.
Therefore, the correct answer is:
$$3^3$$
Exam Tip:
Always verify equivalent expressions numerically.
Q4. Which of the following numbers is rational?
A) $$\sqrt{17}$$
B) $$\pi$$
C) $$\sqrt{144}$$
D) $$\sqrt{7}$$
Answer:
$$\sqrt{144}$$
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:
$$\sqrt{144} = 12$$
Since 12 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{144}$$
Exam Tip:
Perfect square roots are always rational numbers.
Q5. Simplify:
$$(2^4)^2$$
A) $$2^8$$
B) $$16^2$$
C) $$256$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
$$(a^m)^n = a^{mn}$$
Concept Behind This Question:
Students should apply the power of a power rule correctly.
Step-by-Step Solution:
$$(2^4)^2 = 2^{4 \times 2}$$
$$= 2^8$$
$$= 256$$
Also,
$$16^2 = 256$$
Hence:
$$2^8 = 16^2 = 256$$
Therefore, the correct answer is:
All of these
Exam Tip:
Different mathematical expressions may represent the same value.
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
$$a^m \times a^n = a^{m+n}$$
$$\frac{a^m}{a^n} = a^{m-n}$$
$$(a^m)^n = a^{mn}$$
$$a^0 = 1,\quad a \ne 0$$
5. Decimal Expansion Rule
A rational number has a terminating decimal expansion if its denominator contains only prime factors 2 and/or 5 after simplification.
FAQs
1. Is $$0.999\ldots$$ equal to 1?
Yes, $$0.999\ldots = 1$$.
2. Is every irrational number a real number?
Yes, every irrational number belongs to the set of real numbers.
3. Which square roots are rational?
Square roots of perfect squares are rational.
4. What is a terminating decimal?
A decimal that ends after a finite number of digits.
5. Can a number be both rational and irrational?
No, a number cannot be both rational and irrational.
Common Mistakes
❌ Treating recurring decimals as irrational.
❌ Forgetting exponent rules.
❌ Assuming all square roots are irrational.
❌ Ignoring denominator factorization.
❌ Selecting equivalent-looking options without verification.
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.
✔ Use exponent laws carefully.
✔ Every irrational number is a real number.
Conclusion
Number Systems is a foundational chapter in Class 9 Mathematics that helps students understand the properties and classification of numbers. A strong grasp of rational numbers, irrational numbers, decimal expansions, and exponent laws improves problem-solving skills and prepares students for advanced mathematical concepts. Regular MCQ practice enhances confidence, accuracy, and exam performance.
Related Links
- Class 9 Maths- Number Systems
- Class 9 Maths Chapter 1 Number Systems laws of exponents
- Class 9 Maths Chapter 1 Number Systems, irrational numbers
- Class 9 Maths Chapter 1 Number Systems, decimal expansion
- Class 9 Maths Chapter 1 Number Systems real numbers
- Class 9 Maths Chapter 1 Number Systems decimal expansion
- Class 9 Maths Chapter 1 Number Systems
- Class 9 Maths Chapter 1 Number Systems real numbers
- Class 9 Maths Chapter 1 Number Systems, irrational & rational numbers
- Class 9 Maths Decimal Expansion, Exponents
- Class9 Maths- Number Systems, decimal expansion, exponents
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