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Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn irrational numbers, decimal expansion, laws of exponents, and real 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 a fundamental chapter in Class 9 Mathematics that introduces students to rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents. These concepts are essential for understanding higher-level mathematics and solving real-life numerical problems.
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?
The concepts of Number Systems are used extensively in mathematics and science. A strong understanding of this chapter improves logical reasoning, analytical 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) $$\frac{4}{11}$$
B) $$0.375$$
C) $$\sqrt{12}$$
D) $$0.666\ldots$$
Answer:
$$\sqrt{12}$$
Useful Formula for this Question:
An irrational number cannot be written in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
This question checks whether students can identify irrational numbers.
Step-by-Step Solution:
- $$\frac{4}{11}$$ is rational.
- $$0.375 = \frac{3}{8}$$ is rational.
- $$0.666\ldots = \frac{2}{3}$$ is rational.
- $$\sqrt{12} = 2\sqrt{3}$$ and $$\sqrt{3}$$ is irrational.
Therefore:
$$\sqrt{12}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{12}$$
Exam Tip:
Square roots of non-perfect squares are irrational numbers.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{7}{45}$$
B) $$\frac{9}{125}$$
C) $$\frac{11}{18}$$
D) $$\frac{13}{42}$$
Answer:
$$\frac{9}{125}$$
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 expansions using prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$45 = 3^2 \times 5$$
- $$125 = 5^3$$
- $$18 = 2 \times 3^2$$
- $$42 = 2 \times 3 \times 7$$
Only $$125$$ contains the prime factor 5 only.
Therefore:
$$\frac{9}{125}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{9}{125}$$
Exam Tip:
Always simplify the fraction before checking the denominator.
Q3. Evaluate:
$$4^3 \times 4^2$$
A) $$4^5$$
B) $$4^6$$
C) $$8^5$$
D) $$16^2$$
Answer:
$$4^5$$
Useful Formula for this Question:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
This question checks the application of multiplication laws of exponents.
Step-by-Step Solution:
$$4^3 \times 4^2 = 4^{3+2}$$
$$= 4^5$$
$$= 1024$$
Therefore, the correct answer is:
$$4^5$$
Exam Tip:
Add exponents while multiplying powers with the same base.
Q4. Which of the following numbers is rational?
A) $$\sqrt{28}$$
B) $$\pi$$
C) $$\sqrt{100}$$
D) $$\sqrt{15}$$
Answer:
$$\sqrt{100}$$
Useful Formula for this Question:
The square root of a perfect square is rational.
Concept Behind This Question:
Students should identify rational numbers correctly.
Step-by-Step Solution:
$$\sqrt{100} = 10$$
Since 10 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{100}$$
Exam Tip:
Perfect square roots are always rational numbers.
Q5. Simplify:
$$(5^2)^3$$
A) $$5^5$$
B) $$5^6$$
C) $$25^3$$
D) Both B and C
Answer:
Both B and C
Useful Formula for this Question:
$$(a^m)^n = a^{mn}$$
Concept Behind This Question:
Students should apply the power law of exponents correctly.
Step-by-Step Solution:
$$(5^2)^3 = 5^{2 \times 3}$$
$$= 5^6$$
Also,
$$25^3 = (5^2)^3 = 5^6$$
Thus, both expressions are equal.
Therefore, the correct answer is:
Both B and C
Exam Tip:
When a power is raised to another power, multiply the exponents.
Important Formulas & Concepts
1. Rational Numbers
$$\frac{p}{q}, \quad q \ne 0$$
2. Irrational Numbers
Cannot be expressed in the form:
$$\frac{p}{q}$$
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 are rational numbers?
Rational numbers can be written in the form $$\frac{p}{q}$$ where $$q \ne 0$$.
2. Is $$\pi$$ a real number?
Yes, $$\pi$$ is an irrational real number.
3. Which square roots are rational?
Square roots of perfect squares are rational.
4. What are terminating decimals?
Decimals that end after a finite number of digits.
5. Are all irrational numbers real?
Yes, every irrational number is a real number.
Common Mistakes
❌ Confusing rational and irrational numbers.
❌ Forgetting to simplify fractions.
❌ Applying exponent laws incorrectly.
❌ Assuming every decimal is irrational.
❌ Ignoring perfect squares.
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.
Conclusion
Number Systems is an important chapter in Class 9 Mathematics that forms the foundation for advanced mathematical concepts. Understanding rational numbers, irrational numbers, decimal expansions, and exponents helps students develop strong problem-solving skills and achieve better results in examinations. Regular MCQ practice strengthens concepts and boosts confidence.
Related Links
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