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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, real numbers, decimal expansion, and laws of exponents with concept-based 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 advanced mathematical topics and improving problem-solving abilities.
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. Understanding these concepts strengthens logical reasoning and builds a strong foundation for algebra and geometry.
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) $$\frac{13}{25}$$
B) $$0.125$$
C) $$\sqrt{15}$$
D) $$0.4444\ldots$$
Answer:
$$\sqrt{15}$$
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:
Students should identify irrational numbers among various forms.
Step-by-Step Solution:
- $$\frac{13}{25}$$ is rational.
- $$0.125 = \frac{1}{8}$$ is rational.
- $$0.4444\ldots = \frac{4}{9}$$ is rational.
- $$15$$ is not a perfect square.
Therefore:
$$\sqrt{15}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{15}$$
Exam Tip:
The square roots of non-perfect squares are irrational numbers.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{11}{45}$$
B) $$\frac{7}{125}$$
C) $$\frac{13}{24}$$
D) $$\frac{17}{28}$$
Answer:
$$\frac{7}{125}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion if its denominator contains only prime factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should determine decimal expansion using prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$45 = 3^2 \times 5$$
- $$125 = 5^3$$
- $$24 = 2^3 \times 3$$
- $$28 = 2^2 \times 7$$
Only $$125$$ contains prime factor 5 only.
Therefore:
$$\frac{7}{125}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{7}{125}$$
Exam Tip:
A denominator containing only 2 and/or 5 gives a terminating decimal.
Q3. Evaluate:
$$8^2 \div 8^1$$
A) $$8$$
B) $$8^2$$
C) $$16$$
D) $$1$$
Answer:
$$8$$
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:
$$8^2 \div 8^1 = 8^{2-1}$$
$$= 8^1$$
$$= 8$$
Therefore, the correct answer is:
$$8$$
Exam Tip:
Subtract exponents when dividing powers with the same base.
Q4. Which of the following is a rational number?
A) $$\sqrt{32}$$
B) $$\pi$$
C) $$\sqrt{169}$$
D) $$\sqrt{19}$$
Answer:
$$\sqrt{169}$$
Useful Formula for this Question:
The square root of a perfect square is rational.
Concept Behind This Question:
Students should identify perfect squares.
Step-by-Step Solution:
$$\sqrt{169} = 13$$
Since 13 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{169}$$
Exam Tip:
Perfect square roots are always rational numbers.
Q5. Simplify:
$$(3^2)^3$$
A) $$3^6$$
B) $$9^3$$
C) $$729$$
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 law of exponents.
Step-by-Step Solution:
$$(3^2)^3 = 3^{2 \times 3}$$
$$= 3^6$$
$$= 729$$
Also,
$$9^3 = 729$$
Therefore:
$$3^6 = 9^3 = 729$$
Hence, the correct answer is:
All of these
Exam Tip:
Equivalent expressions may have different forms but 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 terminates only when the denominator contains prime factors 2 and/or 5 after simplification.
FAQs
1. What are irrational numbers?
Irrational numbers cannot be expressed as fractions.
2. Is $$\sqrt{169}$$ rational?
Yes, because $$\sqrt{169} = 13$$.
3. Is every integer a rational number?
Yes, every integer can be written in the form $$\frac{p}{1}$$.
4. Which fractions have terminating decimals?
Fractions whose denominators contain only 2 and/or 5 after simplification.
5. Are irrational numbers real numbers?
Yes, all irrational numbers are real numbers.
Common Mistakes
❌ Treating non-terminating recurring decimals as irrational.
❌ Forgetting exponent laws.
❌ Assuming all square roots are irrational.
❌ Ignoring denominator factorization.
❌ Not simplifying expressions completely.
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.
✔ Every irrational number is a real number.
Conclusion
Number Systems is one of the most important chapters in Class 9 Mathematics. A strong understanding of rational numbers, irrational numbers, decimal expansions, and exponent laws helps students solve mathematical problems efficiently and perform well in examinations. Regular MCQ practice improves accuracy, confidence, and conceptual understanding.
Related Links
- Class 9 Maths – Number Systems, real numbers
- 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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