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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, 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
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, and real numbers along with their properties. Understanding these concepts helps students solve mathematical problems efficiently and prepares them for higher-level mathematics.
What You Will Learn?
✔ Rational Numbers
✔ Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion
✔ Laws of Exponents
✔ Representation of Numbers on the Number Line
✔ Board Exam Preparation
Why This Topic Is Important?
Number Systems provide the foundation for many topics in mathematics. A clear understanding of number classification and exponent laws improves logical reasoning and problem-solving skills.
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) $$\frac{9}{11}$$
B) $$0.625$$
C) $$\sqrt{19}$$
D) $$0.333\ldots$$
Answer:
$$\sqrt{19}$$
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 tests students’ ability to identify irrational numbers.
Step-by-Step Solution:
- $$\frac{9}{11}$$ is rational.
- $$0.625 = \frac{5}{8}$$ is rational.
- $$0.333\ldots = \frac{1}{3}$$ is rational.
- $$19$$ is not a perfect square.
Therefore:
$$\sqrt{19}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{19}$$
Exam Tip:
Square roots of non-perfect squares are irrational numbers.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{7}{12}$$
B) $$\frac{9}{25}$$
C) $$\frac{5}{18}$$
D) $$\frac{11}{21}$$
Answer:
$$\frac{9}{25}$$
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 know how denominator factorization determines decimal expansion.
Step-by-Step Solution:
- $$12 = 2^2 \times 3$$ → Contains 3
- $$25 = 5^2$$ → Only factor 5
- $$18 = 2 \times 3^2$$ → Contains 3
- $$21 = 3 \times 7$$ → Contains 3 and 7
Only $$\frac{9}{25}$$ has a terminating decimal expansion.
Therefore, the correct answer is:
$$\frac{9}{25}$$
Exam Tip:
Always simplify the fraction before checking the denominator.
Q3. Evaluate:
$$3^2 \times 3^4$$
A) $$3^6$$
B) $$3^8$$
C) $$9^4$$
D) $$6^3$$
Answer:
$$3^6$$
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:
$$3^2 \times 3^4 = 3^{2+4}$$
$$= 3^6$$
$$= 729$$
Therefore, the correct answer is:
$$3^6$$
Exam Tip:
When multiplying powers with the same base, add the exponents.
Q4. Which of the following is a real number?
A) $$\sqrt{3}$$
B) $$-\frac{4}{7}$$
C) $$8$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Real numbers include all rational and irrational numbers.
Concept Behind This Question:
Students should understand the classification of real numbers.
Step-by-Step Solution:
- $$\sqrt{3}$$ is irrational.
- $$-\frac{4}{7}$$ is rational.
- $$8$$ is an integer and hence rational.
All these numbers belong to the set of real numbers.
Therefore, the correct answer is:
All of these
Exam Tip:
Every rational number and irrational number is a real number.
Q5. Simplify:
$$(2^3)^2$$
A) $$2^5$$
B) $$2^6$$
C) $$4^3$$
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 of a power rule correctly.
Step-by-Step Solution:
$$(2^3)^2 = 2^{3 \times 2}$$
$$= 2^6$$
Also,
$$4^3 = 64$$
and
$$2^6 = 64$$
Therefore, both options represent the same value.
Hence, 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
Numbers that 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 terminates only if its denominator contains prime factors 2 and/or 5.
FAQs
1. What are real numbers?
Real numbers include both rational and irrational numbers.
2. Is $$\sqrt{19}$$ irrational?
Yes, because 19 is not a perfect square.
3. Can a recurring decimal be rational?
Yes, every recurring decimal is rational.
4. What are terminating decimals?
Decimals that end after a finite number of digits.
5. Is every integer a real number?
Yes, every integer is a real number.
Common Mistakes
❌ Treating recurring decimals as irrational numbers.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Applying exponent rules incorrectly.
❌ Assuming all square roots are irrational.
❌ Confusing rational numbers with real numbers.
Quick Revision Notes
✔ Rational numbers can be written as fractions.
✔ Non-perfect square roots are irrational.
✔ Real numbers include rational and irrational numbers.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ Apply exponent laws carefully.
Conclusion
Number Systems is an essential chapter that builds the foundation for advanced mathematical concepts. Understanding rational numbers, irrational numbers, real numbers, and exponent laws helps students improve their analytical skills and perform well in examinations. Regular MCQ practice strengthens conceptual understanding and boosts confidence.
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