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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, 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 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. A thorough understanding of these concepts forms the foundation for algebra, geometry, and higher mathematics.
What You Will Learn?
✔ Rational Numbers
✔ Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion of Rational Numbers
✔ Laws of Exponents
✔ Number Representation on the Number Line
✔ Board Exam Preparation
Why This Topic Is Important?
The concepts of Number Systems are used extensively in mathematics. Understanding these concepts helps students improve logical thinking, analytical skills, and problem-solving abilities required in advanced topics.
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) $$\frac{13}{17}$$
B) $$0.625$$
C) $$\sqrt{18}$$
D) $$0.777\ldots$$
Answer:
$$\sqrt{18}$$
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 different numerical forms.
Step-by-Step Solution:
- $$\frac{13}{17}$$ is rational.
- $$0.625 = \frac{5}{8}$$ is rational.
- $$0.777\ldots = \frac{7}{9}$$ is rational.
- $$\sqrt{18} = 3\sqrt{2}$$ and $$\sqrt{2}$$ is irrational.
Therefore:
$$\sqrt{18}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{18}$$
Exam Tip:
If the number inside the square root is not a perfect square, the result is usually irrational.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{5}{24}$$
B) $$\frac{7}{32}$$
C) $$\frac{11}{27}$$
D) $$\frac{13}{42}$$
Answer:
$$\frac{7}{32}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion if the denominator contains only prime factors 2 and/or 5.
Concept Behind This Question:
Students should determine the type of decimal expansion using prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$24 = 2^3 \times 3$$
- $$32 = 2^5$$
- $$27 = 3^3$$
- $$42 = 2 \times 3 \times 7$$
Only $$32$$ contains the prime factor 2 only.
Therefore:
$$\frac{7}{32}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{7}{32}$$
Exam Tip:
A denominator containing only 2 and/or 5 always gives a terminating decimal.
Q3. Evaluate:
$$2^4 \times 2^3$$
A) $$2^7$$
B) $$2^{12}$$
C) $$4^7$$
D) $$8^2$$
Answer:
$$2^7$$
Useful Formula for this Question:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
This question checks understanding of multiplication laws of exponents.
Step-by-Step Solution:
$$2^4 \times 2^3 = 2^{4+3}$$
$$= 2^7$$
$$= 128$$
Therefore, the correct answer is:
$$2^7$$
Exam Tip:
When multiplying powers with the same base, add the exponents.
Q4. Which of the following numbers is rational?
A) $$\sqrt{81}$$
B) $$\pi$$
C) $$\sqrt{21}$$
D) $$\sqrt{6}$$
Answer:
$$\sqrt{81}$$
Useful Formula for this Question:
The square root of a perfect square is rational.
Concept Behind This Question:
Students should identify perfect squares and rational numbers.
Step-by-Step Solution:
$$\sqrt{81} = 9$$
Since 9 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{81}$$
Exam Tip:
Always check whether the number under the square root is a perfect square.
Q5. Simplify:
$$\frac{9^5}{9^3}$$
A) $$9^2$$
B) $$9^8$$
C) $$81^2$$
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:
$$\frac{9^5}{9^3} = 9^{5-3}$$
$$= 9^2$$
Also,
$$81^2 = (9^2)^2 = 9^4$$
Since $$81^2 \ne 9^2$$, option C is incorrect.
Therefore, the correct answer is:
$$9^2$$
Exam Tip:
After simplifying exponents, verify equivalent expressions carefully.
Important Correction
Note: Although option D says “Both A and C”, it is incorrect because:
$$81^2 = 6561$$
while
$$9^2 = 81$$
Hence, only option A is correct.
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 after simplification.
FAQs
1. What are irrational numbers?
Irrational numbers cannot be expressed as fractions.
2. Is $$\sqrt{81}$$ rational?
Yes, because $$\sqrt{81} = 9$$.
3. Which fractions have terminating decimals?
Fractions whose denominators contain only 2 and/or 5 after simplification.
4. Are all rational numbers real numbers?
Yes, every rational number is a real number.
5. Is $$\pi$$ irrational?
Yes, $$\pi$$ is an irrational number.
Common Mistakes
❌ Confusing rational and irrational numbers.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Applying exponent laws incorrectly.
❌ Assuming every square root is irrational.
❌ Not verifying equivalent expressions.
Quick Revision Notes
✔ Rational numbers can be written as fractions.
✔ Non-perfect square roots are irrational.
✔ Perfect square roots are rational.
✔ Every rational number is a real number.
✔ Use exponent laws carefully.
Conclusion
Number Systems is a foundational chapter in Class 9 Mathematics that introduces students to different sets of numbers and their properties. A strong understanding of rational numbers, irrational numbers, decimal expansions, and exponent laws helps students solve mathematical problems efficiently and perform well in examinations.
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