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Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn decimal expansion, irrational numbers, real numbers, exponents, and number representation 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 an important chapter in Class 9 Mathematics that introduces students to different categories of numbers and their properties. Concepts such as rational numbers, irrational numbers, decimal expansions, and laws of exponents form the basis of higher mathematics. A strong understanding of this chapter helps students solve mathematical problems accurately and efficiently.
What You Will Learn?
✔ Rational and Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion of Rational Numbers
✔ Laws of Exponents
✔ Number Representation on the Number Line
✔ Mathematical Reasoning
✔ Board Exam Preparation
Why This Topic Is Important?
The concepts of Number Systems are widely used in algebra, geometry, and advanced mathematics. Learning these concepts improves logical thinking and strengthens problem-solving abilities.
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 has a non-terminating recurring decimal expansion?
A) $$\frac{1}{8}$$
B) $$\frac{5}{16}$$
C) $$\frac{2}{3}$$
D) $$\frac{7}{20}$$
Answer:
$$\frac{2}{3}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion only if the denominator contains prime factors 2 and/or 5.
Concept Behind This Question:
Students should understand how the prime factorization of the denominator determines the type of decimal expansion.
Step-by-Step Solution:
- $$8 = 2^3$$ → Terminating decimal
- $$16 = 2^4$$ → Terminating decimal
- $$3$$ contains a prime factor other than 2 and 5 → Non-terminating recurring decimal
- $$20 = 2^2 \times 5$$ → Terminating decimal
Therefore, the correct answer is:
$$\frac{2}{3}$$
Exam Tip:
If the denominator contains any prime factor other than 2 or 5, the decimal expansion is non-terminating recurring.
Q2. Which of the following is an irrational number?
A) $$0.125$$
B) $$\frac{11}{13}$$
C) $$\sqrt{17}$$
D) $$0.272727\ldots$$
Answer:
$$\sqrt{17}$$
Useful Formula for this Question:
The square root of a non-perfect square is irrational.
Concept Behind This Question:
This question checks students’ understanding of irrational numbers.
Step-by-Step Solution:
- $$0.125 = \frac{1}{8}$$ is rational.
- $$\frac{11}{13}$$ is rational.
- $$0.272727\ldots$$ is a recurring decimal and hence rational.
- $$17$$ is not a perfect square.
Therefore:
$$\sqrt{17}$$ is irrational.
Exam Tip:
Recurring decimals are always rational numbers.
Q3. Simplify:
$$5^4 \div 5^2$$
A) $$5^6$$
B) $$5^2$$
C) $$25^2$$
D) $$10^2$$
Answer:
$$5^2$$
Useful Formula for this Question:
For the same base:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should know how to apply exponent laws while dividing powers.
Step-by-Step Solution:
$$5^4 \div 5^2 = 5^{4-2}$$
$$= 5^2$$
$$= 25$$
Therefore, the correct answer is:
$$5^2$$
Exam Tip:
When dividing powers with the same base, subtract the exponents.
Q4. Which of the following numbers is not a rational number?
A) $$-3$$
B) $$\frac{7}{11}$$
C) $$\sqrt{13}$$
D) $$0.75$$
Answer:
$$\sqrt{13}$$
Useful Formula for this Question:
Rational numbers can always be written in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
Students should distinguish between rational and irrational numbers.
Step-by-Step Solution:
- $$-3 = \frac{-3}{1}$$ is rational.
- $$\frac{7}{11}$$ is rational.
- $$0.75 = \frac{3}{4}$$ is rational.
- $$\sqrt{13}$$ is irrational because 13 is not a perfect square.
Therefore, the correct answer is:
$$\sqrt{13}$$
Exam Tip:
Every integer is also a rational number.
Q5. Which of the following statements is correct?
A) Every irrational number is rational.
B) Every rational number is irrational.
C) Every integer is a rational number.
D) Irrational numbers are integers.
Answer:
Every integer is a rational number.
Useful Formula for this Question:
Any integer $$n$$ can be written as:
$$\frac{n}{1}$$
Concept Behind This Question:
This question checks students’ understanding of the relationship between different number systems.
Step-by-Step Solution:
Any integer can be expressed in fractional form:
$$n = \frac{n}{1}$$
Therefore, every integer is a rational number.
The other statements are incorrect.
Hence, the correct answer is:
Every integer is a rational number.
Exam Tip:
Remember the hierarchy:
Natural Numbers ⊂ Integers ⊂ Rational Numbers ⊂ Real Numbers
Important Formulas & Concepts
1. Rational Number
$$\frac{p}{q}, \quad q \ne 0$$
2. Irrational Number
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
Terminating decimals occur only when the denominator contains factors 2 and/or 5 after simplification.
FAQs
1. What are irrational numbers?
Irrational numbers cannot be expressed in the form $$\frac{p}{q}$$.
2. Is every recurring decimal rational?
Yes, every recurring decimal is a rational number.
3. Is $$\sqrt{13}$$ irrational?
Yes, because 13 is not a perfect square.
4. Are integers rational numbers?
Yes, every integer is rational.
5. Which denominators give terminating decimals?
Denominators having only prime factors 2 and/or 5.
Common Mistakes
❌ Confusing recurring decimals with irrational numbers.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Applying exponent laws incorrectly.
❌ Assuming all square roots are irrational.
❌ Ignoring the denominator’s prime factors.
Quick Revision Notes
✔ Rational numbers can be written as fractions.
✔ Irrational numbers cannot be expressed as fractions.
✔ Recurring decimals are rational numbers.
✔ Non-perfect square roots are irrational.
✔ Apply exponent laws carefully.
Conclusion
Number Systems is a foundational chapter in Class 9 Mathematics that introduces students to different categories of numbers and their properties. Mastering concepts such as rational numbers, irrational numbers, decimal expansions, and exponents helps students build strong mathematical skills and perform well in examinations. Regular MCQ practice improves speed, accuracy, and conceptual clarity.
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