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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 a foundational chapter in Class 9 Mathematics that introduces students to rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents. A clear understanding of these concepts helps students build strong mathematical reasoning and prepares them for advanced topics in higher classes.
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 study of Number Systems helps students understand the classification and properties of numbers. These concepts are widely used in algebra, geometry, and many real-life applications of mathematics.
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) $$\frac{7}{10}$$
B) $$0.45$$
C) $$\sqrt{14}$$
D) $$0.2222\ldots$$
Answer:
$$\sqrt{14}$$
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:
- $$\frac{7}{10}$$ is rational.
- $$0.45 = \frac{45}{100} = \frac{9}{20}$$ is rational.
- $$0.2222\ldots = \frac{2}{9}$$ is rational.
- $$14$$ is not a perfect square.
Therefore:
$$\sqrt{14}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{14}$$
Exam Tip:
The square root of a non-perfect square is always irrational.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{9}{14}$$
B) $$\frac{11}{16}$$
C) $$\frac{7}{18}$$
D) $$\frac{13}{21}$$
Answer:
$$\frac{11}{16}$$
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 analyze the denominator to determine the type of decimal expansion.
Step-by-Step Solution:
Prime factorization of denominators:
- $$14 = 2 \times 7$$
- $$16 = 2^4$$
- $$18 = 2 \times 3^2$$
- $$21 = 3 \times 7$$
Only $$16$$ contains the prime factor 2 only.
Therefore:
$$\frac{11}{16}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{11}{16}$$
Exam Tip:
After simplification, denominators with only 2 and/or 5 give terminating decimals.
Q3. Simplify:
$$(3^2)^4$$
A) $$3^6$$
B) $$3^8$$
C) $$9^4$$
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 law of exponents correctly.
Step-by-Step Solution:
$$(3^2)^4 = 3^{2 \times 4}$$
$$= 3^8$$
Also,
$$9^4 = (3^2)^4 = 3^8$$
Therefore, both expressions are equal.
Hence, the correct answer is:
Both B and C
Exam Tip:
Multiply exponents when a power is raised to another power.
Q4. Which of the following numbers is a real number?
A) $$\sqrt{10}$$
B) $$-\frac{3}{8}$$
C) $$12$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Real numbers include rational and irrational numbers.
Concept Behind This Question:
This question checks understanding of the real number system.
Step-by-Step Solution:
- $$\sqrt{10}$$ is irrational but real.
- $$-\frac{3}{8}$$ is rational and real.
- $$12$$ is an integer and hence real.
Therefore, all the given numbers are real numbers.
Hence, the correct answer is:
All of these
Exam Tip:
Every rational number and irrational number belongs to the set of real numbers.
Q5. Evaluate:
$$6^2 \div 6^1$$
A) $$6$$
B) $$6^2$$
C) $$12$$
D) $$1$$
Answer:
$$6$$
Useful Formula for this Question:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should apply exponent laws while dividing powers.
Step-by-Step Solution:
$$6^2 \div 6^1 = 6^{2-1}$$
$$= 6^1$$
$$= 6$$
Therefore, the correct answer is:
$$6$$
Exam Tip:
Subtract exponents while dividing powers with the same base.
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
$$a^m \times a^n = a^{m+n}$$
$$\frac{a^m}{a^n} = a^{m-n}$$
$$(a^m)^n = a^{mn}$$
5. Decimal Expansion Rule
A rational number terminates if the denominator contains only prime factors 2 and/or 5 after simplification.
FAQs
1. What are real numbers?
Real numbers include all rational and irrational numbers.
2. Is $$\sqrt{10}$$ irrational?
Yes, because 10 is not a perfect square.
3. What is a terminating decimal?
A decimal that ends after a finite number of digits.
4. Are integers rational numbers?
Yes, every integer is a rational number.
5. Which fractions produce terminating decimals?
Fractions whose denominators contain only 2 and/or 5 after simplification.
Common Mistakes
❌ Treating recurring decimals as irrational numbers.
❌ Forgetting to simplify fractions.
❌ Applying exponent laws incorrectly.
❌ Assuming irrational numbers are not real numbers.
❌ Ignoring prime factorization of denominators.
Quick Revision Notes
✔ Rational numbers can be written in the form $$\frac{p}{q}$$.
✔ Non-perfect square roots are irrational.
✔ Every rational number is a real number.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ Use exponent laws carefully.
Conclusion
Number Systems is an essential chapter in Class 9 Mathematics that develops students’ understanding of different types of numbers and their properties. A strong grasp of rational numbers, irrational numbers, real numbers, and exponent laws helps students solve mathematical problems confidently and perform well in examinations. Regular MCQ practice improves conceptual clarity and analytical skills.
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