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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 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: Easy to Moderate
Based On: NCERT Latest Syllabus
Introduction:
Number Systems is one of the fundamental chapters in Class 9 Mathematics. It introduces students to different types of numbers such as natural numbers, integers, rational numbers, irrational numbers, and real numbers. Understanding this chapter helps students develop a strong mathematical foundation and improves problem-solving skills for higher classes.
What You Will Learn?
✔ Rational Numbers
✔ Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion
✔ Representation of Numbers on the Number Line
✔ Laws of Exponents
✔ Board Exam Preparation
Why This Topic Is Important?
Number Systems form the basis of many mathematical concepts used in algebra, geometry, and arithmetic. A clear understanding of rational and irrational numbers helps students solve advanced mathematical problems with confidence.
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) $$\frac{3}{5}$$
B) $$0.125$$
C) $$\sqrt{7}$$
D) $$0.666\ldots$$
Answer:
$$\sqrt{7}$$
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:
This question checks whether students can identify irrational numbers among different types of numbers.
Step-by-Step Solution:
- $$\frac{3}{5}$$ is rational.
- $$0.125 = \frac{1}{8}$$ is rational.
- $$0.666\ldots = \frac{2}{3}$$ is rational.
- $$\sqrt{7}$$ is the square root of a non-perfect square.
Therefore, $$\sqrt{7}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{7}$$
Exam Tip:
The square root of a non-perfect square is generally irrational.
Q2. Which of the following is a rational number?
A) $$\pi$$
B) $$\sqrt{11}$$
C) $$\frac{7}{9}$$
D) $$\sqrt{15}$$
Answer:
$$\frac{7}{9}$$
Useful Formula for this Question:
A rational number can be written in the form:
$$\frac{p}{q}, \quad q \ne 0$$
Concept Behind This Question:
Students should understand the definition and properties of rational numbers.
Step-by-Step Solution:
- $$\pi$$ is irrational.
- $$\sqrt{11}$$ is irrational.
- $$\frac{7}{9}$$ is of the form $$\frac{p}{q}$$.
- $$\sqrt{15}$$ is irrational.
Therefore, the rational number is:
$$\frac{7}{9}$$
Exam Tip:
Fractions with integers in the numerator and denominator are rational numbers.
Q3. The decimal expansion of $$\frac{3}{8}$$ is:
A) $$0.375$$
B) $$0.625$$
C) $$0.875$$
D) $$0.125$$
Answer:
$$0.375$$
Useful Formula for this Question:
Divide the numerator by the denominator to obtain the decimal form.
Concept Behind This Question:
This question tests students’ understanding of decimal expansion of rational numbers.
Step-by-Step Solution:
$$\frac{3}{8} = 3 \div 8$$
$$3 \div 8 = 0.375$$
Therefore, the decimal expansion is:
$$0.375$$
Hence, the correct answer is:
$$0.375$$
Exam Tip:
Fractions with denominators having only factors 2 and 5 produce terminating decimals.
Q4. Which of the following numbers is a real number?
A) $$\sqrt{2}$$
B) $$\frac{5}{6}$$
C) $$-7$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
Real numbers include both rational and irrational numbers.
Concept Behind This Question:
Students should know the classification of numbers under the real number system.
Step-by-Step Solution:
- $$\sqrt{2}$$ is irrational.
- $$\frac{5}{6}$$ is rational.
- $$-7$$ is an integer and therefore rational.
Since rational and irrational numbers together form real numbers, all the given numbers are real numbers.
Therefore, the correct answer is:
All of these
Exam Tip:
Every rational number and every irrational number is a real number.
Q5. Evaluate:
$$2^3 \times 2^2 = ?$$
A) $$2^5$$
B) $$2^6$$
C) $$4^5$$
D) $$8^2$$
Answer:
$$2^5$$
Useful Formula for this Question:
For the same bases:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
This question checks the application of laws of exponents.
Step-by-Step Solution:
$$2^3 \times 2^2 = 2^{3+2}$$
$$= 2^5$$
$$= 32$$
Therefore, the correct answer is:
$$2^5$$
Exam Tip:
When multiplying powers with the same base, add their exponents.
Important Formulas & Concepts
- Rational Number:
$$\frac{p}{q}, \quad q \ne 0$$
- Irrational Number:
Cannot be expressed as:
$$\frac{p}{q}$$
- Real Numbers:
$$\text{Real Numbers = Rational Numbers + Irrational Numbers}$$
- Laws of Exponents:
$$a^m \times a^n = a^{m+n}$$
$$\frac{a^m}{a^n} = a^{m-n}$$
$$\left(a^m\right)^n = a^{mn}$$
- Decimal Expansion:
A rational number has a terminating decimal expansion if the denominator has only factors 2 and/or 5.
FAQs
1. What are real numbers?
Real numbers include all rational and irrational numbers.
2. What is an irrational number?
An irrational number cannot be expressed in the form $$\frac{p}{q}$$.
3. Is $$\sqrt{2}$$ irrational?
Yes, $$\sqrt{2}$$ is an irrational number.
4. Which numbers have terminating decimal expansions?
Numbers whose denominators contain only factors 2 and/or 5.
5. Is every integer a rational number?
Yes, every integer can be written in the form $$\frac{p}{q}$$.
Common Mistakes
❌ Assuming every decimal number is irrational.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Confusing rational numbers with integers.
❌ Applying exponent rules incorrectly.
❌ Treating non-perfect square roots as rational numbers.
Quick Revision Notes
✔ Rational numbers can be expressed as $$\frac{p}{q}$$.
✔ Irrational numbers cannot be expressed as fractions.
✔ Real numbers include rational and irrational numbers.
✔ Denominators containing only 2 and 5 produce terminating decimals.
✔ Use exponent laws carefully while simplifying expressions.
Conclusion
Number Systems is an essential chapter in Class 9 Mathematics that builds the foundation for advanced mathematical concepts. Mastering rational numbers, irrational numbers, decimal expansions, and exponent laws helps students perform better in school and board examinations. Regular practice of MCQs improves conceptual understanding and increases confidence in solving mathematical problems.
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