Welcome To My School Study
Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn real numbers, irrational numbers, decimal expansion, exponents, and rational numbers with detailed solutions for CBSE board exams.
Do You Know
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 fundamental chapters in Class 9 Mathematics. It introduces students to rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents. A strong understanding of these concepts helps students solve mathematical problems accurately and forms the basis for higher-level 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 throughout mathematics. Understanding different types of numbers and their properties improves logical thinking and problem-solving skills 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) $$\frac{11}{20}$$
B) $$0.625$$
C) $$\sqrt{31}$$
D) $$0.777\ldots$$
Answer:
$$\sqrt{31}$$
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 tests students’ understanding of irrational numbers.
Step-by-Step Solution:
- $$\frac{11}{20}$$ is rational.
- $$0.625 = \frac{5}{8}$$ is rational.
- $$0.777\ldots = \frac{7}{9}$$ is rational.
- $$31$$ is not a perfect square.
Therefore:
$$\sqrt{31}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{31}$$
Exam Tip:
Square roots of non-perfect squares are always irrational.
Q2. Which of the following fractions has a non-terminating recurring decimal expansion?
A) $$\frac{7}{8}$$
B) $$\frac{9}{20}$$
C) $$\frac{5}{14}$$
D) $$\frac{11}{25}$$
Answer:
$$\frac{5}{14}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion only if its denominator contains prime factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should identify the nature of decimal expansions using prime factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$8 = 2^3$$
- $$20 = 2^2 \times 5$$
- $$14 = 2 \times 7$$
- $$25 = 5^2$$
Since $$14$$ contains the prime factor $$7$$ in addition to $$2$$, its decimal expansion is non-terminating recurring.
Therefore, the correct answer is:
$$\frac{5}{14}$$
Exam Tip:
If the denominator contains any prime factor other than 2 or 5, the decimal expansion becomes non-terminating recurring.
Q3. Simplify:
$$(4^2)^3$$
A) $$4^5$$
B) $$4^6$$
C) $$8^3$$
D) $$16^3$$
Answer:
$$4^6$$
Useful Formula for this Question:
$$(a^m)^n = a^{mn}$$
Concept Behind This Question:
This question checks students’ understanding of exponent laws.
Step-by-Step Solution:
$$(4^2)^3 = 4^{2 \times 3}$$
$$= 4^6$$
Therefore, the correct answer is:
$$4^6$$
Exam Tip:
When a power is raised to another power, multiply the exponents.
Q4. Which of the following numbers is irrational?
A) $$\sqrt{64}$$
B) $$\sqrt{50}$$
C) $$\frac{13}{17}$$
D) $$0.4$$
Answer:
$$\sqrt{50}$$
Useful Formula for this Question:
The square root of a non-perfect square is irrational.
Concept Behind This Question:
Students should determine whether the given square roots are perfect squares.
Step-by-Step Solution:
- $$\sqrt{64} = 8$$ is rational.
- $$\sqrt{50} = 5\sqrt{2}$$ and $$\sqrt{2}$$ is irrational.
- $$\frac{13}{17}$$ is rational.
- $$0.4 = \frac{2}{5}$$ is rational.
Therefore:
$$\sqrt{50}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{50}$$
Exam Tip:
Always check whether the number under the square root is a perfect square.
Q5. Which of the following statements is true?
A) Every irrational number is an integer.
B) Every real number is rational.
C) Every rational number is a real number.
D) Every whole number is irrational.
Answer:
Every rational number is a real number.
Useful Formula for this Question:
$$\text{Real Numbers = Rational Numbers + Irrational Numbers}$$
Concept Behind This Question:
Students should understand the relationship between different sets of numbers.
Step-by-Step Solution:
- Irrational numbers are not integers.
- Real numbers include both rational and irrational numbers.
- Every rational number belongs to the set of real numbers.
- Whole numbers are rational numbers.
Therefore, the correct answer is:
Every rational number is a real number.
Exam Tip:
Remember the hierarchy:
$$\text{Natural Numbers} \subset \text{Whole Numbers} \subset \text{Integers} \subset \text{Rational Numbers} \subset \text{Real Numbers}$$
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 has a terminating decimal expansion if the denominator contains only prime factors 2 and/or 5.
FAQs
1. What are real numbers?
Real numbers include all rational and irrational numbers.
2. Is $$\sqrt{50}$$ irrational?
Yes, because it contains $$\sqrt{2}$$, which is irrational.
3. What is a terminating decimal?
A decimal that ends after a finite number of digits.
4. Are all integers rational numbers?
Yes, because every integer can be written as $$\frac{p}{1}$$.
5. Can a rational number be irrational?
No, a number cannot be both rational and irrational.
Common Mistakes
❌ Assuming every square root is irrational.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Applying exponent laws incorrectly.
❌ Confusing real numbers with rational numbers.
❌ Ignoring the hierarchy of number systems.
Quick Revision Notes
✔ Rational numbers can be expressed as fractions.
✔ Irrational numbers cannot be written as fractions.
✔ Every rational number is a real number.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ Apply exponent rules carefully.
Conclusion
Number Systems is a foundational chapter in Class 9 Mathematics that helps students understand the classification and properties of numbers. A strong grasp of rational numbers, irrational numbers, decimal expansions, and exponent laws is essential for solving advanced mathematical problems. Regular MCQ practice improves conceptual clarity, accuracy, and confidence for examinations.
Related Links
- Class 9 Maths Decimal Expansion, Exponents
- Class9 Maths- Number Systems, decimal expansion, exponents
- Class 9 Maths Chapter 1 Number Systems MCQ with Solutions
- Class 9 Maths Chapter 1 Number Systems MCQ Q&A, Solutions
- Class 9 SST: Deccan Plateau, Fundamental Rights
- Class 9 Science: Evaporation, Pressure, Atomic Structure
- Class 9 Science: Boiling, Momentum, Electron, Speed and Parenchyma
- Class 9 Science MCQ Quiz: Force, Mole Concept, Motion and Plant Tissues
- Class 9 MCQ Questions Answers– History, Geography, Civics
- Class 9 SST MCQs with Detailed Explanations
Latest Posts
- Class 7 Maths Chapter 1 Integers, number line, subtraction
- Class 8 Maths additive inverse, multiplicative inverse MCQ
- Class 9 Maths Chapter 1 Number Systems laws of exponents
- Class 10 Maths Chapter 2 Polynomials MCQ linear polynomial
- Class 10 Maths Chapter 2 Polynomials, linear polynomial
Join Our Other Communities
Instagram , Youtube , Facebook
