Welcome To My School Study
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.
Do You Know
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 strong understanding of these concepts builds a solid foundation for algebra and higher mathematics.
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 concepts of Number Systems are widely used in mathematics. Understanding these concepts helps students improve analytical thinking, logical reasoning, and problem-solving skills.
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) $$\frac{8}{15}$$
B) $$0.625$$
C) $$\sqrt{27}$$
D) $$0.121212\ldots$$
Answer:
$$\sqrt{27}$$
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 representations.
Step-by-Step Solution:
- $$\frac{8}{15}$$ is rational.
- $$0.625 = \frac{5}{8}$$ is rational.
- $$0.121212\ldots$$ is recurring and hence rational.
- $$\sqrt{27} = 3\sqrt{3}$$ and $$\sqrt{3}$$ is irrational.
Therefore:
$$\sqrt{27}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{27}$$
Exam Tip:
Square roots of non-perfect squares are irrational numbers.
Q2. Which of the following fractions has a non-terminating recurring decimal expansion?
A) $$\frac{11}{50}$$
B) $$\frac{7}{25}$$
C) $$\frac{13}{30}$$
D) $$\frac{9}{40}$$
Answer:
$$\frac{13}{30}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion only if the denominator contains prime factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should determine the type of decimal expansion using denominator factorization.
Step-by-Step Solution:
Prime factorization of denominators:
- $$50 = 2 \times 5^2$$
- $$25 = 5^2$$
- $$30 = 2 \times 3 \times 5$$
- $$40 = 2^3 \times 5$$
Since $$30$$ contains the prime factor $$3$$ along with 2 and 5, its decimal expansion is non-terminating recurring.
Therefore, the correct answer is:
$$\frac{13}{30}$$
Exam Tip:
A denominator containing any prime factor other than 2 or 5 produces a non-terminating recurring decimal.
Q3. Evaluate:
$$7^2 \times 7^3$$
A) $$7^5$$
B) $$7^6$$
C) $$14^5$$
D) $$49^3$$
Answer:
$$7^5$$
Useful Formula for this Question:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
This question checks the application of exponent laws.
Step-by-Step Solution:
$$7^2 \times 7^3 = 7^{2+3}$$
$$= 7^5$$
$$= 16807$$
Therefore, the correct answer is:
$$7^5$$
Exam Tip:
Add exponents while multiplying powers having the same base.
Q4. Which of the following is an irrational number?
A) $$\sqrt{49}$$
B) $$\frac{9}{16}$$
C) $$\sqrt{11}$$
D) $$0.75$$
Answer:
$$\sqrt{11}$$
Useful Formula for this Question:
The square root of a non-perfect square is irrational.
Concept Behind This Question:
Students should identify irrational numbers correctly.
Step-by-Step Solution:
- $$\sqrt{49} = 7$$ is rational.
- $$\frac{9}{16}$$ is rational.
- $$0.75 = \frac{3}{4}$$ is rational.
- $$11$$ is not a perfect square.
Therefore:
$$\sqrt{11}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{11}$$
Exam Tip:
Perfect square roots are rational, while non-perfect square roots are usually irrational.
Q5. Simplify:
$$\frac{8^5}{8^3}$$
A) $$8^2$$
B) $$8^8$$
C) $$64^2$$
D) Both A and C
Answer:
$$8^2$$
Useful Formula for this Question:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should apply division laws of exponents correctly.
Step-by-Step Solution:
$$\frac{8^5}{8^3} = 8^{5-3}$$
$$= 8^2$$
$$= 64$$
Now,
$$64^2 = 4096$$
Thus,
$$64^2 \ne 8^2$$
Therefore, only option A is correct.
Hence, the correct answer is:
$$8^2$$
Exam Tip:
Always verify equivalent expressions before selecting options like “Both A and C.”
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 terminates only if its denominator contains prime factors 2 and/or 5 after simplification.
FAQs
1. What are irrational numbers?
Irrational numbers cannot be expressed as fractions.
2. Is $$\sqrt{11}$$ irrational?
Yes, because 11 is not a perfect square.
3. Are all rational numbers real numbers?
Yes, every rational number is a real number.
4. Which fractions have terminating decimals?
Fractions whose denominators contain only prime factors 2 and/or 5.
5. Can an irrational number be expressed as a fraction?
No, irrational numbers cannot be written in the form $$\frac{p}{q}$$.
Common Mistakes
❌ Treating recurring decimals as irrational numbers.
❌ Ignoring denominator factorization.
❌ Applying exponent rules incorrectly.
❌ Assuming all square roots are irrational.
❌ Selecting equivalent-looking options without verification.
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.
✔ Apply exponent laws carefully.
Conclusion
Number Systems is a fundamental chapter in Class 9 Mathematics that introduces students to different categories of numbers and their properties. A strong understanding of rational numbers, irrational numbers, decimal expansions, and exponents helps students develop problem-solving skills and perform well in examinations. Regular MCQ practice strengthens concepts and boosts confidence.
Related Links
- Class 9 Maths Chapter 1 Number Systems decimal expansion
- Class 9 Maths Chapter 1 Number Systems
- Class 9 Maths Chapter 1 Number Systems real numbers
- Class 9 Maths Chapter 1 Number Systems, irrational & rational numbers
- 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 Science: Boiling, Momentum, Electron, Speed and Parenchyma
- Class 9 Science MCQ Quiz: Force, Mole Concept, Motion and Plant Tissues
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
