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 expansions, and laws of exponents with concept-based 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 forms the 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 and science. Understanding these concepts helps students develop logical reasoning and analytical skills required for advanced studies.
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) $$\frac{7}{12}$$
B) $$0.25$$
C) $$\sqrt{45}$$
D) $$0.8888\ldots$$
Answer:
$$\sqrt{45}$$
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 correctly.
Step-by-Step Solution:
- $$\frac{7}{12}$$ is rational.
- $$0.25 = \frac{1}{4}$$ is rational.
- $$0.8888\ldots = \frac{8}{9}$$ is rational.
- $$\sqrt{45} = 3\sqrt{5}$$ and $$\sqrt{5}$$ is irrational.
Therefore:
$$\sqrt{45}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{45}$$
Exam Tip:
The square root of a non-perfect square is irrational.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{11}{15}$$
B) $$\frac{7}{50}$$
C) $$\frac{13}{18}$$
D) $$\frac{17}{21}$$
Answer:
$$\frac{7}{50}$$
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 know how denominator factorization determines decimal expansion.
Step-by-Step Solution:
Prime factorization of denominators:
- $$15 = 3 \times 5$$
- $$50 = 2 \times 5^2$$
- $$18 = 2 \times 3^2$$
- $$21 = 3 \times 7$$
Only $$50$$ contains prime factors 2 and 5 only.
Therefore:
$$\frac{7}{50}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{7}{50}$$
Exam Tip:
Always simplify fractions before checking the denominator.
Q3. Evaluate:
$$2^6 \div 2^2$$
A) $$2^3$$
B) $$2^4$$
C) $$4^2$$
D) Both B and C
Answer:
Both B and C
Useful Formula for this Question:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should apply exponent laws correctly.
Step-by-Step Solution:
$$2^6 \div 2^2 = 2^{6-2}$$
$$= 2^4$$
Also,
$$4^2 = 16$$
and
$$2^4 = 16$$
Thus, both expressions are equal.
Therefore, the correct answer is:
Both B and C
Exam Tip:
Always verify equivalent expressions numerically.
Q4. Which of the following numbers is rational?
A) $$\sqrt{72}$$
B) $$\pi$$
C) $$\sqrt{49}$$
D) $$\sqrt{10}$$
Answer:
$$\sqrt{49}$$
Useful Formula for this Question:
The square root of a perfect square is rational.
Concept Behind This Question:
Students should identify perfect squares correctly.
Step-by-Step Solution:
$$\sqrt{49} = 7$$
Since 7 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{49}$$
Exam Tip:
Square roots of perfect squares are rational numbers.
Q5. Simplify:
$$(7^2)^2$$
A) $$7^4$$
B) $$49^2$$
C) $$2401$$
D) All of these
Answer:
All of these
Useful Formula for this Question:
$$(a^m)^n = a^{mn}$$
Concept Behind This Question:
This question checks the application of exponent laws.
Step-by-Step Solution:
$$(7^2)^2 = 7^{2 \times 2}$$
$$= 7^4$$
$$= 2401$$
Also,
$$49^2 = 2401$$
Hence,
$$7^4 = 49^2 = 2401$$
Therefore, the correct answer is:
All of these
Exam Tip:
Different expressions may represent the same numerical value.
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 has a terminating decimal expansion if its denominator contains only prime factors 2 and/or 5 after simplification.
FAQs
1. What are rational numbers?
Rational numbers can be written in the form $$\frac{p}{q}$$ where $$q \ne 0$$.
2. Is $$\sqrt{49}$$ rational?
Yes, because $$\sqrt{49} = 7$$.
3. Are all irrational numbers real?
Yes, every irrational number belongs to the set of real numbers.
4. Which fractions produce terminating decimals?
Fractions whose simplified denominators contain only 2 and/or 5.
5. What is a recurring decimal?
A decimal in which one or more digits repeat indefinitely.
Common Mistakes
❌ Treating recurring decimals as irrational numbers.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Applying exponent laws incorrectly.
❌ Assuming all square roots are irrational.
❌ Ignoring equivalent expressions.
Quick Revision Notes
✔ Rational numbers can be expressed as fractions.
✔ Non-perfect square roots are irrational.
✔ Perfect square roots are rational.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ 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 rational numbers, irrational numbers, decimal expansions, and exponent laws helps students build strong mathematical skills and perform better in examinations. Regular MCQ practice improves conceptual clarity, accuracy, and confidence.
Related Links
- Class 9 Maths Chapter 1 Number Systems, irrational numbers
- Class 9 Maths Chapter 1 Number Systems, decimal expansion
- Class 9 Maths Chapter 1 Number Systems real numbers
- 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
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
