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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, laws of 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 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 helps students solve mathematical problems efficiently 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 concepts of Number Systems are widely used in algebra, geometry, and arithmetic. Learning this chapter improves logical reasoning and strengthens mathematical foundations.
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) $$\frac{9}{14}$$
B) $$0.5$$
C) $$\sqrt{8}$$
D) $$0.272727\ldots$$
Answer:
$$\sqrt{8}$$
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.
Step-by-Step Solution:
- $$\frac{9}{14}$$ is rational.
- $$0.5 = \frac{1}{2}$$ is rational.
- $$0.272727\ldots$$ is recurring and therefore rational.
- $$\sqrt{8} = 2\sqrt{2}$$ and $$\sqrt{2}$$ is irrational.
Therefore:
$$\sqrt{8}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{8}$$
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) $$\frac{7}{16}$$
B) $$\frac{11}{25}$$
C) $$\frac{13}{28}$$
D) $$\frac{9}{20}$$
Answer:
$$\frac{13}{28}$$
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:
- $$16 = 2^4$$
- $$25 = 5^2$$
- $$28 = 2^2 \times 7$$
- $$20 = 2^2 \times 5$$
Since $$28$$ contains the prime factor $$7$$, its decimal expansion is non-terminating recurring.
Therefore, the correct answer is:
$$\frac{13}{28}$$
Exam Tip:
A denominator containing prime factors other than 2 and 5 produces a non-terminating recurring decimal.
Q3. Evaluate:
$$5^4 \times 5^1$$
A) $$5^5$$
B) $$5^4$$
C) $$25^2$$
D) $$10^5$$
Answer:
$$5^5$$
Useful Formula for this Question:
$$a^m \times a^n = a^{m+n}$$
Concept Behind This Question:
Students should apply the multiplication law of exponents.
Step-by-Step Solution:
$$5^4 \times 5^1 = 5^{4+1}$$
$$= 5^5$$
$$= 3125$$
Therefore, the correct answer is:
$$5^5$$
Exam Tip:
Add exponents when multiplying powers with the same base.
Q4. Which of the following is a rational number?
A) $$\sqrt{18}$$
B) $$\pi$$
C) $$\sqrt{121}$$
D) $$\sqrt{7}$$
Answer:
$$\sqrt{121}$$
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:
$$\sqrt{121} = 11$$
Since 11 is an integer, it is rational.
The remaining options are irrational.
Therefore, the correct answer is:
$$\sqrt{121}$$
Exam Tip:
Square roots of perfect squares are always rational.
Q5. Simplify:
$$\frac{10^5}{10^3}$$
A) $$10^2$$
B) $$10^8$$
C) $$100^2$$
D) Both A and C
Answer:
Both A 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:
$$\frac{10^5}{10^3} = 10^{5-3}$$
$$= 10^2$$
Also,
$$100 = 10^2$$
But,
$$100^2 = 10000$$
Therefore:
$$100^2 \ne 10^2$$
Hence, only option A is correct.
Exam Tip:
Always check whether equivalent expressions actually have the same value.
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 if its denominator contains only prime factors 2 and/or 5 after simplification.
FAQs
1. What is a rational number?
A rational number can be written in the form $$\frac{p}{q}$$ where $$q \ne 0$$.
2. Is $$\sqrt{121}$$ rational?
Yes, because $$\sqrt{121} = 11$$.
3. What is a recurring decimal?
A decimal in which digits repeat indefinitely.
4. Are irrational numbers real numbers?
Yes, every irrational number is a real number.
5. Which denominators give terminating decimals?
Denominators containing only 2 and/or 5 after simplification.
Common Mistakes
❌ Assuming all square roots are irrational.
❌ Forgetting to simplify fractions.
❌ Applying exponent rules incorrectly.
❌ Ignoring denominator factorization.
❌ Selecting combined options without verification.
Quick Revision Notes
✔ Rational numbers can be written as fractions.
✔ Non-perfect square roots are irrational.
✔ Perfect square roots are rational.
✔ Denominators with only 2 and/or 5 give terminating decimals.
✔ Use exponent laws carefully.
Conclusion
Number Systems is an essential chapter of Class 9 Mathematics that helps students understand different categories of numbers and their properties. Mastering rational numbers, irrational numbers, decimal expansions, and exponent laws strengthens problem-solving skills and improves exam performance. Regular MCQ practice increases confidence and conceptual clarity.
Related Links
- Class 9 Maths Chapter 1 Number Systems laws of exponents
- 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
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