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Practice Class 9 Maths Chapter 1 Number Systems MCQ Questions with Answers based on NCERT syllabus. Learn irrational numbers, decimal expansion, exponents, real numbers, and rational 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
Based On: NCERT Latest Syllabus
Introduction:
Number Systems is a fundamental chapter in Class 9 Mathematics that introduces students to various types of numbers and their properties. Concepts such as rational numbers, irrational numbers, real numbers, decimal expansions, and laws of exponents are essential for solving mathematical problems and understanding advanced topics in higher classes.
What You Will Learn?
✔ Rational Numbers
✔ Irrational Numbers
✔ Real Numbers
✔ Decimal Expansion
✔ Laws of Exponents
✔ Number Representation 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. A strong understanding of these concepts helps students develop logical thinking and improve problem-solving abilities.
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) $$\frac{4}{9}$$
B) $$0.875$$
C) $$\sqrt{29}$$
D) $$0.121212\ldots$$
Answer:
$$\sqrt{29}$$
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 the ability to identify irrational numbers.
Step-by-Step Solution:
- $$\frac{4}{9}$$ is rational.
- $$0.875 = \frac{7}{8}$$ is rational.
- $$0.121212\ldots$$ is recurring and hence rational.
- $$29$$ is not a perfect square.
Therefore:
$$\sqrt{29}$$ is irrational.
Hence, the correct answer is:
$$\sqrt{29}$$
Exam Tip:
The square root of a non-perfect square is always irrational.
Q2. Which of the following fractions has a terminating decimal expansion?
A) $$\frac{7}{15}$$
B) $$\frac{11}{40}$$
C) $$\frac{5}{18}$$
D) $$\frac{13}{21}$$
Answer:
$$\frac{11}{40}$$
Useful Formula for this Question:
A rational number has a terminating decimal expansion if its denominator contains only factors 2 and/or 5 after simplification.
Concept Behind This Question:
Students should know how to determine the nature of decimal expansions.
Step-by-Step Solution:
Prime factorization of denominators:
- $$15 = 3 \times 5$$
- $$40 = 2^3 \times 5$$
- $$18 = 2 \times 3^2$$
- $$21 = 3 \times 7$$
Only $$40$$ contains prime factors 2 and 5 only.
Therefore:
$$\frac{11}{40}$$ has a terminating decimal expansion.
Hence, the correct answer is:
$$\frac{11}{40}$$
Exam Tip:
Always simplify the fraction before checking its denominator.
Q3. Evaluate:
$$5^3 \times 5^2$$
A) $$5^5$$
B) $$5^6$$
C) $$10^5$$
D) $$25^3$$
Answer:
$$5^5$$
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:
$$5^3 \times 5^2 = 5^{3+2}$$
$$= 5^5$$
$$= 3125$$
Therefore, the correct answer is:
$$5^5$$
Exam Tip:
When multiplying powers with the same base, add the exponents.
Q4. Which of the following numbers is not a real number?
A) $$\sqrt{16}$$
B) $$\frac{7}{9}$$
C) $$\sqrt{-9}$$
D) $$\pi$$
Answer:
$$\sqrt{-9}$$
Useful Formula for this Question:
The square root of a negative number is not a real number.
Concept Behind This Question:
Students should distinguish between real and non-real numbers.
Step-by-Step Solution:
- $$\sqrt{16} = 4$$ is real.
- $$\frac{7}{9}$$ is rational and real.
- $$\pi$$ is irrational but real.
- $$\sqrt{-9}$$ is not defined in the set of real numbers.
Therefore, the correct answer is:
$$\sqrt{-9}$$
Exam Tip:
Square roots of negative numbers are not real numbers.
Q5. Simplify:
$$\frac{7^5}{7^2}$$
A) $$7^3$$
B) $$7^7$$
C) $$49^3$$
D) $$14^3$$
Answer:
$$7^3$$
Useful Formula for this Question:
$$\frac{a^m}{a^n} = a^{m-n}$$
Concept Behind This Question:
Students should know the law of exponents for division.
Step-by-Step Solution:
$$\frac{7^5}{7^2} = 7^{5-2}$$
$$= 7^3$$
$$= 343$$
Therefore, the correct answer is:
$$7^3$$
Exam Tip:
Subtract the exponents when dividing powers with the same base.
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 the denominator has only prime factors 2 and/or 5.
FAQs
1. What is a rational number?
A number that can be expressed in the form $$\frac{p}{q}$$ where $$q \ne 0$$.
2. Is $$\pi$$ a real number?
Yes, $$\pi$$ is an irrational but real number.
3. Which square roots are irrational?
Square roots of non-perfect squares are irrational.
4. Is $$\sqrt{-9}$$ a real number?
No, it is not a real number.
5. Which fractions have terminating decimals?
Fractions whose simplified denominator contains only 2 and/or 5.
Common Mistakes
❌ Assuming every decimal number is rational.
❌ Forgetting to simplify fractions before checking decimal expansion.
❌ Confusing irrational numbers with non-real numbers.
❌ Applying exponent laws incorrectly.
❌ Treating square roots of negative numbers as real numbers.
Quick Revision Notes
✔ Rational numbers can be written as fractions.
✔ Irrational numbers cannot be expressed as fractions.
✔ Real numbers include rational and irrational numbers.
✔ Square roots of negative numbers are not real.
✔ Apply exponent laws carefully.
Conclusion
Number Systems is an important chapter that helps students understand the classification and properties of numbers. Mastering rational numbers, irrational numbers, decimal expansions, and exponents strengthens mathematical reasoning and prepares students for higher-level concepts. Regular MCQ practice enhances accuracy, confidence, and exam performance.
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