Chapter Exam

Chapter 3: The World of Numbers — Online MCQ Test

Q: Which of the following is a rational number?

Answer: C. 3/7 — A rational number can be expressed as p/q where p and q are integers and q ≠ 0. 3/7 fits this definition, while √2, π, and √5 are irrational numbers.

Q: The decimal expansion of an irrational number is:

Answer: C. Non-terminating and non-repeating — Irrational numbers have decimal expansions that never end and never repeat in a pattern, distinguishing them from rational numbers which either terminate or have repeating decimals.

Q: What is the square root of 144?

Answer: B. 12 — √144 = 12 because 12 × 12 = 144. This is a direct calculation of the principal square root.

Q: On a number line, where would you place √3?

Answer: C. Between 1.7 and 1.8 — Since 1.7² = 2.89 and 1.8² = 3.24, √3 lies between 1.7 and 1.8 on the number line.

Q: Which of the following is NOT a surd?

Answer: B. √9 — A surd is an irrational root of a positive integer. √9 = 3, which is a rational number, so it is not a surd. The other options are surds as they represent irrational roots.

Q: If a = 2^(1/3) and b = 2^(1/2), then which of the following is true?

Answer: B. a 1, we have 2^(1/3) < 2^(1/2), so a < b.

Q: The product of two irrational numbers √2 and √8 equals:

Answer: A. A rational number 4 — √2 × √8 = √(2×8) = √16 = 4, which is a rational number. This demonstrates that the product of two irrational numbers can be rational.

Q: Consider the following statements: I. Every integer is a rational number II. Every rational number is a real number III. Every real number is a rational number Which statements are true?

Answer: A. Only I and II — Statement I is true: integers can be expressed as p/1. Statement II is true: both rational and irrational numbers are real. Statement III is false: irrational numbers are real but not rational.

Q: On the Pythagorean number spiral, if the first square has side length 1, what is the length of the hypotenuse of the right triangle formed in the second step?

Answer: B. √3 — In the Pythagorean spiral, the first hypotenuse is √2. In the second step, a perpendicular of length 1 is added to √2, creating a hypotenuse of √((√2)² + 1²) = √(2+1) = √3.

MATHS · Grade 9 · CBSE(NCERT)

Practice Chapter 3: The World of Numbers with a free chapter-wise online MCQ test for CBSE(NCERT) Grade 9 MATHS. This chapter covers: Real Numbers Rational Numbers Irrational Numbers Number Line Decimal Expansion Square Root Spiral Proof Surds Exponents Root Two Understanding rational and irrational numbers logic.... AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 3: The World of Numbers — Important Questions & Answers (FAQ)

Frequently asked questions from CBSE(NCERT) Grade 9 MATHS — Chapter 3: The World of Numbers, with answers and explanations. These are sample questions; the exam has its own separate question set.

Which of the following is a rational number?

A. √2
B. π
C. 3/7 ✓
D. √5

Answer: C. 3/7
A rational number can be expressed as p/q where p and q are integers and q ≠ 0. 3/7 fits this definition, while √2, π, and √5 are irrational numbers.

The decimal expansion of an irrational number is:

A. Terminating
B. Non-terminating and repeating
C. Non-terminating and non-repeating ✓
D. Both terminating and repeating

Answer: C. Non-terminating and non-repeating
Irrational numbers have decimal expansions that never end and never repeat in a pattern, distinguishing them from rational numbers which either terminate or have repeating decimals.

What is the square root of 144?

A. 11
B. 12 ✓
C. 13
D. 14

Answer: B. 12
√144 = 12 because 12 × 12 = 144. This is a direct calculation of the principal square root.

Which statement is correct about the number √2?

A. It is a rational number that can be written as 1.414
B. It is an irrational number with non-terminating, non-repeating decimal expansion ✓
C. It is a rational number equal to 1.414214...
D. It is a natural number between 1 and 2

Answer: B. It is an irrational number with non-terminating, non-repeating decimal expansion
√2 is irrational because it cannot be expressed as a ratio of two integers, and its decimal expansion (1.41421356...) neither terminates nor repeats.

On a number line, where would you place √3?

A. Between 1 and 2
B. Between 1.5 and 2
C. Between 1.7 and 1.8 ✓
D. Between 2 and 3

Answer: C. Between 1.7 and 1.8
Since 1.7² = 2.89 and 1.8² = 3.24, √3 lies between 1.7 and 1.8 on the number line.

Which of the following is NOT a surd?

A. √7
B. √9 ✓
C. ∛5
D. √13

Answer: B. √9
A surd is an irrational root of a positive integer. √9 = 3, which is a rational number, so it is not a surd. The other options are surds as they represent irrational roots.

If a = 2^(1/3) and b = 2^(1/2), then which of the following is true?

A. a > b
B. a < b ✓
C. a = b
D. Cannot be determined

Answer: B. a < b
2^(1/3) ≈ 1.26 and 2^(1/2) ≈ 1.41. Since 1/3 < 1/2 and the base is 2 > 1, we have 2^(1/3) < 2^(1/2), so a < b.

The product of two irrational numbers √2 and √8 equals:

A. A rational number 4 ✓
B. An irrational number √16
C. An irrational number 2√4
D. An irrational number √10

Answer: A. A rational number 4
√2 × √8 = √(2×8) = √16 = 4, which is a rational number. This demonstrates that the product of two irrational numbers can be rational.

Consider the following statements: I. Every integer is a rational number II. Every rational number is a real number III. Every real number is a rational number Which statements are true?

A. Only I and II ✓
B. Only II and III
C. Only I and III
D. All three are true

Answer: A. Only I and II
Statement I is true: integers can be expressed as p/1. Statement II is true: both rational and irrational numbers are real. Statement III is false: irrational numbers are real but not rational.

On the Pythagorean number spiral, if the first square has side length 1, what is the length of the hypotenuse of the right triangle formed in the second step?

A. √2
B. √3 ✓
C. √4
D. 2

Answer: B. √3
In the Pythagorean spiral, the first hypotenuse is √2. In the second step, a perpendicular of length 1 is added to √2, creating a hypotenuse of √((√2)² + 1²) = √(2+1) = √3.

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