Chapter 3: The World of Numbers — Online MCQ Test
MATHS · Grade 9 · CBSE(NCERT)
Practice Chapter 3: The World of Numbers with a free chapter-wise online MCQ test.
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....
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Chapter 3: The World of Numbers — Important Questions & Answers
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.
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.
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.
√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.
√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.
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.
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.
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.
√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.
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.
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.