1. Which of the following is considered a natural number?
a) -3 b) 0 c) 2.5 d) 5
Answer: d) 5
Explanation: Natural numbers are the set of positive integers starting from 1 and increasing by increments of 1 (i.e., 1, 2, 3, 4, 5, …). They are used for counting and ordering. Option d) 5 is a positive whole number and fits the definition of a natural number.
- a) -3 is an integer but negative, so it’s not a natural number.
- b) 0 is considered a whole number but is not traditionally included in the set of natural numbers.
- c) 2.5 is a decimal (fractional number) and not a whole number.
2. Real numbers include:
a) Rational numbers b) Irrational numbers c) Both a and b d) Neither a nor b
Answer: c) Both a and b
Explanation: The set of real numbers consists of all the numbers that can be found on the number line. This includes all rational numbers (numbers that can be expressed as a fraction of two integers) and all irrational numbers (numbers that cannot be expressed as a simple fraction). Therefore, real numbers include both rational and irrational numbers.
3. Which number system includes both positive and negative whole numbers?
a) Natural numbers b) Real numbers c) Integers d) Rational numbers
Answer: c) Integers
Explanation: Integers are the set of whole numbers that include zero, positive whole numbers, and negative whole numbers (i.e., …, -3, -2, -1, 0, 1, 2, 3, …).
- a) Natural numbers include only positive whole numbers starting from 1.
- b) Real numbers include all rational and irrational numbers.
- d) Rational numbers include fractions and integers, but the term doesn’t specifically refer to whole numbers only.
4. The number √2 is an example of a:
a) Rational number b) Natural number c) Whole number d) Irrational number
Answer: d) Irrational number
Explanation: The square root of 2 (√2) is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-terminating and non-repeating (approximately 1.4142135…).
5. What is the primary difference between rational and irrational numbers?
a) Rational numbers can be expressed as fractions; irrational numbers cannot b) Rational numbers are always whole numbers; irrational numbers are not c) Rational numbers are less than zero; irrational numbers are greater than zero d) Rational numbers cannot be expressed as decimals; irrational numbers can
Answer: a) Rational numbers can be expressed as fractions; irrational numbers cannot
Explanation:
- Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where q ≠ 0.
- Irrational numbers cannot be expressed as a simple fraction; their decimal expansions are non-terminating and non-repeating.
- Options b), c), and d) are incorrect because:
- Rational numbers are not limited to whole numbers (they include fractions and decimals).
- Rational numbers can be both less than and greater than zero.
- Rational numbers can be expressed as decimals (terminating or repeating).
6. Which of the following is an example of a rational number?
a) π (Pi) b) 4/5 c) √3 d) e (Euler’s number)
Answer: b) 4/5
Explanation:
- Option b) 4/5 is a fraction of two integers (4 and 5), making it a rational number.
- Option a) π is an irrational number with a non-terminating, non-repeating decimal expansion.
- Option c) √3 is an irrational number.
- Option d) e (approximately 2.71828) is also an irrational number.
7. What is the set of natural numbers usually denoted by?
a) ℝ b) ℤ c) ℕ d) ℚ
Answer: c) ℕ
Explanation:
- ℕ represents the set of natural numbers (1, 2, 3, 4, …).
- ℝ represents the set of real numbers.
- ℤ represents the set of integers.
- ℚ represents the set of rational numbers.
8. Which number is NOT a part of the real number system?
a) 7 b) -1 c) √-1 (i) d) 3.14
Answer: c) √-1 (i)
Explanation:
- √-1 is an imaginary unit denoted by i in mathematics. It is not a real number because no real number squared equals -1.
- Options a) 7, b) -1, and d) 3.14 are all real numbers.
9. The number 0 is considered to be:
a) A natural number b) An integer c) A real number d) Both b and c
Answer: d) Both b and c
Explanation:
- 0 is an integer (it is part of the set of whole numbers that include negative numbers, zero, and positive numbers).
- 0 is also a real number.
- There is debate about whether 0 is a natural number; traditionally, natural numbers start from 1, but some definitions include 0.
10. The set of rational numbers is denoted by which symbol?
a) ℕ b) ℚ c) ℤ d) ℝ
Answer: b) ℚ
Explanation:
- ℚ represents the set of rational numbers.
- ℕ represents natural numbers.
- ℤ represents integers.
- ℝ represents real numbers.
