Question 1 of 5
What type of number is 22?
A
Natural Number
B
Composite Number
C
Irrational Number
D
Fraction
Why: 22 is a **natural number** because natural numbers are positive counting numbers starting from 1 (1, 2, 3, ...). They are used for counting objects and do not include zero, negatives, decimals, or fractions. 22 fits this definition perfectly as it is a positive whole number greater than zero used in counting. Options B, C, and D do not apply: composite refers to numbers with factors other than 1 and itself (though 22 is composite, the primary classification here is natural), irrational numbers cannot be expressed as fractions (like √2), and fraction implies non-integer rational.[1]
Question 2 of 5
What type of number is 2.43?
A
Composite Number
B
Mixed Number
C
Imaginary Number
D
Rational Number
Why: 2.43 is a **rational number** because it is a terminating decimal that can be expressed as the fraction \( \frac{243}{100} \), where both numerator and denominator are integers and denominator ≠ 0. Rational numbers include all integers, terminating decimals, and repeating decimals. Composite numbers are positive integers greater than 1 that are not prime (2.43 is not an integer), mixed numbers are improper fractions written as whole + proper fraction (2.43 is pure decimal), and imaginary numbers involve \( i = \sqrt{-1} \) (2.43 is real).[1]
Question 3 of 5
Which one of the following is not a cube number? a) 1 b) 27 c) 64 d) 81
Why: A cube number is the result of multiplying an integer by itself twice (third power). Checking each: a) \( 1^3 = 1 \) ✓, b) \( 3^3 = 27 \) ✓, c) \( 4^3 = 64 \) ✓, d) \( 81 = 3^4 = 9^2 \), not a perfect cube (\( 4^3 = 64 \), \( 5^3 = 125 \)). Thus, 81 is not a cube number. Cube numbers follow pattern: 1, 8, 27, 64, 125, etc.[2]
Question 4 of 5
List all the factors of 45.
Why: Factors of 45 are numbers that divide 45 exactly without remainder. Using pair method: \( 1 \times 45 = 45 \), \( 3 \times 15 = 45 \), \( 5 \times 9 = 45 \). Thus, factors are 1, 3, 5, 9, 15, 45. Prime factorization confirms: \( 45 = 3^2 \times 5^1 \), so factors = \( (2+1)(1+1) = 6 \) numbers matching the list.[2]
Question 5 of 5
The number 4 is not included in which group of numbers? A. Integers B. Whole numbers C. Irrational numbers D. Natural numbers
A
Integers
B
Whole numbers
C
Irrational numbers
D
Natural numbers
Why: 4 belongs to integers {...,-2,-1,0,1,2,4,...}, whole numbers {0,1,2,3,4,...}, natural numbers {1,2,3,4,...}. Irrational numbers cannot be expressed as \( \frac{p}{q} \) where p,q integers, q≠0 (e.g., π, √2). 4 = \( \frac{4}{1} \) is rational, not irrational. Answer C.[6]
