Question

Which representation shows the correct placement of numbers in the sets and subsets of rational numbers?

a) Option 1: Rational Numbers -2.6, 0.9, 0

b) Option 2: Whole Numbers 3, 1; Integers -2, 0; Rational Numbers 0.9, -2.0, 12

c) Option 3: Rational Numbers -2.6, 0.9, 0; Whole Numbers 3, 1

d) Option 4: Whole Numbers 3, 1; Rational Numbers 0.9, -2.0, 12; Integers -3, 0

Answer 1

Option 2 is the correct answer, as it accurately reflects the classifications within the sets of whole numbers, integers, and rational numbers according to their definitions.

Step-by-step explanation:

The correct placement of numbers in the sets and subsets of rational numbers must follow the definitions of these mathematical sets. Option 2 aligns with the proper classification of numbers within these sets:

• Whole Numbers: Non-negative integers without fractions or decimals (e.g., 0, 3, 9).
• Integers: All whole numbers including negatives (e.g., -4, 0, 2).
• Rational Numbers: Numbers that can be expressed as a fraction with integers in the numerator and non-zero integers in the denominator, which also includes integers and whole numbers (e.g., 1/2, 3, -4, 0.75).

Therefore, Option 2 which states 'Whole Numbers 3, 1; Integers -2, 0; Rational Numbers 0.9, -2.0, 12' shows the correct classification where whole numbers and integers are also subsets of rational numbers.