Which number belongs to the set of rational numbers but does not belong to the set of whole numbers?
A. -1 B. 0 C. 1 D. 2
The correct answer and explanation is:
The correct answer is A. -1.
Explanation:
- Rational Numbers: Rational numbers are numbers that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In other words, any number that can be written in the form of ab\frac{a}{b}, where aa and bb are integers, and b≠0b \neq 0, is a rational number. For example, -1 can be written as −11\frac{-1}{1}, which makes it a rational number.
- Whole Numbers: Whole numbers are a set of numbers that include all the natural numbers (0, 1, 2, 3, …) and do not include any negative numbers or fractions. Whole numbers are non-negative integers, meaning they are 0 and all the numbers that are equal to or greater than 0 without any decimal or fractional parts. Therefore, the set of whole numbers is {0, 1, 2, 3, 4, …}.
- Analysis of the Options:
- A. -1: -1 is a rational number since it can be written as −11\frac{-1}{1}. However, it is not a whole number because whole numbers only include non-negative numbers. Hence, -1 is rational but not a whole number.
- B. 0: 0 is a whole number and can also be considered a rational number since 01\frac{0}{1} is a valid fraction.
- C. 1: 1 is both a whole number and a rational number because it can be expressed as 11\frac{1}{1}.
- D. 2: 2 is also both a whole number and a rational number since it can be written as 21\frac{2}{1}.
Thus, -1 is the only number in the options that is a rational number but not a whole number.