Question
Which set of rational numbers is always rational? The choices are negative numbers, non terminating decimals, decimals, or whole numbers?
Answers
GPT-4o mini
The set of rational numbers that is always rational is **whole numbers**.
Here's a brief explanation of the options:
- **Negative numbers**: This set can include both rational and irrational numbers, depending on the specific number chosen (e.g., \(-1\) is rational, but \(-\sqrt{2}\) is not).
- **Non-terminating decimals**: This set includes irrational numbers (e.g., \(\pi\)), so it is not exclusively rational.
- **Decimals**: This set can include both terminating decimals (which are rational) and non-terminating decimals (which can be irrational).
- **Whole numbers**: This set (0, 1, 2, 3, ...) consists entirely of rational numbers since they can be expressed as a fraction (e.g., \(x = \frac{x}{1}\)).
Therefore, the answer is whole numbers, as they are always rational.
Here's a brief explanation of the options:
- **Negative numbers**: This set can include both rational and irrational numbers, depending on the specific number chosen (e.g., \(-1\) is rational, but \(-\sqrt{2}\) is not).
- **Non-terminating decimals**: This set includes irrational numbers (e.g., \(\pi\)), so it is not exclusively rational.
- **Decimals**: This set can include both terminating decimals (which are rational) and non-terminating decimals (which can be irrational).
- **Whole numbers**: This set (0, 1, 2, 3, ...) consists entirely of rational numbers since they can be expressed as a fraction (e.g., \(x = \frac{x}{1}\)).
Therefore, the answer is whole numbers, as they are always rational.