Question

Which of the following are true statements? Select all that apply.
All integers are rational numbers.
Repeating decimals are not rational numbers.
StartFraction 715 over negative 14 EndFractionis not a rational number.
Terminating decimals are rational numbers.
0.278254 is a terminating decimal, therefore it is a rational number.

Answer 1

Let's evaluate each statement to determine which are true:

1. **All integers are rational numbers.**
- **True.** An integer can be expressed as a fraction (for example, \(5 = \frac{5}{1}\)), so all integers are indeed rational numbers.

2. **Repeating decimals are not rational numbers.**
- **False.** Repeating decimals (such as \(0.333...\) or \(0.121212...\)) are rational numbers because they can be expressed as a fraction.

3. **\( \frac{715}{-14} \) is not a rational number.**
- **False.** \( \frac{715}{-14} \) is a rational number because it can be expressed as a fraction (even though it has a negative denominator).

4. **Terminating decimals are rational numbers.**
- **True.** Terminating decimals (such as \(0.5\) or \(0.75\)) can be expressed as fractions, making them rational numbers.

5. **0.278254 is a terminating decimal, therefore it is a rational number.**
- **True.** Since \(0.278254\) is a terminating decimal, it can be expressed as a fraction and is therefore a rational number.

### Summary of True Statements
- All integers are rational numbers.
- Terminating decimals are rational numbers.
- 0.278254 is a terminating decimal, therefore it is a rational number.