Let's evaluate each statement to determine which are true:
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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.
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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.
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\( \frac{715}{-14} \) 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).
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Terminating decimals are rational numbers.
- True. Terminating decimals (such as \(0.5\) or \(0.75\)) can be expressed as fractions, making them rational numbers.
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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.