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.

1 answer

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.