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Which kinds of numbers are rational? Select all that apply.\newlineMulti-select Choices:\newline(A) integers\newline(B) nonterminating, nonrepeating decimals\newline(C) fractions of whole numbers\newline(D) terminating decimals\newline(E) nonterminating, repeating decimals

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Checkpoint: Rational and irrational numbersright chevron icon

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Q. Which kinds of numbers are rational? Select all that apply.\newlineMulti-select Choices:\newline(A) integers\newline(B) nonterminating, nonrepeating decimals\newline(C) fractions of whole numbers\newline(D) terminating decimals\newline(E) nonterminating, repeating decimals
  1. Define rational numbers: Step 11: Define rational numbers. Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
  2. Integers: Step 22: Analyze choice (A) - integers.\newlineIntegers (like −1-1, 00, 11, 22) can be expressed as fractions (e.g., 11 can be written as 11\frac{1}{1}). Therefore, integers are rational numbers.
  3. Nonterminating decimals: Step 33: Analyze choice (B) - nonterminating, nonrepeating decimals.\newlineNonterminating, nonrepeating decimals (like π\pi or the square root of 22) cannot be expressed as fractions of whole numbers. Hence, they are not rational numbers.
  4. Fractions of whole numbers: Step 44: Analyze choice (C) - fractions of whole numbers.\newlineFractions of whole numbers (like 12\frac{1}{2}, 34\frac{3}{4}) are the very definition of rational numbers, as they can be expressed as a ratio of two integers.
  5. Terminating decimals: Step 55: Analyze choice (D) - terminating decimals.\newlineTerminating decimals (like 0.50.5, 0.750.75) can be expressed as fractions (0.50.5 as 12\frac{1}{2}, 0.750.75 as 34\frac{3}{4}), making them rational numbers.
  6. Nonterminating, repeating decimals: Step 66: Analyze choice (E) - nonterminating, repeating decimals.\newlineNonterminating, repeating decimals (like 0.333…0.333\ldots, 0.666…0.666\ldots) can be expressed as fractions (0.333…0.333\ldots as 13\frac{1}{3}, 0.666…0.666\ldots as 23\frac{2}{3}), so they are rational numbers.

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