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Which of the following statements are true?

A. All integers are rational numbers
B. Repeating decimals are not rational numbers
C. Both A and B
D. Neither A nor B

User John Jiang
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1 Answer

5 votes

Final answer:

Statement A is true because integers can be expressed as a fraction with denominator 1, making them rational. Statement B is false because repeating decimals can be written as fractions, so they are rational. The correct option is 'Neither A nor B' since A is true and B is false.

Step-by-step explanation:

The question about which statements are true concerning integers and rational numbers can be answered by understanding the definitions of these two sets of numbers. Integers are whole numbers that can be positive, negative, or zero. Rational numbers, on the other hand, are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since every integer can be expressed as a fraction with the denominator as 1, all integers are indeed rational numbers. Therefore, statement A is true.

Statement B refers to repeating decimals, which are decimals that have one or more digits that repeat indefinitely. Repeating decimals can be converted into fractions, which means they can be written as the quotient of two integers. Thus, they are considered rational numbers. Therefore, statement B is false.

The correct option that combines these truths is Neither A nor B, which means none of the given combination statements are true since statement A is true (All integers are rational numbers), and statement B is false (Repeating decimals are rational numbers).

User Radical Edward
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