Question
Which set of numbers is always rational?(1 point)
Responses
integers
integers
positive numbers
positive numbers
decimals
decimals
negative numbers
Responses
integers
integers
positive numbers
positive numbers
decimals
decimals
negative numbers
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The set of numbers that is always rational is **integers**.
Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since integers can be expressed in this form (e.g., any integer \( n \) can be written as \( \frac{n}{1} \)), all integers are rational numbers.
Positive numbers, decimals, and negative numbers do not specifically guarantee being rational, as positive numbers could include irrational numbers (like \(\sqrt{2}\)), decimals could refer to repeating or non-repeating decimals, and negative numbers can also include irrational numbers.
Rational numbers are defined as numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Since integers can be expressed in this form (e.g., any integer \( n \) can be written as \( \frac{n}{1} \)), all integers are rational numbers.
Positive numbers, decimals, and negative numbers do not specifically guarantee being rational, as positive numbers could include irrational numbers (like \(\sqrt{2}\)), decimals could refer to repeating or non-repeating decimals, and negative numbers can also include irrational numbers.
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