Question
Which set of numbers is always rational?
(1 point)
• decimals
• positive numbers
• integers
• negative numbers
(1 point)
• decimals
• positive numbers
• integers
• 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 in the form of a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \). Since integers can be expressed as themselves divided by 1 (e.g., \( 5 = \frac{5}{1} \), \(-3 = \frac{-3}{1}\)), all integers are rational numbers.
While decimals can be rational (like 0.5), they can also be irrational (like 0.333...). Positive and negative numbers can also include irrational numbers, so they are not always rational.
Thus, the correct answer is **integers**.
Rational numbers are defined as numbers that can be expressed in the form of a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers, and \( b \neq 0 \). Since integers can be expressed as themselves divided by 1 (e.g., \( 5 = \frac{5}{1} \), \(-3 = \frac{-3}{1}\)), all integers are rational numbers.
While decimals can be rational (like 0.5), they can also be irrational (like 0.333...). Positive and negative numbers can also include irrational numbers, so they are not always rational.
Thus, the correct answer is **integers**.
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