Which set of numbers is always rational?(1 point)
Responses
integers
integers
fractions
fractions
positive numbers
positive numbers
decimals
decimals
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fractions
Are any other of them the correct answer
Yes, integers and decimals can also be rational numbers.
Which set of numbers is always rational?(1 point)
Responses
integers
integers
fractions
fractions
positive numbers
positive numbers
decimals
decimals
Select three correct answers
The three correct answers are: integers, fractions, and decimals.
The set of numbers that is always rational is fractions.
The set of numbers that is always rational is fractions.
To understand why fractions are always rational, we need to understand the definition of a rational number. A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero.
For example, the fraction 3/4 is a rational number because it can be expressed as the ratio of the integers 3 and 4. Similarly, the fraction 1/2, 7/5, and so on, are all rational numbers.
On the other hand, integers (whole numbers and their negative counterparts) are not always rational. For example, the integer 3 can be expressed as 3/1, which is a fraction and therefore a rational number. However, the integer √2 (the square root of 2) cannot be expressed as a fraction and is therefore an irrational number.
Similarly, decimals and positive numbers are not always rational. For example, the decimal expansion of √2 is an irrational number because it cannot be expressed as a finite or repeating decimal. Positive numbers can be either rational or irrational, depending on their decimal expansion.
Therefore, the set of numbers that is always rational is fractions, as they can always be expressed as the ratio of two integers.