Identify which condition is necessary for a number to be rational.(1 point)
Responses
It must be written as a fraction.
It must not be negative.
It must be able to be expressed as an integer divided by a nonzero integer.
It must not be an endless decimal.
It must be able to be expressed as an integer divided by a nonzero integer.
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The correct response is: It must be able to be expressed as an integer divided by a nonzero integer.
The correct answer is: It must be able to be expressed as an integer divided by a nonzero integer.
To understand why this is the necessary condition for a number to be rational, let's first define what it means for a number to be rational. A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.
To determine if a number is rational, you need to check if it can be written as a fraction. This means that it can be expressed as the ratio of two integers, with a nonzero integer as the denominator. For example, the number 2 can be written as 2/1, which is the fraction of two integers. Similarly, 3/4, -5/2, and 0/6 are all examples of rational numbers because they can all be expressed as the quotient of two integers.
Now, let's consider the other options provided:
1. It must be written as a fraction: This is not the correct condition because there are irrational numbers that cannot be expressed as fractions. Examples of these numbers include π (pi) and √2 (the square root of 2).
2. It must not be negative: This is not the correct condition because negative numbers can still be rational. For instance, -3/4 and -7/5 are both rational numbers.
3. It must not be an endless decimal: This is not the correct condition because some rational numbers have decimal representations that either terminate or repeat. For example, 1/4 is a rational number that terminates as 0.25, and 1/3 is a rational number that repeats as 0.333...
To sum up, the correct condition for a number to be rational is that it can be expressed as an integer divided by a nonzero integer. This condition ensures that the number is a fraction and not an irrational or imaginary number.