Which of the following is true about -9?
1. It is an integer but not a rational number
2. It is an integer but not a whole number
3. It is a whole number but not an integer
4. It is both an integer and a whole number
4. It is both an integer and a whole number
The correct answer is:
4. It is both an integer and a whole number.
Explanation:
-9 is an integer because it is a whole number without a fractional or decimal part. Additionally, -9 is also a whole number because it belongs to the set of numbers including all positive and negative integers, as well as zero.
To determine which statement is true about -9, let's first define the terms involved.
An integer is a number that can be positive, negative, or zero without any decimal or fractional parts. Basically, it includes all whole numbers and their negatives, including zero.
A rational number is a number that can be expressed as a fraction, where the numerator and denominator are integers. It includes both integers and fractions.
A whole number is a non-negative integer (including zero), but it does not include any negative numbers or fractions.
Now, let's analyze each statement:
1. It is an integer but not a rational number:
This statement is incorrect because -9 is both an integer (a negative whole number) and a rational number (it can be expressed as -9/1).
2. It is an integer but not a whole number:
This statement is correct. -9 is an integer because it is a negative whole number, but it is not a whole number as it is negative.
3. It is a whole number but not an integer:
This statement is incorrect. -9 is not a whole number because it is negative, and whole numbers exclude negative numbers.
4. It is both an integer and a whole number:
This statement is incorrect. As we discussed earlier, -9 is an integer (because it is a negative whole number) but is not a whole number since it is negative.
Therefore, the correct statement is:
-9 is an integer but not a whole number (Option 2).