Which of the following is true about −9?
It is an integer but not a whole number.
It is a whole number but not an integer.
It is both an integer and a whole number.
It is an integer but not a rational number.
It is both an integer and a whole number.
The correct statement is: It is both an integer and a whole number.
An integer is a number that can be positive, negative, or zero and does not include fractions or decimals. The number -9 is an integer because it is a negative number and does not include fractions or decimals.
A whole number is a number that is non-negative and does not include fractions or decimals. The number -9 is a whole number because it is non-negative (it is negative) and does not include fractions or decimals.
Therefore, the statement "It is both an integer and a whole number" is true about -9.
To determine which statement is true about the number -9, let's understand the definitions of the terms involved:
1. Integer: Integers are numbers without a fractional or decimal component. They include positive numbers, negative numbers, and zero. Examples of integers are -3, -2, -1, 0, 1, 2, 3, etc.
2. Whole number: Whole numbers are non-negative numbers without a fractional or decimal component. They include zero and all positive integers. Examples of whole numbers are 0, 1, 2, 3, etc.
3. Rational number: Rational numbers are numbers that can be expressed as a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Examples of rational numbers are 1/2, -3/4, 6/5, etc.
Now let's evaluate each statement:
Statement 1: -9 is an integer but not a whole number.
Since -9 satisfies the definition of an integer and includes negative numbers, it is an integer. However, it is not a whole number because whole numbers only include non-negative (positive and zero) integers. Therefore, statement 1 is false.
Statement 2: -9 is a whole number but not an integer.
Since -9 is a negative integer and not a non-negative integer, it does not qualify as a whole number. Hence, statement 2 is false.
Statement 3: -9 is both an integer and a whole number.
-9 is an integer because it satisfies the definition of an integer. It is also a whole number because it is a non-negative integer (-9 is not non-negative, but 0 is a whole number). Therefore, statement 3 is true.
Statement 4: -9 is an integer but not a rational number.
Since -9 can be expressed as -9/1, where both the numerator and denominator are integers, it qualifies as a rational number. Therefore, statement 4 is false.
Therefore, the correct statement is: It is both an integer and a whole number.