which of the following is true about -9 ?
it is a whole number but not a integer
it is both an integer and a whole number
it is an integer but not a rational number
it is an integer not a whole number
The correct option is:
-9 is both an integer and a whole number.
The statement "it is both an integer and a whole number" is true about -9.
An integer is a number that can either be positive, negative, or zero, without any decimal or fractional part. -9 qualifies as an integer since it is a negative whole number.
A whole number is a number that can either be positive or zero, without any decimal or fractional part. -9 also qualifies as a whole number since it is not a positive number, but it is still without any decimal or fractional part.
To determine which statement is true about -9, let's define the terms involved:
1. Whole number: Whole numbers are the set of numbers that includes all positive numbers starting from zero and their negative counterparts. So, 0, 1, 2, 3, and so on, are all examples of whole numbers.
2. Integer: Integers are the set of both positive and negative whole numbers, including zero. So, integers include numbers like -3, -2, -1, 0, 1, 2, 3, and so on.
3. Rational number: A rational number is any number that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero. Examples of rational numbers are 1/2, 3/4, and -5/7.
Now let's analyze each statement:
a) "It is a whole number but not an integer": This statement is incorrect because -9 is a negative whole number, as well as an integer. Therefore, it is not solely a whole number.
b) "It is both an integer and a whole number": This statement is correct. As mentioned earlier, -9 is a negative whole number and, at the same time, an integer.
c) "It is an integer but not a rational number": This statement might be misleading. Since -9 can be expressed as -9/1, it can indeed be considered a rational number. Therefore, this statement is not entirely true.
d) "It is an integer, not a whole number": This statement is incorrect because -9 is a whole number as well as an integer.
So, the correct statement is: "-9 is both an integer and a whole number."