Let's go through the step-by-step process to determine the type of the number resulting from the division [tex]\(\frac{0.25}{-0.25}\)[/tex].
1. Calculate the Division:
To start, we need to compute the value of [tex]\(\frac{0.25}{-0.25}\)[/tex].
[tex]\[
\frac{0.25}{-0.25} = -1.0
\][/tex]
2. Identify Whether it is a Whole Number:
A whole number is a non-negative integer (0, 1, 2, 3, ...). Since [tex]\(-1.0\)[/tex] is negative, it is not a whole number.
3. Identify Whether it is an Integer:
An integer is any positive or negative whole number including zero (..., -2, -1, 0, 1, 2, ...). The result [tex]\(-1.0\)[/tex] can be considered an integer because it is equivalent to the integer [tex]\(-1\)[/tex].
4. Identify Whether it is Rational:
A rational number can be expressed as the quotient of two integers. The number [tex]\(-1.0\)[/tex] can be written as [tex]\(\frac{-1}{1}\)[/tex], which clearly shows it is a rational number.
5. Identify Whether it is Irrational:
An irrational number cannot be expressed as a quotient of two integers and has a non-repeating, non-terminating decimal expansion. Since [tex]\(-1.0\)[/tex] can be written as a simple fraction, it is not an irrational number.
Based on these evaluations, we conclude the following types for the number [tex]\(\frac{0.25}{-0.25}\)[/tex]:
- Whole number: No (False)
- Integer: Yes (True)
- Rational: Yes (True)
- Irrational: No (False)
Thus, the correct answers are:
- Integer
- Rational
