From the list of numbers $\left{\frac{22}{2},-25,(-22)^2, \frac{0}{4}, \frac{12}{0}\right}$, which are the whole numbers?
A. $\left{\frac{22}{2}, \frac{12}{0}\right}$
B. $\left{-25, \frac{0}{4},(-22)^2\right}$
C. $\left{\frac{22}{2}, \frac{12}{0}, \frac{0}{4},(-22)^2\right}$
D. $\left{\frac{22}{2}, \frac{0}{4},(-22)^2\right}$
Answer (2)
Evaluate each number in the list: 2 22 = 11 , − 25 is negative, ( − 22 ) 2 = 484 , 4 0 = 0 , and 0 12 is undefined.
Identify the whole numbers: 11, 484, and 0.
Express the whole numbers in terms of the original list: 2 22 , 4 0 , and ( − 22 ) 2 .
The set of whole numbers is { 2 22 , 4 0 , ( − 22 ) 2 } .
Explanation
Understanding the Problem We are given the list of numbers { 2 22 , − 25 , ( − 22 ) 2 , 4 0 , 0 12 } and we need to identify which of these are whole numbers. Whole numbers are non-negative integers, i.e., 0, 1, 2, 3, and so on.
Evaluating Each Number Let's evaluate each number in the list:
2 22 = 11 . This is a whole number.
− 25 is a negative integer, so it is not a whole number.
( − 22 ) 2 = ( − 22 ) × ( − 22 ) = 484 . This is a whole number.
4 0 = 0 . This is a whole number.
0 12 is undefined because division by zero is not allowed. Therefore, it is not a whole number.
Identifying Whole Numbers From the evaluation above, the whole numbers in the given list are 11, 484, and 0. In terms of the original list, these correspond to 2 22 , ( − 22 ) 2 , and 4 0 . Therefore, the set of whole numbers is { 2 22 , 4 0 , ( − 22 ) 2 } .
Final Answer The whole numbers from the list are 2 22 , 4 0 , and ( − 22 ) 2 . Therefore, the correct answer is d. { 2 22 , 4 0 , ( − 22 ) 2 } .
Examples
Whole numbers are fundamental in many real-life scenarios, such as counting objects, measuring discrete quantities, and representing ages. For example, if you have a basket of apples, you can only have a whole number of apples (e.g., 5 apples, not 5.5 apples). Similarly, when counting the number of students in a class, you can only have a whole number of students. Understanding whole numbers is crucial for basic arithmetic and problem-solving in everyday situations.
The whole numbers from the list are 2 22 , 4 0 , and ( − 22 ) 2 , which are 11, 0, and 484 respectively. Therefore, the correct answer is option D: { 2 22 , 4 0 , ( − 22 ) 2 } .
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