Question

Identify the MOST SPECIFIC set to which each of the following numbers belongs.(7 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.

6.263
4.56666....
−25
0
36−−√
9/11
42−−√

Answer 1

To identify the most specific set that each number belongs to, we will categorize them based on their mathematical properties. Here’s the classification for each number:

1. **6.263**: This is a decimal number that does not repeat or terminate, making it a rational number. However, since it's a decimal, it can be categorized specifically as a real number.

2. **4.56666....**: This is a decimal with a repeating component (the '6' repeats). Therefore, it is a rational number and also falls under real numbers.

3. **−25**: This is an integer (also a rational number), and it is also a real number.

4. **0**: This is a whole number, an integer (also rational and real).

5. **36−−√**: The square root of 36 equals 6, which is an integer and belongs to the set of rational numbers and real numbers.

6. **9/11**: This is a fraction that can be expressed as a decimal. It is a rational number and also falls under real numbers.

7. **42−−√**: The square root of 42 is an irrational number (approximately 6.48). Thus, it belongs to the set of irrational numbers and also real numbers.

To summarize:

- **6.263**: Real Number
- **4.56666....**: Rational Number
- **−25**: Integer
- **0**: Integer
- **36−−√**: Integer
- **9/11**: Rational Number
- **42−−√**: Irrational Number

You would input them into the respective slots for their specific classifications.