Question

Identify the MOST SPECIFIC set to which each of the following numbers belongs. (7 points)
4.56666....
√42
0
6.263
9/11
√36
-25
•: Natural Number
:: Irrational Number
•: Rational Number
:: Whole Number
:: Integer

Answer 1

Let's identify the most specific set for each number you provided:

1. **4.56666...**
- This is a repeating decimal, which makes it a **Rational Number**.

2. **√42**
- The square root of 42 is not a perfect square, so it is an **Irrational Number**.

3. **0**
- The number 0 is a whole number and also an integer, but the most specific classification is as a **Whole Number** (we often categorize it as a whole number before integers).

4. **6.263**
- This is not a repeating or terminating decimal; it is a non-repeating decimal, which makes it a **Rational Number**.

5. **9/11**
- This is a fraction that can be expressed as a decimal (0.8181...), which makes it a **Rational Number**.

6. **√36**
- The square root of 36 is 6, which is a whole number and also an integer. The most specific classification is as a **Whole Number**.

7. **-25**
- The number -25 is a negative integer, so it falls into the category of **Integer**.

### Summary of Classifications:
1. **4.56666...** - Rational Number
2. **√42** - Irrational Number
3. **0** - Whole Number
4. **6.263** - Rational Number
5. **9/11** - Rational Number
6. **√36** - Whole Number
7. **-25** - Integer

Let me know if you need further assistance!