Identify the MOST SPECIFIC set to which each of the following numbers belongs. (7 points)

Question

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!