Identify the most specific set to which each of the following numbers belongs:(5 points)

Question

47−−√
0.121212...
0
144−−−√
-9

responses
rational numbers
irrational number
whole number
natural number
integer

Answer 1

Let's classify each of the given numbers:

1. \( \sqrt{47} \): This number is an irrational number because it cannot be expressed as a fraction of two integers.

2. 0.121212...: This number is a repeating decimal, which can be expressed as a fraction. Therefore, it belongs to the set of rational numbers.

3. 0: This number is an integer (it can also be classified as a whole number and a rational number, but integer is the most specific set for it).

4. \( \sqrt{144} \): This number equals 12, which is a whole number (and also a natural number and an integer, but whole number is the most specific classification).

5. -9: This number is an integer (it cannot be classified as a natural number or a whole number, but it is a member of the integer set).

So the specific sets are:

1. \( \sqrt{47} \): Irrational number
2. 0.121212...: Rational numbers
3. 0: Integer
4. \( \sqrt{144} \): Whole number
5. -9: Integer