Identify the most specific set to which each of the following numbers belongs:

Question

0.121212...
√144
√47
-9
0

options:

Whole Number
Integer
Irrational Number
Rational Number
Natural Number

(please use an option only once. use each option)

Answer 1

Here’s the identification of each number along with the most specific set it belongs to:

1. 0.121212... - Rational Number (it can be expressed as a fraction, specifically 12/99 or 4/33).

2. √144 - Whole Number (since √144 = 12, which is a whole number).

3. √47 - Irrational Number (since 47 is not a perfect square, √47 cannot be simplified to a fraction).

4. -9 - Integer (it is a whole number but specifically a negative whole number).

5. 0 - Natural Number (note that traditionally, natural numbers start from 1, but in some definitions, 0 is included).

So the final assignments are:

• 0.121212... - Rational Number
• √144 - Whole Number
• √47 - Irrational Number
• -9 - Integer
• 0 - Natural Number

(Note: The classification of 0 as a natural number can vary depending on the definition used, so it might be valid to say that 0 belongs to the set of Integers instead. Here, I have categorized it based on the definition including 0 as a natural number.)