Question

to which subsets of the real numbers does each number belong?
A. 15 natural numbers, whole numbers, integers, rational numbers
B. -1.4583 rational numbers (since -1.4583 is a terminating decimal)
C. 57 squared irrational numbers (since 57 is not a perfect square)

Answer 1

Let's categorize each of the given numbers into their appropriate subsets of the real numbers:

A. **15**
- **Natural Numbers**: Yes, 15 is a natural number.
- **Whole Numbers**: Yes, whole numbers include all natural numbers and zero.
- **Integers**: Yes, integers include all whole numbers and their negative counterparts.
- **Rational Numbers**: Yes, 15 can be expressed as a fraction (e.g., 15/1).

So, 15 belongs to the subsets: **Natural numbers, Whole numbers, Integers, Rational numbers**.

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B. **-1.4583**
- **Natural Numbers**: No, it is negative.
- **Whole Numbers**: No, it is negative.
- **Integers**: No, it is not a whole number or a non-negative integer.
- **Rational Numbers**: Yes, -1.4583 is a rational number because it can be expressed as a fraction (-14583/10000), and it is a terminating decimal.

So, -1.4583 belongs to the subset: **Rational numbers**.

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C. **57 squared**
- **57 squared** equals \( 57^2 = 3249 \).
- **Natural Numbers**: Yes, it is positive.
- **Whole Numbers**: Yes, it is a whole number.
- **Integers**: Yes, it is an integer.
- **Rational Numbers**: Yes, it can be expressed as a fraction (e.g., 3249/1).
- **Irrational Numbers**: No, 3249 is a perfect square (it is the square of 57), thus it is not an irrational number.

So, **57 squared (3249)** belongs to the subsets: **Natural numbers, Whole numbers, Integers, Rational numbers**.

To summarize:
- A. 15: Natural numbers, Whole numbers, Integers, Rational numbers.
- B. -1.4583: Rational numbers.
- C. 57 squared (3249): Natural numbers, Whole numbers, Integers, Rational numbers.