To determine the subsets of the real numbers to which each number belongs, let's evaluate each option and their properties.
A. 9 squared:
- Calculation: \( 9^2 = 81 \)
- 81 is a positive integer, so it belongs to the following subsets:
- Natural numbers (\(\mathbb{N}\))
- Whole numbers (\(\mathbb{W}\))
- Integers (\(\mathbb{Z}\))
- Rational numbers (\(\mathbb{Q}\))
- Real numbers (\(\mathbb{R}\))
B. 3/10:
- This is a fraction which is a positive rational number.
- It belongs to the following subsets:
- Rational numbers (\(\mathbb{Q}\))
- Real numbers (\(\mathbb{R}\))
C. -0.45:
- This is a negative decimal number.
- It belongs to the following subsets:
- Rational numbers (\(\mathbb{Q}\)) (since it can be expressed as \(-\frac{45}{100}\))
- Real numbers (\(\mathbb{R}\))
- Note: It does not belong to natural numbers, whole numbers, or integers.
D. 12 squared:
- Calculation: \( 12^2 = 144 \)
- 144 is a positive integer, so it belongs to the following subsets:
- Natural numbers (\(\mathbb{N}\))
- Whole numbers (\(\mathbb{W}\))
- Integers (\(\mathbb{Z}\))
- Rational numbers (\(\mathbb{Q}\))
- Real numbers (\(\mathbb{R}\))
Summary of Subset Membership:
- A. \( 81 \): \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)
- B. \( \frac{3}{10} \): \(\mathbb{Q}, \mathbb{R}\)
- C. \( -0.45 \): \(\mathbb{Q}, \mathbb{R}\)
- D. \( 144 \): \(\mathbb{N}, \mathbb{W}, \mathbb{Z}, \mathbb{Q}, \mathbb{R}\)