Select the Real Number Subset that each number belongs to:
A. 459
4
5
9
B. −12
−
12
C. 0
0
D. 3π
3
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A. 459 belongs to the set of Natural numbers.
B. -12 belongs to the set of Integers.
C. 0 belongs to the set of Whole numbers.
D. 3π belongs to the set of Irrational numbers.
To determine the real number subset that each number belongs to, we need to understand the different subsets of real numbers.
1. Natural numbers (N): Includes all positive whole numbers starting from 1.
2. Whole numbers (W): Includes all positive whole numbers starting from 0.
3. Integers (Z): Includes both positive and negative whole numbers and zero.
4. Rational numbers (Q): Includes all numbers that can be expressed as a fraction (ratio) of two integers.
5. Irrational numbers (I): Includes numbers that cannot be expressed as a fraction and have non-terminating, non-repeating decimal representations.
6. Real numbers (R): Includes all rational and irrational numbers.
Now, let's analyze the given numbers:
A. 459: The number 459 is a whole number, an integer, and a rational number, as it can be expressed as 459/1.
Therefore, it belongs to the subsets W, Z, and Q.
B. -12: The number -12 is an integer and a rational number because it can be expressed as -12/1.
Therefore, it belongs to the subsets Z and Q.
C. 0: The number 0 is an integer and a rational number, as it can be expressed as 0/1.
Therefore, it belongs to the subsets Z and Q.
D. 3π: The number 3π is an irrational number since it cannot be expressed as a fraction and has a non-repeating, non-terminating decimal representation.
Therefore, it belongs to the subset I.
To summarize:
A. 459: W, Z, Q
B. -12: Z, Q
C. 0: Z, Q
D. 3π: I
A. For subset A:
- The number 459 belongs to the subset of Real Numbers.
- The number 4 belongs to the subset of Real Numbers.
- The number 5 belongs to the subset of Real Numbers.
- The number 9 belongs to the subset of Real Numbers.
B. For subset B:
- The number -12 belongs to the subset of Real Numbers.
- The number - belongs to the subset of Real Numbers.
- The number 12 belongs to the subset of Real Numbers.
C. For subset C:
- The number 0 belongs to the subset of Real Numbers.
D. For subset D:
- The number 3π belongs to the subset of Real Numbers.
- The number 3 belongs to the subset of Real Numbers.
- The symbol π, or pi, is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is also a Real Number.