Classify the number 2/3 in the proper sets.
To classify the number 2/3 in the proper sets, we need to determine whether it can be classified as a natural number, whole number, integer, rational number, or irrational number.
- Natural numbers (N): Natural numbers are the set of positive integers starting from 1. Since 2/3 is not a positive integer, it cannot be classified as a natural number.
- Whole numbers (W): Whole numbers are the set of positive integers including zero. Since 2/3 is not an integer, it cannot be classified as a whole number.
- Integers (Z): Integers are the set of positive and negative whole numbers, including zero. Since 2/3 is not an integer, it cannot be classified as an integer.
- Rational numbers (Q): Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers. The number 2/3 is represented as a fraction and can be expressed as the ratio of two integers (numerator 2, denominator 3). Therefore, 2/3 is a rational number.
- Irrational numbers (I): Irrational numbers are numbers that cannot be expressed as a fraction and have an infinite non-repeating decimal representation. Since 2/3 can be expressed as a fraction and has a finite decimal representation (0.666...), it is not classified as an irrational number.
In summary, the number 2/3 can be classified as a rational number, but not as a natural number, whole number, integer, or irrational number.