Describe all the sets and subsets the number 2/3 belongs to and enter the number corresponding to the correct answer as your response.
Enter Number 1: Rational Numbers, Integers, Whole Numbers, Natural Numbers
Enter Number 2: Rational numbers, Integers, Whole Numbers
Enter Number 3: Rational Numbers, Integers
Enter Number 4: Rational Numbers
Enter Number 5: Irrational Numbers
Enter Number 3: Rational Numbers, Integers
The number 2/3 belongs to the following sets and subsets:
1) Rational Numbers (since 2/3 can be expressed as a fraction)
2) Integers (since every integer can be expressed as a fraction)
3) Whole Numbers (since every whole number can be expressed as a fraction)
4) Natural Numbers (since every natural number can be expressed as a fraction)
Therefore, the correct answer is:
Enter Number 1: Rational Numbers, Integers, Whole Numbers, Natural Numbers
To determine the sets and subsets that the number 2/3 belongs to, we need to understand the definitions of these mathematical terms:
1. Rational Numbers: Numbers that can be expressed as a ratio of two integers, where the denominator is not zero.
2. Integers: Whole numbers (both positive and negative) and zero.
3. Whole Numbers: Positive numbers (including zero) without any fractional or decimal parts.
4. Natural Numbers: Positive whole numbers excluding zero.
5. Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers and have non-repeating, non-terminating decimal representations.
Since 2/3 can be expressed as a ratio of two integers (2 and 3), it belongs to the set of rational numbers.
Now, let's categorize 2/3 into the different subsets:
- Rational Numbers: Yes, 2/3 is a rational number.
- Integers: No, integers can only be whole numbers, and 2/3 is not a whole number.
- Whole Numbers: No, whole numbers cannot have any fractional or decimal parts, and 2/3 is not a whole number.
- Natural Numbers: No, natural numbers are positive whole numbers excluding zero, and 2/3 is not a natural number.
- Irrational Numbers: No, 2/3 can be expressed as a ratio of two integers and has a terminating decimal representation (0.666...), which means it is not an irrational number.
Based on the above explanations, the correct answer is Number 2: Rational numbers, Integers, Whole Numbers.