Choose which set or sets the following number belongs to. Be sure to account for ALL sets.-17
The number -17 belongs to the following sets:
1. Whole numbers: The set of whole numbers is defined as all positive numbers including zero and their negatives. Since -17 is a negative number, it belongs to the set of whole numbers.
2. Integers: The set of integers includes all whole numbers, including zero, and their negatives. -17 is an integer because it is a negative whole number.
3. Rational numbers: Rational numbers are numbers that can be expressed as a fraction where the numerator and denominator are both integers. -17 can be written as -17/1, so it is a rational number.
4. Real numbers: The set of real numbers includes all rational and irrational numbers. Since -17 is a rational number, it is also a real number.
Therefore, the number -17 belongs to the sets of whole numbers, integers, rational numbers, and real numbers.
To determine which set or sets the number -17 belongs to, we need to consider the different number sets.
1. Natural Numbers (N): These are the positive whole numbers, excluding zero. Since -17 is not a positive number, it does not belong to the set of natural numbers.
2. Whole Numbers (W): These are the non-negative integers, including zero. Similar to the natural numbers, -17 is not a non-negative number, so it does not belong to the set of whole numbers.
3. Integers (Z): Integers include both positive and negative whole numbers, along with zero. Since -17 is a negative whole number, it does belong to the set of integers.
4. Rational Numbers (Q): Rational numbers include any number that can be expressed as a fraction, where the numerator and denominator are integers. -17 can be written as the fraction -17/1, so it belongs to the set of rational numbers.
5. Real Numbers (R): Real numbers include both rational numbers and irrational numbers, such as square roots of non-perfect squares. Since -17 is a rational number, it also belongs to the set of real numbers.
Therefore, the number -17 belongs to the sets of integers (Z), rational numbers (Q), and real numbers (R).