Choose which group of sets the following number belongs to. Be sure to account for ALL sets.
5
whole numbers, integers, rational numbers, natural numbers, real numbers
whole numbers, integers, rational numbers, real numbers
whole numbers, integers, irrational numbers, natural numbers, real numbers
whole numbers, integers, natural numbers, real numbers
The number 5 belongs to the group of sets: whole numbers, integers, rational numbers, natural numbers, real numbers.
The number 5 belongs to the following groups of sets:
1. Whole numbers: Whole numbers include all positive integers (including zero). So, 5 is a whole number.
2. Integers: Integers include all positive and negative whole numbers (including zero). Since 5 is a positive whole number, it is also an integer.
3. Rational numbers: Rational numbers include all numbers that can be expressed as a ratio of two integers. Since 5 can be expressed as 5/1, it is a rational number.
4. Real numbers: Real numbers include all numbers on the number line, including both rational and irrational numbers. Since 5 is a rational number, it is also a real number.
Therefore, the number 5 belongs to the following group of sets:
whole numbers, integers, rational numbers, real numbers.
To determine which group of sets the number 5 belongs to, we need to understand the definitions of each set.
1. Whole numbers: Whole numbers include all non-negative integers (0, 1, 2, 3, ...). They do not include any negative numbers or fractions.
2. Integers: Integers include all positive and negative whole numbers, as well as zero (-3, -2, -1, 0, 1, 2, 3, ...).
3. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero (for example, -3/4, 1/2, 2/1, 3, etc.). They include all integers and fractions.
4. Natural numbers: Natural numbers are also known as counting numbers and include all positive whole numbers (1, 2, 3, ...). Some definitions also include zero as a natural number, while others do not.
5. Real numbers: Real numbers include all rational and irrational numbers. They encompass all possible values on the number line.
Now let's determine which group of sets the number 5 belongs to:
Option 1: whole numbers, integers, rational numbers, natural numbers, real numbers
- 5 is a positive whole number and thus belongs to the set of whole numbers, integers, rational numbers, and natural numbers.
- Additionally, 5 can be expressed as a fraction of two integers (5/1), making it a rational number.
- Lastly, 5 is also a real number.
- Therefore, option 1 is correct.
Option 2: whole numbers, integers, rational numbers, real numbers
- 5 is a positive whole number and thus belongs to the set of whole numbers, integers, and rational numbers.
- Additionally, 5 can be expressed as a fraction of two integers (5/1), making it a rational number.
- Lastly, 5 is also a real number.
- Therefore, option 2 is correct.
Option 3: whole numbers, integers, irrational numbers, natural numbers, real numbers
- 5 is not an irrational number because it can be expressed as a fraction of two integers.
- Thus, option 3 is incorrect.
Option 4: whole numbers, integers, natural numbers, real numbers
- 5 is a positive whole number and thus belongs to the set of whole numbers, integers, and natural numbers.
- Additionally, 5 is also a real number.
- Therefore, option 4 is correct.
So, the correct answer is either option 1 or option 2, depending on whether zero is considered a natural number.