Match the Real Number subset to the set of numbers given. Each subset will be used.
{6π, 15−−√}
The Real Number subsets are:
1) Natural numbers (N)
2) Whole numbers (W)
3) Integers (Z)
4) Rational numbers (Q)
5) Irrational numbers (I)
6) Real numbers (R)
The set of numbers {6π, 15−−√} belongs to the subsets:
- Irrational numbers (I): both 6π and 15−−√, cannot be expressed as a fraction and their decimal representations go on infinitely without repeating.
- Real numbers (R): all numbers that can be expressed on a number line, including both rational and irrational numbers.
So, the Real Number subsets that match the set of numbers {6π, 15−−√} are: Irrational numbers (I) and Real numbers (R).
To match the real number subsets to the set of numbers {6π, 15−−√}, let's consider the following subsets:
1. Rational numbers: Numbers that can be expressed as a ratio of two integers.
2. Irrational numbers: Numbers that cannot be expressed as a ratio of two integers.
3. Integer numbers: Whole numbers, including positive, negative, and zero.
4. Whole numbers: Positive integers and zero.
5. Natural numbers: Positive integers (excluding zero).
Now, let's match each subset to the given set of numbers:
1. Rational numbers: The number 6π is a rational number since it can be expressed as the ratio of two integers (6 and π is a constant). Therefore, 6π belongs to the subset of rational numbers.
2. Irrational numbers: The number 15−−√ is an irrational number because it involves the square root of a non-perfect square. Therefore, 15−−√ belongs to the subset of irrational numbers.
3. Integer numbers: None of the given numbers, 6π and 15−−√, can be classified as integers since they are not whole numbers.
4. Whole numbers: Again, neither 6π nor 15−−√ can be classified as whole numbers since they are not positive integers or zero.
5. Natural numbers: Similar to the previous subsets, none of the given numbers fall into the subset of natural numbers since they are not positive integers.
Therefore, the matching subsets for the numbers {6π, 15−−√} are:
Rational numbers: {6π}
Irrational numbers: {15−−√}
Integer numbers: None
Whole numbers: None
Natural numbers: None
To match the Real Number subset to the set of numbers {6π, 15−−√}, we need to identify the subsets of Real Numbers that each number belongs to.
First, let's look at the given numbers:
1. 6π: This is a multiple of π, so it belongs to the subset of Real Numbers known as Irrational Numbers.
2. 15−−√: This is the square root of 15, which is a positive real number. Therefore, it belongs to the subset of Real Numbers known as Rational Numbers.
Now, let's match these numbers with the corresponding Real Number subset:
1. 6π belongs to the subset of Real Numbers known as Irrational Numbers.
2. 15−−√ belongs to the subset of Real Numbers known as Rational Numbers.
So the matching subsets for the given set of numbers {6π, 15−−√} are:
- Irrational Numbers: {6π}
- Rational Numbers: {15−−√}
Remember, these classifications are based on the properties of Real Numbers, specifically whether they can be expressed as a fraction or not.