The Number System Unit Test
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Question
Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
All rational numbers are also integers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
The correct statement is: Whole numbers include all natural numbers and 0.
The statement that is true about the relationships between the number sets is:
Whole numbers include all natural numbers and 0.
To answer this question, we need to understand the relationships between different number sets.
The number sets mentioned in the question are:
1. Rational numbers: These are numbers that can be expressed as a fraction of two integers. Examples include 1/2, 3/4, and -2/7.
2. Integers: Integers are a subset of rational numbers that include all whole numbers (positive, negative, or zero) and their opposites. Examples include -3, 0, and 5.
3. Natural numbers: These are the counting numbers, starting from 1 and going to infinity. Examples include 1, 2, 3, and so on.
4. Real numbers: Real numbers include both rational and irrational numbers. They are the set of all possible numbers on the number line. Examples include 3.14, -2.5, and √2.
5. Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers or numbers with non-terminating and non-repeating decimals. Examples include π (pi) and √2.
Now let's analyze each statement:
Statement 1: "All rational numbers are also integers."
This statement is false. Rational numbers can include fractions and decimals, which are not integers. For example, 1/2 and 3.14 are rational numbers but not integers.
Statement 2: "Not all natural numbers are real numbers."
This statement is true. Natural numbers are a subset of real numbers, but real numbers also include non-countable numbers such as fractions and decimals. For example, 1 is a natural number and also a real number, but 1/2 is a real number but not a natural number.
Statement 3: "Some irrational numbers are also integers."
This statement is false. By definition, irrational numbers cannot be expressed as fractions or integers. They are usually irrational because their decimal representations are non-terminating and non-repeating. Therefore, irrational numbers cannot be integers.
Statement 4: "Whole numbers include all natural numbers and 0."
This statement is true. Whole numbers are a subset of natural numbers and also include the number 0. Therefore, all natural numbers (1, 2, 3, etc.) are also whole numbers.
Based on the explanations above, the correct response to the question would be: "Not all natural numbers are real numbers."