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Answer questions from Math 8A unit 2 sudy Guide
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which statement is true about the relationship between the number sets?
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are all irrational numbers also integers
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is every number a whole number
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does a whole number include all natural numbers and 0
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why does a whole number include all natural numbers and 0
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what is true about -47 when using number system
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is -47 a rational number explain why
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is -47 a whole number
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what set of numbers is always rational when using the number system
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are integers always rational
Answered by GPT 3.5
I apologize, but I am an AI language model and I don't have access to specific study guides. However, if you provide me with the questions, I'll do my best to help you with them.
Answered by GPT 3.5
Without specific information about the number sets you are referring to, it is difficult to determine which statement is true about their relationship. Please provide more information or specific statements about the number sets you are comparing, and I will be glad to assist you further.
Answered by GPT 3.5
No, not all irrational numbers are integers. In fact, by definition, irrational numbers cannot be written as a fraction or ratio of two integers. They are numbers that cannot be expressed as a terminating or repeating decimal.

On the other hand, integers include whole numbers (positive and negative) and zero, but they do not include fractions or decimals.

Therefore, while irrational numbers and integers are both types of real numbers, not all irrational numbers are integers.
Answered by GPT 3.5
No, not every number is a whole number.

Whole numbers include all the non-negative integers (0, 1, 2, 3, ...), and they do not include any negative numbers or fractions.

There are other types of numbers beyond whole numbers, such as negative integers, rational numbers (which include fractions and decimals that terminate or repeat), irrational numbers (decimals that do not terminate or repeat), and complex numbers, to name a few.

So, while every whole number is a number, not every number is a whole number.
Answered by GPT 3.5
Yes, a whole number includes all natural numbers (positive integers) and zero. So, the set of whole numbers is {0, 1, 2, 3, ...}.
Answered by GPT 3.5
A whole number includes all natural numbers and zero because the concept of whole numbers was introduced to extend the set of natural numbers by including zero.

The natural numbers are the counting numbers starting from 1 (1, 2, 3, 4, ...), and they do not include zero. However, when the concept of whole numbers was introduced, it was done to include zero as an element of the set.

Including zero in the set of whole numbers allows for a more comprehensive representation of numbers. It enables operations such as addition, subtraction, and multiplication to be performed with zero as a valid element.

So, by convention and mathematical convention, zero is considered a whole number, and the set of whole numbers incorporates both natural numbers and zero.
Answered by GPT 3.5
In the number system, the number -47 is an integer. Integers include all whole numbers (positive and negative) and zero, and they are denoted by the symbol Z.

Specifically, -47 is a negative integer since it is less than zero. It represents a quantity that is 47 units less than zero on the number line.

Integers are a fundamental part of the number system and are used to represent both positive and negative values in various mathematical operations and applications.
Answered by GPT 3.5
Yes, -47 is a rational number. A rational number is any number that can be expressed as a fraction of two integers, where the denominator is not zero.

We can express -47 as the fraction -47/1, where the numerator (-47) and the denominator (1) are both integers. Since -47 can be expressed as a ratio of two integers, it is classified as a rational number.

It's important to note that the "-47" in the fraction is the numerator, and the "1" in the denominator does not affect the rationality of the number. As long as the number can be expressed as the ratio of two integers, it is considered rational.
Answered by GPT 3.5
No, -47 is not a whole number. Whole numbers are non-negative integers, including zero. However, -47 is a negative integer, which means it is less than zero. Whole numbers don't include negative numbers, only positive integers and zero.
Answered by GPT 3.5
In the number system, the set of numbers that is always rational is the set of rational numbers, denoted by Q.

Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero. These numbers can be written as fractions or terminating/repeating decimals.

The set of rational numbers includes integers (positive, negative, and zero), fractions (such as 1/2, -3/4, etc.), and decimals that terminate or repeat (like 0.25, -0.75, 0.333..., etc.).

So, whenever you have a number that can be expressed as a fraction or a decimal that terminates or repeats, it is a rational number.
Answered by GPT 3.5
Yes, integers are always rational numbers.

To be classified as an integer, a number must be a whole number (including zero) or its negative counterpart.

Rational numbers, on the other hand, are numbers that can be expressed as the quotient or ratio of two integers. Since integers can be written as fractions with a denominator of 1, they can always be expressed as the ratio of two integers.

For example, the integer 5 can be written as 5/1. Similarly, the integer -3 can be written as -3/1. In both cases, the numerator and denominator are integers, satisfying the definition of a rational number.

Therefore, integers are a subset of rational numbers, as they can always be expressed as ratios of integers.