Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
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Question 1:Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
Answer 1: rational numbers, integers, whole numbers, natural numbers
Question 2:Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.
Answer 2:Irrational
Question 3:To which sets of real numbers does zero belong?
Answer 3:whole numbers, integers, and rational numbers
Question 4:Use the image to answer the question. A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
Answer 4 :the diagonal of one of the cube’s faces
Question 5:Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?
Answer 5:
2 3/4
Hope this helps.....it will.....but here are the answers...
I apologize for the incorrect response in my previous answer. Here are the correct answers:
Question 1: The accurate hierarchy of number sets within the real number system, from largest to smallest, is natural numbers, whole numbers, integers, rational numbers.
Question 2: The set of numbers that are real numbers but cannot be expressed as one integer divided by another is called irrational numbers.
Question 3: Zero belongs to the sets of whole numbers, integers, and rational numbers.
Question 4: The measurement that will require the use of irrational numbers is the diagonal of one of the cube's faces.
Question 5: The number that could be used to specify how many cups of flour should be used in a bread recipe is 2 3/4.
Thank you for pointing out the mistakes, and I apologize for any confusion caused.
The accurate hierarchy of number sets within the real number system, from largest to smallest, is as follows:
1. Real numbers: This set includes all rational and irrational numbers. It is the largest set within the real number system.
2. Irrational numbers: This set includes numbers that cannot be expressed as a ratio of two integers, such as √2, π, or e. Irrational numbers are non-repeating and non-terminating decimals.
3. Rational numbers: This set includes numbers that can be expressed as a ratio of two integers, such as 1/2, 0.75, or -3. Rational numbers can be either terminating (such as 2.5) or repeating (such as 0.333...).
4. Integers: This set includes all positive and negative whole numbers (0, 1, -1, 2, -2, etc.) along with zero.
5. Whole numbers: This set includes all positive whole numbers and zero (0, 1, 2, 3, etc.). It does not include negative numbers.
6. Natural numbers: This set includes all positive whole numbers (1, 2, 3, etc.). It does not include zero or negative numbers.
So, the accurate hierarchy of number sets within the real number system, from largest to smallest, is Real numbers > Irrational numbers > Rational numbers > Integers > Whole numbers > Natural numbers.
Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
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The real number system hierarchy starts from the largest set to the smallest set. Here is an accurate hierarchy of number sets within the real number system, from largest to smallest:
1. Complex Numbers: Complex numbers are formed by the combination of real numbers and imaginary numbers. They are represented in the form a + bi, where a and b are real numbers and i is the imaginary unit.
2. Real Numbers: Real numbers include the rational and irrational numbers. They are represented as numbers that can be placed on the number line, including both positive and negative numbers.
3. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction p/q where p and q are integers and q is not equal to zero. Rational numbers include integers, whole numbers, and terminating or repeating decimals.
4. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction p/q and have non-terminating, non-repeating decimal representations. Examples of irrational numbers include pi (π) and the square root of 2 (√2).
5. Integers: Integers are whole numbers (positive, negative, or zero) and their opposites. They do not include fractions or decimal numbers.
6. Whole Numbers: Whole numbers include all positive integers and zero. They do not include negative numbers or fractions.
7. Natural Numbers: Natural numbers, also known as counting numbers, are the numbers used for counting and ordering. They start from 1 and go infinitely without including zero or negative numbers.
This hierarchy represents the inclusion of number sets within the real number system, from the largest set (complex numbers) to the smallest set (natural numbers).
To find the accurate hierarchy of number sets within the real number system, you need to understand the different types of number sets and how they relate to one another. Here is the correct hierarchy from largest to smallest within the real number system:
1. Counting Numbers (Natural Numbers): These are the positive whole numbers starting from 1 and continuing indefinitely (1, 2, 3, 4, ...).
2. Whole Numbers: This set includes all the counting numbers along with zero (0, 1, 2, 3, 4, ...).
3. Integers: Integers include all the whole numbers along with their negatives (-3, -2, -1, 0, 1, 2, 3, ...).
4. Rational Numbers: Rational numbers are numbers that can be expressed as fractions, where the numerator and denominator are both integers (such as 1/2 or -5/3). Rational numbers include integers and fractions, including terminating decimals (e.g., 0.5) and repeating decimals (e.g., 0.3333...).
5. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as fractions or the ratio of two integers. They have non-repeating, non-terminating decimal representations, like π (pi) or √2 (square root of 2).
6. Real Numbers: The set of real numbers includes both rational and irrational numbers, encompassing all possible numbers on the number line.
So, the correct hierarchy of number sets within the real number system, from largest to smallest, is: Real Numbers > Irrational Numbers > Rational Numbers > Integers > Whole Numbers > Counting Numbers.