Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
Responses
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers
natural numbers, whole numbers, integers, rational numbers
The correct answer is: rational numbers, integers, whole numbers, natural numbers
The Real Number System Quick Check
2 of 52 of 5 Items
Question
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
Responses
rational
rational
irrational
irrational
negative
negative
improper
The correct answer is: irrational
To which sets of real numbers does zero belong?(1 point)
Responses
whole numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
natural numbers, integers, and rational numbers
The correct answer is: whole numbers, integers, and rational numbers.
The Real Number System Quick Check
4 of 54 of 5 Items
Question
Use the image to answer the question.
The length, width, and height of a cube are all labeled a.
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
(1 point)
Responses
the surface area of the cube
the surface area of the cube
the diagonal of one of the cube’s faces
the diagonal of one of the cube’s faces
the area of one of the cube’s faces
the area of one of the cube’s faces
the volume of the cube
The correct answer is: the diagonal of one of the cube's faces.
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?(1 point)
Responses
−3
negative 3
square root of 3
square root of 3
47
Start Fraction 4 over 7 End Fraction
2 3/4
The correct answer is: 47 and 2 3/4
The correct answer is:
rational numbers, integers, whole numbers, natural numbers.
To determine the hierarchy of number sets within the real number system from largest to smallest, we need to understand the definitions of each set.
1. Rational numbers: Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Rational numbers include integers, fractions, and decimals that either terminate or repeat.
2. Integers: Integers are the set of whole numbers and their negatives, including zero. It includes both positive and negative whole numbers.
3. Whole numbers: Whole numbers are the set of positive integers including zero. It does not include negative numbers or fractions.
4. Natural numbers: Natural numbers are the set of positive integers excluding zero. Natural numbers are the counting numbers starting from one.
By comparing the definitions and sets, we can see that rational numbers include integers, whole numbers, and natural numbers. Integers include whole numbers and natural numbers. Whole numbers include natural numbers. Therefore, the correct hierarchy from largest to smallest is: rational numbers, integers, whole numbers, natural numbers.