Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
Responses
natural numbers, whole numbers, integers, rational numbers
natural numbers, whole numbers, integers, rational 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
integers, rational numbers, natural numbers, whole numbers
rational numbers, integers, whole numbers, natural numbers
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
Responses
negative
negative
rational
rational
improper
improper
irrational
irrational
irrational
To which sets of real numbers does zero belong?(1 point)
Responses
whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
whole numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
natural numbers, integers, and rational numbers
natural numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
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 volume of the cube
the volume of the cube
the area of one of the cube’s faces
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
square root of 3
square root of 3
234
2 Start Fraction 3 over 4 End Fraction
47
Start Fraction 4 over 7 End Fraction
−3
negative 3
2 Start Fraction 3 over 4 End Fraction
The correct hierarchy of number sets within the real number system, from largest to smallest, is:
integers, rational numbers, whole numbers, natural numbers.
To understand this hierarchy, let's break it down:
1. Integers: Integers are the set of all positive and negative whole numbers, including zero. It includes numbers like -3, -2, -1, 0, 1, 2, 3, and so on.
2. Rational Numbers: Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. This includes integers as well. Examples of rational numbers are -2/3, 1/2, 3/4, and so on.
3. Whole Numbers: Whole numbers are the set of all positive integers and zero. It includes numbers like 0, 1, 2, 3, and so on. Whole numbers do not include negative numbers.
4. Natural Numbers: Natural numbers are the set of all positive integers. It includes numbers like 1, 2, 3, and so on, but excludes zero and negative numbers.
So, the correct hierarchy from largest to smallest within the real number system is:
Integers, Rational numbers, Whole numbers, Natural numbers.
Therefore, the answer is:
integers, rational numbers, whole numbers, natural numbers.