Of the following numbers, which is an integer but does not belong in either of the subsets of integers: −13
, 0, or 13?(1 point)
The number -13 is an integer and does not belong in either of the subsets of integers because it is not a positive integer.
Which of the following is an integer but not a whole number: 0, −2
, 7, 783?(1 point)
The number -2 is an integer but not a whole number because it is a negative integer.
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Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
rational numbers, integers, whole numbers, natural numbers
natural numbers, whole numbers, integers, rational numbers
irrational numbers, square roots, endless decimals, pi
integers, rational numbers, natural numbers, whole numbers
The correct hierarchy of number sets within the real number system, from largest to smallest, is:
integers, rational numbers, whole numbers, natural numbers
Therefore, the correct answer is:
integers, rational numbers, natural numbers, whole numbers
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
The set of real numbers that cannot be expressed as one integer divided by another are called irrational numbers. These numbers cannot be written as the ratio of two integers and they have non-repeating and non-terminating decimal representations. Examples of irrational numbers include π (pi), e (Euler's number), √2 (the square root of 2), and √3 (the square root of 3).
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
negative
rational
irrational
improper
The correct answer is "irrational."
To which sets of real numbers does zero belong?(1 point)
whole numbers, integers, and rational numbers
natural numbers, integers, and irrational numbers
natural numbers, integers, and rational numbers
whole numbers, integers, and irrational numbers
Zero belongs to the sets of real numbers:
- whole numbers: Zero is a whole number because it is neither negative nor positive.
- integers: Zero is an integer because it can be represented as both a positive and a negative whole number.
- rational numbers: Zero is a rational number because it can be written as 0/1, which is the ratio of two integers.
Therefore, the correct answer is:
whole numbers, integers, and rational numbers
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)
the diagonal of one of the cube’s faces
the volume of the cube
the area of one of the cube’s faces
the surface area of the cube
The measurement that will require the use of irrational numbers is the diagonal of one of the cube's faces.
The length, width, and height of the cube, which are all labeled as "a," are rational numbers. However, the diagonal of one of the cube's faces, which can be found using the Pythagorean theorem, will involve the square root of 2. Since the square root of 2 is an irrational number, the diagonal of one of the cube's faces would require the use of irrational numbers.
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?(1 point)
47
−3
square root of 3
234
The number that could be used to specify how many cups of flour should be used in a bread recipe is 47.
Which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe?(1 point)
4/7
−3
square root of 3
234
The number that could be used to specify how many cups of flour should be used in a bread recipe is 4/7.
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
the diagonal of one of the cube’s faces
the volume of the cube
the area of one of the cube’s faces
the area of one of the cube’s faces
the surface area of the cube