Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
Responses
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi
natural numbers, whole numbers, integers, rational numbers
natural numbers, whole numbers, integers, rational numbers
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural 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
irrational
irrational
negative
negative
improper
improper
rational
irrational
To which sets of real numbers does zero belong?(1 point)
Responses
natural numbers, integers, and rational numbers
natural numbers, integers, and rational 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
whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational 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 area of one of the cube’s faces
the area of one of the cube’s faces
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 surface area of the cube
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
47
Start Fraction 4 over 7 End Fraction
−3
negative 3
234
2 Start Fraction 3 over 4 End Fraction
square root of 3
47
The correct answer is:
integers, rational numbers, natural numbers, whole numbers
To understand why this is the correct hierarchy within the real number system, let's break it down:
1. Integers: This set includes all positive and negative whole numbers, including zero. Integers are considered a subset of the real numbers.
2. Rational numbers: These are numbers that can be expressed as a fraction or ratio of two integers. This includes integers since they can be expressed as a fraction with a denominator of 1 (e.g., 3 = 3/1). Rational numbers also include decimals that either terminate or repeat, such as 0.5 (1/2) or 0.333... (1/3).
3. Natural numbers: Also known as counting numbers, these are the positive integers greater than zero. Natural numbers do not include negative numbers or zero.
4. Whole numbers: Whole numbers include zero and all positive integers. They do not include negative numbers or fractions.
So, the correct hierarchy is integers, rational numbers, natural numbers, whole numbers.