Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)

Question

Responses

natural numbers, whole numbers, integers, rational numbers
natural numbers, whole numbers, integers, rational numbers

rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers

irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi

integers, rational numbers, natural numbers, whole numbers

Answer 1

The correct hierarchy of number sets within the real number system, from largest to smallest, is:

Rational numbers, integers, whole numbers, natural numbers.

So the accurate response from your list is:

rational numbers, integers, whole numbers, natural numbers.

Answer 2

Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
Responses

negative
negative

improper
improper

rational
rational

irrational

Answer 3

The set of numbers that are real numbers but cannot be expressed as one integer divided by another are called irrational numbers.

So the correct response is:

irrational.

Answer 4

To which sets of real numbers does zero belong?(1 point)
Responses

natural numbers, integers, and rational numbers
natural numbers, integers, and rational numbers

whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers

whole numbers, integers, and rational numbers
whole numbers, integers, and rational numbers

natural numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers

Answer 5

Zero belongs to the following sets of real numbers:

• Whole numbers
• Integers
• Rational numbers

It does not belong to the set of natural numbers, as natural numbers typically start from 1.

So the correct response is:

whole numbers, integers, and rational numbers.

Answer 6

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 volume of the cube
the volume 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 surface area of the cube

Answer 7

In a cube, all edges are equal, and if the edge length \(a\) is a rational number, the following calculations can be made:

• Volume of the cube is given by \(V = a^3\), which will also be a rational number.
• Area of one of the cube’s faces is given by \(A = a^2\), which will also be a rational number.
• Surface area of the cube is given by \(SA = 6a^2\), which is also a rational number.

However, the diagonal of one of the cube’s faces can be calculated using the Pythagorean theorem:

\[ d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2}. \]

Since \(\sqrt{2}\) is an irrational number, the diagonal measurement will require the use of irrational numbers.

So the correct response is:

the diagonal of one of the cube’s faces.

Answer 8

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

234
2 Start Fraction 3 over 4 End Fraction

47
Start Fraction 4 over 7 End Fraction

square root of 3

Answer 9

In a recipe, the amount of an ingredient like flour cannot be negative, and it should generally be a positive rational number represented in a meaningful way (for instance, whole cups or fractions of a cup).

Let's evaluate the options:

1. −3: Negative number, not valid for cups of flour.
2. 234: Positive whole number, valid.
3. 47: Positive whole number, valid.
4. \( \frac{4}{7} \): Positive fraction, valid.
5. Square root of 3: While it is a positive number, it is irrational and not practical for measuring cups in a recipe.

Based on this analysis, the numbers that could be used to specify how many cups of flour should be used in a bread recipe are:

234, 47, and \( \frac{4}{7} \).

Since you can only choose one option, the best choice is 234, as it is a definite number of cups that can be used.