Which list shows an accurate hierarchy of

Question

number sets within the real number system,
from largest to smallest? (1 point)
integers, rational numbers, natural
numbers, whole numbers
rational numbers, integers, whole
numbers, natural numbers
natural numbers, whole numbers,
integers, rational numbers
irrational numbers, square roots,
endless decimals, pi

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

However, since this exact option is not listed, the closest correct representation choice is:

rational numbers, integers, whole numbers, natural numbers.

This arrangement indicates that rational numbers encompass integers, which include whole numbers, which in turn contain natural numbers. The other lists provided in your question do not accurately represent the hierarchy.

Answer 2

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

Answer 3

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

Irrational numbers cannot be represented as a fraction of two integers, unlike rational numbers. Examples of irrational numbers include the square root of non-perfect squares (like √2), π (pi), and e (the base of natural logarithms).

Answer 4

To which sets of real numbers does zero belong? (1 point)
natural numbers, integers, and irrational numbers
natural numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
whole numbers, integers, and irrational numbers

Answer 5

Zero belongs to the following sets of real numbers:

whole numbers, integers, and rational numbers.

• Whole numbers: The set of whole numbers includes 0 and all positive integers (0, 1, 2, 3, ...).
• Integers: The set of integers includes all whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...).
• Rational numbers: Zero can be expressed as a fraction (0/1, for example), making it a rational number.

Thus, the correct choice from your options is: whole numbers, integers, and rational numbers.

Answer 6

A cube has an edge length, , that is a rational number of
centimeters. Identify which measurement will require the use of
irrational numbers.
(1 point)
a
the diagonal of one of the cube’s faces
the surface area of the cube
the area of one of the cube’s faces
the volume of the cube

Answer 7

To identify which measurement will require the use of irrational numbers for a cube with a rational edge length (denoted as \( a \)), we can analyze each option:

1. The diagonal of one of the cube’s faces: The diagonal \( d \) of a face (which is a square) can be calculated using the Pythagorean theorem. The formula is \( d = \sqrt{a^2 + a^2} = \sqrt{2a^2} = a\sqrt{2} \). Since \( \sqrt{2} \) is an irrational number, the diagonal will be irrational.

2. The surface area of the cube: The surface area \( S \) of a cube is given by \( S = 6a^2 \), which is rational since it involves only rational numbers.

3. The area of one of the cube’s faces: The area \( A \) of one face of the cube is \( A = a^2 \), which is also rational.

4. The volume of the cube: The volume \( V \) of the cube is \( V = a^3 \), which is rational.

Based on this analysis, the measurement that will require the use of irrational numbers is:

the diagonal of one of the cube’s faces.

Answer 8

whats the answer
a
b
c
d

Answer 9

The answer is:

a - the diagonal of one of the cube’s faces.

Answer 10

Which of the following numbers could be used to specify how many
cups of flour should be used in a bread recipe? (1 point)
−3
square root of 3
2
3
4
4
7

Answer 11

To specify how many cups of flour should be used in a bread recipe, you would need a non-negative number that makes sense in the context of measuring ingredients.

From the options you provided:

• −3: Not possible, as you cannot have a negative amount of flour.
• square root of 3: While this is a positive number, it is irrational and not typically used for measuring cups in a recipe.
• 2: Valid and non-negative.
• 3: Valid and non-negative.
• 4: Valid and non-negative.
• 4: (duplicate) Valid and non-negative.
• 7: Valid and non-negative.

Thus, the acceptable options for specifying how many cups of flour should be used are 2, 3, 4, and 7. If you can only select one number, you could choose any non-negative number from those available.