Which list shows an Accurate hierarchy of number sets within the real number system, from largest to smallest?

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

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

Rational numbers, integers, whole numbers, natural numbers

The set of numbers that are real numbers but cannot be expressed as one integer divided by another is called irrational numbers. These numbers cannot be written as a fraction or ratio of two integers. They are numbers that cannot be expressed as terminating or repeating decimals and have infinite, non-repeating decimal expansions. Examples of irrational numbers include the square root of 2 (√2), pi (π), e, and the golden ratio.

Congratulations on scoring 4/5! Well done.

Regarding the answer to the fourth question, my apologies for the incorrect response. You are correct, "The diagonal of one of the cube's faces" is the measurement that will require the use of a rational number.

Great job on your performance! If you have any more questions or need assistance with anything else, feel free to ask.

Thank you

You're welcome! If you have any more questions, feel free to ask.

Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.

Improper

Negative

Irrational

Rational

To which sets of real numbers does 0 belong?

Natural numbers, integers, and rational number

Natural numbers, integers, and irrational numbers

Whole numbers, integers, and rational numbers

Whole numbers, integers, and rational numbers

The correct answer is:

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 a rational numbers.

The diagonal of one of the cube's faces

The surface area of the cube

The volume of the cube

The area of one of the cubes faces

The measurement that will require the use of a rational number is the volume of the cube. The volume of a cube is given by the formula V = a^3, where a is the length of one side of the cube. Since the edge length, a, is given to be a rational number, the resulting volume will also be a rational number.