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Which lists shows an accurate hierarchy of number sets within the real number system, from largest to smallest? Integers, rational numbers, natural numbers, whole numbers. Irrational numbers, square roots, endless decimals, pi. Rational numbers, integers, whole numbers, natural numbers. National numbers, whole numbers, integers, rational numbers.

9 answers

To understand the hierarchy of number sets within the real number system, we need to know the definitions of each of these sets:

  1. Natural Numbers (N): {1, 2, 3, ...} (sometimes includes 0)
  2. Whole Numbers (W): {0, 1, 2, 3, ...}
  3. Integers (Z): {..., -3, -2, -1, 0, 1, 2, 3, ...}
  4. Rational Numbers (Q): Numbers that can be expressed as a fraction where both the numerator and denominator are integers (e.g., 1/2, 3, -4).
  5. Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., π, √2, endless non-repeating decimals).

Now, let's clarify the inclusivity of each set:

  • Natural Numbers are a subset of Whole Numbers.
  • Whole Numbers are a subset of Integers.
  • Integers are a subset of Rational Numbers.
  • Rational Numbers consist of both terminating and repeating decimals, while Irrational Numbers consist of non-terminating, non-repeating decimals.

Now, based on these definitions, we can determine the hierarchy. The correct order from largest set to smallest set should include:

  1. Real Numbers (which encompass all these sets) 2. Rational Numbers (including both integers and irrational numbers) 3. Integers (a subset of rational numbers) 4. Whole Numbers (a subset of integers) 5. Natural Numbers (a subset of whole numbers)

Considering the options:

  1. "Integers, rational numbers, natural numbers, whole numbers": Incorrect
  2. "Irrational numbers, square roots, endless decimals, pi": Incorrect and not a hierarchy
  3. "Rational numbers, integers, whole numbers, natural numbers": Is a correct order from the largest to the smallest.
  4. "Natural numbers, whole numbers, integers, rational numbers": Incorrect

Thus, the correct hierarchy from largest to smallest in your list is:

Rational numbers, integers, whole numbers, natural numbers.

Can you just say the answer without the explanation

The correct hierarchy is: 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. Negative. Improper. Rational. Irrational.

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

to which sets of real numbers does zero belong? whole numbers, integers, and rational numbers. natural numbers, integers, and rational numbers. natural numbers, integers, and irrational numbers. whole numbers, integers, and irrational numbers.

Zero belongs to the following sets of real numbers: whole numbers, integers, and rational numbers.

which of the following numbers could be used to specify how many cups of flour should be used in a bread recipe? -3. 2 3/4. square root of 3. 4/7.

The number that could be used to specify how many cups of flour should be used in a bread recipe is 2 3/4.