Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest? (1 point)
Responses
rational numbers, integers, whole numbers, natural numbers
natural numbers, whole numbers, integers, rational numbers
integers, rational numbers, natural numbers, whole numbers
irrational numbers, square roots, endless decimals, pi
integers, rational numbers, natural numbers, whole numbers
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Describe the set of numbers that are real numbers that cannot be expressed as one integer divided by another
The correct hierarchy of number sets within the real number system, from largest to smallest, is:
integers, rational numbers, natural numbers, whole numbers
The correct answer is: integers, rational numbers, natural numbers, whole numbers.
To understand how to determine the hierarchy of number sets within the real number system, we need to understand the definitions of each set:
1. Natural Numbers: The set of all positive integers (1, 2, 3, ...). This set does not include zero or negative numbers.
2. Whole Numbers: The set of all natural numbers including zero (0, 1, 2, 3, ...). This set includes all natural numbers.
3. Integers: The set of all positive and negative whole numbers, including zero (... -3, -2, -1, 0, 1, 2, 3, ...). This set includes all natural and whole numbers.
4. Rational Numbers: The set of numbers that can be expressed as a fraction or a ratio of two integers (including integers and fractions) (1/2, 3/4, 5, -2, 6/3, ...). This set includes all natural numbers, whole numbers, and integers.
Now, comparing the answer choices given:
A. rational numbers, integers, whole numbers, natural numbers - This list is in reverse order. It starts with the largest set (rational numbers) and goes down to the smallest set (natural numbers).
B. natural numbers, whole numbers, integers, rational numbers - This list is also in reverse order. It starts with the largest set (natural numbers) and goes down to the smallest set (rational numbers).
C. integers, rational numbers, natural numbers, whole numbers - This list is in the correct order. It starts with the largest set (integers) and goes down to the smallest set (whole numbers).
D. irrational numbers, square roots, endless decimals, pi - This list includes irrational numbers and specific examples (square roots, endless decimals, pi), but it does not cover the complete hierarchy of number sets within the real number system.
Therefore, the correct answer is C: integers, rational numbers, natural numbers, whole numbers.