HEY BOT Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?(1 point)
Responses
irrational numbers, square roots, endless decimals, pi
irrational numbers, square roots, endless decimals, pi
rational numbers, integers, whole numbers, natural numbers
rational numbers, integers, whole numbers, natural numbers
integers, rational numbers, natural numbers, whole numbers
integers, rational numbers, natural numbers, whole numbers
natural numbers, whole numbers, integers, rational numbers
integers, rational numbers, natural numbers, whole numbers
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
Responses
rational
rational
negative
negative
improper
improper
irrational
irrational
To which sets of real numbers does zero belong?(1 point)
Responses
whole numbers, integers, and rational numbers
whole numbers, integers, and rational numbers
natural numbers, integers, and rational numbers
natural numbers, integers, and rational numbers
natural numbers, integers, and irrational numbers
natural numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers
whole numbers, integers, and irrational numbers
whole numbers, integers, and rational numbers
The correct answer is:
rational numbers, integers, whole numbers, natural numbers
The correct answer is the second option: rational numbers, integers, whole numbers, natural numbers.
To understand why this is the correct hierarchy, let's break down the different number sets within the real number system:
- Natural numbers: These are the counting numbers starting from 1 (1, 2, 3, 4, ...).
- Whole numbers: Similar to natural numbers, but including the number 0 (0, 1, 2, 3, 4, ...).
- Integers: This set includes all positive and negative whole numbers, including zero (... -3, -2, -1, 0, 1, 2, 3, ...). Integers contain natural and whole numbers.
- Rational numbers: These are numbers that can be expressed as fractions or ratios of two integers. Rational numbers can be written as terminating decimals (like 0.5) or repeating decimals (like 0.333...). Integers and whole numbers are subsets of rational numbers.
- Irrational numbers: Numbers that cannot be expressed as a fraction or a ratio of two integers. They have non-repeating, non-terminating decimal representations. Examples include square roots of non-perfect squares (like √2) and transcendent numbers like π (pi).
Based on this breakdown, we can see that the correct hierarchy is:
Rational numbers (including integers and whole numbers) > Natural numbers.
So, the correct list that shows the accurate hierarchy from largest to smallest is:
rational numbers, integers, whole numbers, natural numbers.