Which list shows an accurate hierarchy of number sets within the real number system, from largest to smallest?
A. rational numbers, integers, whole numbers, natural numbers
B. natural numbers, whole numbers, integers, rational numbers
C. irrational numbers, square roots, endless decimals, pi
D. integers, rational numbers, natural numbers, whole numbers
B. natural numbers, whole numbers, integers, rational numbers
Describe the set of numbers that are real numbers but cannot be expressed as one integer divided by another.(1 point)
Responses
negative
negative
improper
improper
rational
rational
irrational
Bot help
A. rational numbers, integers, whole numbers, natural numbers
But don't worry, no matter what number set you're in, it's always a good place to be! Unless you're stuck in a never-ending decimal that refuses to become rational, then things might get a bit dicey.
The correct answer is A. rational numbers, integers, whole numbers, natural numbers.
The real number system is composed of different sets, each containing a subset of numbers. To determine the hierarchy of number sets from largest to smallest within the real number system, we need to understand the characteristics and relationships of these sets.
1. Natural Numbers: Natural numbers are the set of counting numbers starting from 1 and going up to infinity. They do not include zero or negative numbers.
2. Whole Numbers: Whole numbers include all the natural numbers plus zero. So, it is an extension of the natural numbers set.
3. Integers: Integers are made up of all whole numbers, including zero, and their negatives. This means that integers include positive numbers, negative numbers, and zero.
4. Rational Numbers: Rational numbers are the set of numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. Rational numbers include integers, fractions, and terminating or repeating decimals.
Based on the characteristics and relationships of these number sets, the correct hierarchy is as follows:
Rational numbers (includes fractions, decimals, and integers) -> Integers (includes positive numbers, negative numbers, and zero) -> Whole numbers (includes positive numbers and zero) -> Natural numbers (includes positive numbers)
Therefore, the correct answer is A. rational numbers, integers, whole numbers, natural numbers.