In Exercises 35–38, list all numbers from the given set that are ...

Question

In Exercises 35–38, list all numbers from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. {-9, -4/5, 0, 0.25, √3, 9.2, √100}

Accepted Answer

Hello Today we're going to be identifying and classifying all the numbers. Even in a given set of numbers. So the set of numbers given to us is negative five. Negative 1/3 0.75 square root of 11, 10.2 and the square root of 81. Now we need to go ahead and identify which one of these are Real numbers, irrational numbers, rational numbers, integers, whole numbers and natural numbers. So let's go ahead and start that. We're gonna first start with the real numbers and the real numbers are any number that can be charted on a number line. All of the values given to us can be charted on a number line. So the entire set of numbers given to us are all considered real numbers, Square root of 11, And the Square Root of 81. Alright, so the entire set of numbers given to us are all classified as real numbers. Let's go ahead and identify the irrational numbers. Now irrational numbers are any numbers that have decimals that are not non terminating and repeating. And really the only number that has a value like that is going to be the square root of 11 because the square root of has an approximate value of 3.31662 dot dot dot continuous. So the only rational number in our set of numbers is going to be the square root of 11. Alright, now we need to find our rational numbers and rational numbers are any numbers that can be represented as a ratio negative five is considered a rational number because negative five could be represented as negative 5/1. zero is considered a rational number because zero could be represented as zero over any number, negative 1/3 is a rational number because it's the ratio of negative one and three 0. can be represented a rational number because 0.75 could be rewritten as 3/4. Mhm. and 10.2 could be represented as a rational number because 10.2 is the same thing as 10 plus 2/10 Which is equal to 51/5. And finally the square root of 81 could be represented as a rational number because the square root of 81 is going to give you nine and nine could be represented as 9/1. So that's gonna be the final rational number. Okay now we need to go ahead and find the integers and the integers are all positive and negative. Whole numbers including zero. The only numbers that fit that description are going to be negative 50. And the square root of 81. Because the square root of 81 could be represented as nine. Alright, now we need to go ahead and find our whole numbers. Whole numbers are all the positive whole numbers including zero. And the only numbers that fit that description are going to be zero and the square root of 81. And finally we need to go ahead and find our natural numbers And natural numbers are all of our positive whole numbers that don't include zero and the only number that fits that description is going to be the square root of 81. Alright, so this is going to be the classifications for all the numbers in our given set of numbers. That means that the answer to this problem is going to be deep. So I hope this video helps you in understanding how to classify all the numbers in a given set of numbers. And I'll go ahead and see you all in the next video.