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. {-11, -5/6, 0, 0.75, √5, π, √64}

Accepted Answer

Hello Today we're going to be classifying the numbers of a set of numbers. So the set of numbers given to us is negative 2/ 0.3 square root of seven pi and the square root of 25. And we need to go ahead and identify all the real numbers, irrational numbers, rational numbers, integers, whole numbers and natural numbers. So let's go ahead and start with the the real numbers. So real numbers are all numbers that could be found on a line graph. That means that this is going to include our entire set of numbers because all of the numbers given to us could be plotted on a number line. Alright, so the entire set of numbers given to us are all going to be classified as real numbers. Now let's go ahead and start with irrational numbers, irrational numbers are any numbers that have a non terminating decimal or repeating decimals. While there's two values in our number set that have that classification, the square root of seven has an approximate decimal of 2.6457 dot dot dot dot non terminating. So this is going to continue for infinity. So square root of seven is classified as an irrational number. And Pie is known as a continuous decimal as it has the value 3.1415 dot dot dot dot and then it keeps going on. So Pie is gonna be our other irrational number and those are going to be the only two numbers in our set of numbers that are classified as irrational. Okay, now let's go ahead and identify the rational numbers. Rational numbers are any numbers that can be represented as a ratio of two numbers. So that includes negative 2/5. Because this is a ratio of negative two and five. We can also include zero as a rational number because zero could be represented as the ratio of zero. And any number, we can also represent 0.3 as a rational number. As 0.3 could be rewritten as 3/10, which is a ratio of 3/10. So 0.3 is a rational number. And we could represent square root 25 as a rational number because the square root of 25 is the perfect square of five and five could be represented as the ratio of five and one. So Square root 25 is gonna be our final rational number. All right now let's go ahead and identify the integers, integers are all positive and negative. Whole numbers that also include zero. And there's only two numbers that match that description. That's going to be zero itself from the set of numbers. And the square root of 25 because again the square root of 25 is positive five. Alright, so that's gonna be all of our integers. Now let's go ahead and find the whole numbers and the whole numbers are going to be all positive whole numbers including zero and that's going to be zero. And the square root of 25. Alright. And now we need to find the natural numbers and natural numbers are only whole numbers that are positive that don't include zero. And the only number from our set of numbers that fit that description is going to be the square root of 25. Alright, So this is going to be the classification for all the numbers in our given set of numbers, which means that the answer to this problem is going to be C. So, I hope this video helps you in understanding how to classify the numbers in a set of numbers. And I'll go ahead and see you all in the next video.

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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. {-11, -5/6, 0, 0.75, √5, π, √64}

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