QuestionIdentify natural numbers from the set: $\{-\frac{3}{5}, 1.\overline{4}, \sqrt{2}, 0, -4\frac{1}{4}, 12, -15, \pi\}$ . Options: A. 12, B. $-4\frac{1}{4}$ , C. -15, D. 0, E. $\pi$ , F. $1.\overline{4}$ , G. $\sqrt{2}$ , H. $-\frac{3}{5}$ .

Studdy Solution

STEP 1

Assumptions1. The given set of numbers is $\left\{-\frac{3}{5},1 . \overline{4}, \sqrt{},0,-4 \frac{1}{4},12,-15, \pi\right\}$ . . We need to categorize these numbers into natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

STEP 2

First, let's define each type of number.
a. Natural numbers These are the set of positive integers, starting from1. b. Whole numbers These are the set of non-negative integers, starting from0. c. Integers These are the set of all whole numbers, both positive and negative. d. Rational numbers These are numbers that can be expressed as a fraction of two integers. e. Irrational numbers These are numbers that cannot be expressed as a fraction of two integers. f. Real numbers These are all numbers that can be located on the number line, including both rational and irrational numbers.

STEP 3

Let's start with natural numbers. From the given set, we need to select the numbers that are positive integers.

STEP 4

From the given set, the only natural number is12. So, the answer to part a is A.12.

STEP 5

Next, let's find the whole numbers. These are non-negative integers, which means they include0 and all positive integers.

STEP 6

From the given set, the whole numbers are0 and12. So, the answer to part b is D.0 and A.12.

STEP 7

Next, let's find the integers. These include all whole numbers, both positive and negative.

STEP 8

From the given set, the integers are -15,0, and12. So, the answer to part c is C. -15, D.0, and A.12.

STEP 9

Next, let's find the rational numbers. These are numbers that can be expressed as a fraction of two integers.

STEP 10

From the given set, the rational numbers are $-\frac{3}{5}$ , $. \overline{4}$ ,0, $-4 \frac{}{4}$ ,12, and -15. So, the answer to part d is H. $-\frac{3}{5}$ , F. $. \overline{4}$ , D.0, B. $-4 \frac{}{4}$ , A.12, and C. -15.

STEP 11

Next, let's find the irrational numbers. These are numbers that cannot be expressed as a fraction of two integers.

STEP 12

From the given set, the irrational numbers are $\sqrt{2}$ and $\pi$ . So, the answer to part e is G. $\sqrt{2}$ and. $\pi$ .

STEP 13

Finally, let's find the real numbers. These are all numbers that can be located on the number line, including both rational and irrational numbers.

STEP 14

All the numbers in the given set are real numbers. So, the answer to part f is all the numbers H. $-\frac{3}{}$ , F. $. \overline{4}$ , G. $\sqrt{2}$ , D.0, B. $-4 \frac{}{4}$ , A.12, C. -, and. $\pi$ .

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QuestionIdentify natural numbers from the set: $\{-\frac{3}{5}, 1.\overline{4}, \sqrt{2}, 0, -4\frac{1}{4}, 12, -15, \pi\}$ . Options: A. 12, B. $-4\frac{1}{4}$ , C. -15, D. 0, E. $\pi$ , F. $1.\overline{4}$ , G. $\sqrt{2}$ , H. $-\frac{3}{5}$ .

Studdy Solution

STEP 1

Assumptions1. The given set of numbers is $\left\{-\frac{3}{5},1 . \overline{4}, \sqrt{},0,-4 \frac{1}{4},12,-15, \pi\right\}$ . . We need to categorize these numbers into natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.

STEP 2

STEP 3

Let's start with natural numbers. From the given set, we need to select the numbers that are positive integers.

STEP 4

From the given set, the only natural number is12. So, the answer to part a is A.12.

STEP 5

Next, let's find the whole numbers. These are non-negative integers, which means they include0 and all positive integers.

STEP 6

From the given set, the whole numbers are0 and12. So, the answer to part b is D.0 and A.12.

STEP 7

Next, let's find the integers. These include all whole numbers, both positive and negative.

STEP 8

From the given set, the integers are -15,0, and12. So, the answer to part c is C. -15, D.0, and A.12.

STEP 9

Next, let's find the rational numbers. These are numbers that can be expressed as a fraction of two integers.

STEP 10

From the given set, the rational numbers are $-\frac{3}{5}$ , $. \overline{4}$ ,0, $-4 \frac{}{4}$ ,12, and -15. So, the answer to part d is H. $-\frac{3}{5}$ , F. $. \overline{4}$ , D.0, B. $-4 \frac{}{4}$ , A.12, and C. -15.

STEP 11

Next, let's find the irrational numbers. These are numbers that cannot be expressed as a fraction of two integers.

STEP 12

From the given set, the irrational numbers are $\sqrt{2}$ and $\pi$ . So, the answer to part e is G. $\sqrt{2}$ and. $\pi$ .

STEP 13

Finally, let's find the real numbers. These are all numbers that can be located on the number line, including both rational and irrational numbers.

STEP 14

All the numbers in the given set are real numbers. So, the answer to part f is all the numbers H. $-\frac{3}{}$ , F. $. \overline{4}$ , G. $\sqrt{2}$ , D.0, B. $-4 \frac{}{4}$ , A.12, C. -, and. $\pi$ .

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Studdy Solution

STEP 1

STEP 2

STEP 3

Let's start with natural numbers. From the given set, we need to select the numbers that are positive integers.

STEP 4

From the given set, the only natural number is12. So, the answer to part a is A.12.

STEP 5

Next, let's find the whole numbers. These are non-negative integers, which means they include0 and all positive integers.

STEP 6

From the given set, the whole numbers are0 and12. So, the answer to part b is D.0 and A.12.

STEP 7

Next, let's find the integers. These include all whole numbers, both positive and negative.

STEP 8

From the given set, the integers are -15,0, and12. So, the answer to part c is C. -15, D.0, and A.12.

STEP 9

Next, let's find the rational numbers. These are numbers that can be expressed as a fraction of two integers.

STEP 10

From the given set, the rational numbers are −35-\frac{3}{5}−53​, .4‾ . \overline{4}.4,0, −44-4 \frac{}{4}−44​,12, and -15. So, the answer to part d is H. −35-\frac{3}{5}−53​, F. .4‾ . \overline{4}.4, D.0, B. −44-4 \frac{}{4}−44​, A.12, and C. -15.

STEP 11

Next, let's find the irrational numbers. These are numbers that cannot be expressed as a fraction of two integers.

STEP 12

From the given set, the irrational numbers are 2\sqrt{2}2​ and π\piπ. So, the answer to part e is G. 2\sqrt{2}2​ and. π\piπ.

STEP 13

Finally, let's find the real numbers. These are all numbers that can be located on the number line, including both rational and irrational numbers.

STEP 14

All the numbers in the given set are real numbers. So, the answer to part f is all the numbers H. −3-\frac{3}{}−3​, F. .4‾ . \overline{4}.4, G. 2\sqrt{2}2​, D.0, B. −44-4 \frac{}{4}−44​, A.12, C. -, and. π\piπ.

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From the given set, the rational numbers are $-\frac{3}{5}$ , $. \overline{4}$ ,0, $-4 \frac{}{4}$ ,12, and -15. So, the answer to part d is H. $-\frac{3}{5}$ , F. $. \overline{4}$ , D.0, B. $-4 \frac{}{4}$ , A.12, and C. -15.

From the given set, the irrational numbers are $\sqrt{2}$ and $\pi$ . So, the answer to part e is G. $\sqrt{2}$ and. $\pi$ .

All the numbers in the given set are real numbers. So, the answer to part f is all the numbers H. $-\frac{3}{}$ , F. $. \overline{4}$ , G. $\sqrt{2}$ , D.0, B. $-4 \frac{}{4}$ , A.12, C. -, and. $\pi$ .