QuestionIdentify the whole numbers from this list: A. $\pi$ , B. $\frac{2}{1}$ , C. $0 . \overline{25}$ , D. $\sqrt{2}$ , E. $-\frac{8}{9}$ , F. None.

Studdy Solution

STEP 1

Assumptions1. Whole numbers are non-negative numbers without any fractional or decimal part. They include zero and all positive integers. . We need to identify the whole numbers from the given list.

STEP 2

Let's start by examining option A, which is $\pi$ . $\pi$ is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means it cannot be expressed as a simple fraction and its decimal representation never ends or repeats. Therefore, $\pi$ is not a whole number.

STEP 3

Next, let's examine option B, which is $\frac{2}{1}$ .
$\frac{2}{1}$ is a fraction that can be simplified to2, which is a whole number. Therefore, $\frac{2}{1}$ is a whole number.

STEP 4

Now, let's examine option C, which is $0 . \overline{25}$ .
$0 . \overline{25}$ represents a repeating decimal, specifically0.252525... While this can be expressed as a fraction (1/4), it is not a whole number because it has a non-zero fractional part.

STEP 5

Next, let's examine option D, which is $\sqrt{2}$ .
$\sqrt{2}$ is the square root of2. It is an irrational number, which means it cannot be expressed as a simple fraction and its decimal representation never ends or repeats. Therefore, $\sqrt{2}$ is not a whole number.

STEP 6

Finally, let's examine option, which is $-\frac{8}{9}$ .
$-\frac{8}{9}$ is a negative fraction. Whole numbers are non-negative, so $-\frac{8}{9}$ is not a whole number.

STEP 7

From the above analysis, we can conclude that the only whole number in the list is $\frac{2}{1}$ , which simplifies to2.

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QuestionIdentify the whole numbers from this list: A. $\pi$ , B. $\frac{2}{1}$ , C. $0 . \overline{25}$ , D. $\sqrt{2}$ , E. $-\frac{8}{9}$ , F. None.

Studdy Solution

STEP 1

Assumptions1. Whole numbers are non-negative numbers without any fractional or decimal part. They include zero and all positive integers. . We need to identify the whole numbers from the given list.

STEP 2

STEP 3

Next, let's examine option B, which is $\frac{2}{1}$ .
$\frac{2}{1}$ is a fraction that can be simplified to2, which is a whole number. Therefore, $\frac{2}{1}$ is a whole number.

STEP 4

Now, let's examine option C, which is $0 . \overline{25}$ .
$0 . \overline{25}$ represents a repeating decimal, specifically0.252525... While this can be expressed as a fraction (1/4), it is not a whole number because it has a non-zero fractional part.

STEP 5

Next, let's examine option D, which is $\sqrt{2}$ .
$\sqrt{2}$ is the square root of2. It is an irrational number, which means it cannot be expressed as a simple fraction and its decimal representation never ends or repeats. Therefore, $\sqrt{2}$ is not a whole number.

STEP 6

Finally, let's examine option, which is $-\frac{8}{9}$ .
$-\frac{8}{9}$ is a negative fraction. Whole numbers are non-negative, so $-\frac{8}{9}$ is not a whole number.

STEP 7

From the above analysis, we can conclude that the only whole number in the list is $\frac{2}{1}$ , which simplifies to2.

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QuestionIdentify the whole numbers from this list: A. π\piπ, B. 21\frac{2}{1}12​, C. 0.25‾0 . \overline{25}0.25, D. 2\sqrt{2}2​, E. −89-\frac{8}{9}−98​, F. None.

Studdy Solution

STEP 1

Assumptions1. Whole numbers are non-negative numbers without any fractional or decimal part. They include zero and all positive integers. . We need to identify the whole numbers from the given list.

STEP 2

STEP 3

Next, let's examine option B, which is 21\frac{2}{1}12​.21\frac{2}{1}12​ is a fraction that can be simplified to2, which is a whole number. Therefore, 21\frac{2}{1}12​ is a whole number.

STEP 4

Now, let's examine option C, which is 0.25‾0 . \overline{25}0.25.0.25‾0 . \overline{25}0.25 represents a repeating decimal, specifically0.252525... While this can be expressed as a fraction (1/4), it is not a whole number because it has a non-zero fractional part.

STEP 5

Next, let's examine option D, which is 2\sqrt{2}2​.2\sqrt{2}2​ is the square root of2. It is an irrational number, which means it cannot be expressed as a simple fraction and its decimal representation never ends or repeats. Therefore, 2\sqrt{2}2​ is not a whole number.

STEP 6

Finally, let's examine option, which is −89-\frac{8}{9}−98​.−89-\frac{8}{9}−98​ is a negative fraction. Whole numbers are non-negative, so −89-\frac{8}{9}−98​ is not a whole number.

STEP 7

From the above analysis, we can conclude that the only whole number in the list is 21\frac{2}{1}12​, which simplifies to2.

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QuestionIdentify the whole numbers from this list: A. $\pi$ , B. $\frac{2}{1}$ , C. $0 . \overline{25}$ , D. $\sqrt{2}$ , E. $-\frac{8}{9}$ , F. None.

Next, let's examine option B, which is $\frac{2}{1}$ .
$\frac{2}{1}$ is a fraction that can be simplified to2, which is a whole number. Therefore, $\frac{2}{1}$ is a whole number.

Now, let's examine option C, which is $0 . \overline{25}$ .
$0 . \overline{25}$ represents a repeating decimal, specifically0.252525... While this can be expressed as a fraction (1/4), it is not a whole number because it has a non-zero fractional part.

Next, let's examine option D, which is $\sqrt{2}$ .
$\sqrt{2}$ is the square root of2. It is an irrational number, which means it cannot be expressed as a simple fraction and its decimal representation never ends or repeats. Therefore, $\sqrt{2}$ is not a whole number.

Finally, let's examine option, which is $-\frac{8}{9}$ .
$-\frac{8}{9}$ is a negative fraction. Whole numbers are non-negative, so $-\frac{8}{9}$ is not a whole number.

From the above analysis, we can conclude that the only whole number in the list is $\frac{2}{1}$ , which simplifies to2.