### Identifying Rational and Irrational NumbersIn this exercise, we will identify whether each given number is rational or irrational. Please review the table below and mark the appropriate category for each number.| Number | Rational | Irrational ||--------------|--------------|--------------|| $\dfrac{14}{20}$ | ⃝ | ⃝ || $-72.91$ | ⃝ | ⃝ || $\sqrt{1}$ | ⃝ | ⃝ || $\sqrt{2}$ | ⃝ | ⃝ || $-16\pi$ | ⃝ | ⃝ |#### Explanation of Terms:- **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers (where the denominator is not zero). - **Irrational Numbers**: These are numbers that cannot be expressed as a simple fraction. Their decimal expansions are non-repeating and non-terminating.### Example Identification:1. **$\dfrac{14}{20}$** - This is the fraction 14 divided by 20, which simplifies to 7/10, a rational number.2. **$-72.91$** - This is a decimal number that terminates, hence it is rational.3. **$\sqrt{1}$** - The square root of 1 is 1, which is a rational number.4. **$\sqrt{2}$** - The square root of 2 cannot be expressed as a fraction, making it an irrational number.5. **$-16\pi$** - The product of a rational number and an irrational number (π) is irrational, hence $-16\pi$ is irrational.Mark the appropriate circles for each number based on the explanations provided above. For instance, $\dfrac{14}{20}$ would be marked under the "Rational" column, while $\sqrt{2}$ would be marked under the "Irrational" column.

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Algebra and Trigonometry (6th Edition)

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Author:Robert F. Blitzer

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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### Identifying Rational and Irrational Numbers

In this exercise, we will identify whether each given number is rational or irrational. Please review the table below and mark the appropriate category for each number.

| Number | Rational | Irrational |
|--------------|--------------|--------------|
| $\dfrac{14}{20}$ | ⃝ | ⃝ |
| $-72.91$ | ⃝ | ⃝ |
| $\sqrt{1}$ | ⃝ | ⃝ |
| $\sqrt{2}$ | ⃝ | ⃝ |
| $-16\pi$ | ⃝ | ⃝ |

#### Explanation of Terms:
- **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers (where the denominator is not zero).
- **Irrational Numbers**: These are numbers that cannot be expressed as a simple fraction. Their decimal expansions are non-repeating and non-terminating.

### Example Identification:
1. **$\dfrac{14}{20}$** - This is the fraction 14 divided by 20, which simplifies to 7/10, a rational number.
2. **$-72.91$** - This is a decimal number that terminates, hence it is rational.
3. **$\sqrt{1}$** - The square root of 1 is 1, which is a rational number.
4. **$\sqrt{2}$** - The square root of 2 cannot be expressed as a fraction, making it an irrational number.
5. **$-16\pi$** - The product of a rational number and an irrational number (π) is irrational, hence $-16\pi$ is irrational.

Mark the appropriate circles for each number based on the explanations provided above. For instance, $\dfrac{14}{20}$ would be marked under the "Rational" column, while $\sqrt{2}$ would be marked under the "Irrational" column.

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