Thank you for the clarification! Let's correct the analysis for the third number, \(-\frac{3}{7}\):

### Revised Analysis:

1. **0.82**:
   - **Rational**: 0.82 is a terminating decimal, so it is rational.

2. **√37**:
   - **Irrational**: The square root of 37 is non-terminating and non-repeating, making it irrational.

3. **\(-\frac{3}{7}\)**:
   - **Rational**: \(-\frac{3}{7}\) is a fraction, and since both the numerator (-3) and the denominator (7) are integers, this number is rational.

4. **√99 / 3**:
   - **Irrational**: As before, √99 is irrational, and dividing it by 3 (a rational number) still results in an irrational number.

### Updated Table:

| Number          | Rational | Irrational |
|-----------------|----------|------------|
| 0.82            | ✓        |            |
| √37             |          | ✓          |
| \(-\frac{3}{7}\) | ✓        |            |
| √99 / 3         |          | ✓          |

Would you like any further explanations?

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Here are some related questions you might find interesting:

1. How can you determine if a fraction is rational or irrational?
2. What is the significance of the numerator and denominator in identifying rational numbers?
3. Are there any cases where the square root of a fraction can be rational?
4. How does the sign (positive or negative) affect the rationality of a number?
5. What is the difference between terminating and non-terminating decimals?

**Tip:** A fraction is always rational as long as the numerator and denominator are both integers, and the denominator is not zero.

Explore the rationality of -3/7 and other numbers including 0.82, √37, and √99 / 3. This analysis covers definitions of rational and irrational numbers, terminating decimals, and the properties of square roots. Suitable for Grades 7-9.

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