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Let's analyze the statements one by one to determine which are true:

1. **"Since it is a terminating decimal, 9.5 is rational."**
   - **True.** A terminating decimal is a number that can be expressed as a fraction of two integers, which makes it a rational number. For example, \( 9.5 = \frac{95}{10} \).

2. **"Since 81 is a perfect square, \(\sqrt{81}\) is irrational."**
   - **False.** The square root of 81 is 9, which is an integer. Therefore, \(\sqrt{81}\) is a rational number.

3. **"Since it is a ratio of two integers, \(\frac{11}{8}\) is irrational."**
   - **False.** A ratio of two integers is a rational number. Since \(\frac{11}{8}\) can be expressed as a fraction, it is rational.

4. **"Since it is a repeating decimal, 6.\overline{3} is rational."**
   - **True.** A repeating decimal is a rational number because it can be expressed as a fraction. For instance, \( 6.\overline{3} = \frac{19}{3} \).

5. **"Since 6 is not a perfect square, \(\sqrt{6}\) is irrational."**
   - **True.** Since 6 is not a perfect square, its square root cannot be expressed as a fraction of two integers, making \(\sqrt{6}\) irrational.

6. **"None of the above statements are true."**
   - **False.** As we found some of the statements to be true, this statement is incorrect.

### **Final Answer:**
The correct statements are:
- "Since it is a terminating decimal, 9.5 is rational."
- "Since it is a repeating decimal, 6.\overline{3} is rational."
- "Since 6 is not a perfect square, \(\sqrt{6}\) is irrational."

Would you like more details or have any questions?

Here are 5 questions related to the problem:

1. What are the characteristics of rational numbers?
2. How can you determine if a square root is rational or irrational?
3. Why are repeating decimals considered rational numbers?
4. Can a non-terminating and non-repeating decimal be rational? Why or why not?
5. What is the difference between terminating and repeating decimals?

**Tip:** When analyzing whether a number is rational or irrational, always consider whether it can be expressed as a fraction of two integers.

Check all statements that are true:
1. Since it is a terminating decimal, 9.5 is rational.
2. Since 81 is a perfect square, √81 is irrational.
3. Since it is a ratio of two integers, 11/8 is irrational.
4. Since it is a repeating decimal, 6.3 (repeating) is rational.
5. Since 6 is not a perfect square, √6 is irrational.
6. None of the above statements are true.

Explore the concepts of rational and irrational numbers through a series of true/false statements. Learn why 9.5 and 6.3 (repeating) are rational, while √6 is irrational. Suitable for students in Grades 6-8.

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