https://file.aiquickdraw.com/mathbot/file/1729051144320ddb88snw.jpg

Let’s go over the numbers from the image to determine whether each is **rational** or **irrational**.

### Quick Reminder:
- **Rational Numbers**: Can be written as a ratio (fraction) of two integers (e.g., 1/2, -3/4, 0.75). They either **terminate** (like 0.25) or **repeat** (like 0.\overline{3}).
- **Irrational Numbers**: Cannot be expressed as a ratio of two integers. Their decimal form **neither terminates nor repeats** (e.g., √2, π).

### Number Analysis:
1. **0.1**:  
   - This decimal terminates, so it's **rational**.  
   **Answer**: Rational.

2. **0.\overline{01}**:  
   - The bar indicates the decimal **repeats** (0.010101...). Since repeating decimals are rational, this is **rational**.  
   **Answer**: Rational.

3. **0.\overline{1}**:  
   - This is a repeating decimal (0.111...), which is equivalent to the fraction 1/9. Therefore, it's **rational**.  
   **Answer**: Rational.

4. **0.\overline{01}**:  
   - Same as the second number (0.\overline{01}), a repeating decimal. This is **rational**.  
   **Answer**: Rational.

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### Final Answers:
- **0.1** → Rational  
- **0.\overline{01}** → Rational  
- **0.\overline{1}** → Rational  
- **0.\overline{01}** → Rational  

Would you like further clarification on any step?

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### 5 Related Questions:
1. What is the difference between a repeating and non-repeating decimal?
2. Can all rational numbers be written as repeating or terminating decimals?
3. How do we convert a repeating decimal into a fraction?
4. What are some examples of common irrational numbers?
5. Why is π considered irrational?

**Tip**: To convert a repeating decimal into a fraction, you can use algebra (e.g., setting it equal to a variable, multiplying to eliminate the repeat, and solving).

Determine whether each number is rational or irrational: 0.1, 0.01̅, 0.1̅, 0.01̅.

Learn how to determine whether the numbers 0.1, 0.01̅, 0.1̅, and 0.01̅ are rational or irrational with a detailed step-by-step solution. This problem covers key concepts in number theory and decimals, suitable for students in Grades 6-8.

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