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.

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?

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).