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The question asks to determine the irrational numbers from the given set \( \{ -4.6, 3.\overline{7}, \pi, \frac{8}{8} \} \).

Let's go through each element of the set:

1. **-4.6**: This is a terminating decimal and can be expressed as a fraction, making it a **rational number**.
2. **3.\overline{7}** (repeating decimal 3.777...): Repeating decimals can be expressed as fractions, so this is a **rational number**.
3. **\( \pi \)**: This is a well-known irrational number because it cannot be expressed as a fraction.
4. **\( \frac{8}{8} \)**: This simplifies to 1, which is a **rational number**.

The only irrational number in the set is **\( \pi \)**.

Thus, the correct answer is **B. \( \pi \)**.

Would you like further details on this, or do you have any questions?

Here are 5 related questions:
1. What is the difference between rational and irrational numbers?
2. Can a repeating decimal ever be irrational?
3. How do you convert a repeating decimal into a fraction?
4. Are all non-repeating, non-terminating decimals irrational?
5. What are some other common examples of irrational numbers?

**Tip**: A number is irrational if it cannot be written as a fraction of two integers and its decimal expansion neither terminates nor repeats.

Use the set {-4.6, 3.7̅, π, 8/8}. List all the elements that are irrational numbers.

Determine the irrational numbers from the set {-4.6, 3.7̅, π, 8/8}. This problem explores the properties of rational and irrational numbers, including decimals, repeating decimals, and fractions. Suitable for students in Grades 6-8.

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