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The task on the worksheet asks for organizing the given real numbers into groups of the user's choice, with explanations for each group. A common way to categorize real numbers is by grouping them as follows:

1. **Natural Numbers** (Positive integers excluding zero): \(1, 2, 3, 4, 5, 10, 25, 999\)
2. **Whole Numbers** (Natural numbers including zero): \(0, 1, 2, 3, 4, 5, 10, 25, 999\)
3. **Integers** (Positive and negative whole numbers, including zero): \(-10, -3, -2, -1, 0, 1, 2, 3, 4, 5, 10, 25, 999\)
4. **Rational Numbers** (Numbers that can be expressed as fractions or ratios of integers): \(\frac{1}{4}, \frac{1}{3}, \frac{3}{7}, \frac{3}{8}, \frac{4}{9}, \frac{5}{7}, 0.5, 0.25, 0.3, -0.6, 0.00, 0.999999\ldots\)
5. **Irrational Numbers** (Numbers that cannot be expressed as fractions or have non-repeating, non-terminating decimals): \(\sqrt{2}, \sqrt{3}, \sqrt{9}, \pi\)

Based on this worksheet's content, you can sort the numbers into the above categories. Would you like me to provide a more detailed explanation of each group?

Here are 5 relative questions to expand on this information:

1. What is the difference between rational and irrational numbers?
2. Why is \( \pi \) considered an irrational number?
3. Can 0.999999... be considered equal to 1? Why?
4. How do square roots determine whether a number is rational or irrational?
5. What are some examples of irrational numbers not listed on this worksheet?

**Tip:** A useful way to check if a number is rational is to see if it can be expressed as a fraction of two integers. If it has a terminating or repeating decimal, it's rational!

Organize the following real numbers into groups of your choice. Be ready to support your explanations of each group.

This problem involves classifying a set of real numbers into categories such as natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Learn how to identify these categories and explain the reasoning behind each classification. Suitable for students in Grades 7-9.

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