The number 0, point, 6, 9, 7, 8, 9, 9, 7, 8, 9, 9, 7, 8, 9, 9, 7, 8, 9, point, point, .0.69789978997899789... is  rationalirrational because  it is the square root of a non-perfect squareit is a decimal that terminatesit is the square root of a perfect squareit is a decimal that repeatsit is a decimal that does not repeat or terminate

The number given, \(0.69789978997899789\ldots\), is **irrational** because **it is a decimal that does not repeat or terminate**. 

This type of decimal expansion is indicative of an irrational number since rational numbers either terminate or have a repeating pattern in their decimal form.

Would you like further details on why this number is classified as irrational? 

Here are 5 questions that expand on this topic:
1. How do we differentiate between terminating and non-terminating decimals?
2. Can all non-repeating decimals be considered irrational?
3. How do repeating decimals relate to rational numbers?
4. What are examples of rational numbers with repeating decimal forms?
5. How is the concept of a perfect square related to rational and irrational numbers?

**Tip:** An easy way to identify a rational number is by checking if its decimal expansion either terminates or repeats. If not, it’s irrational.

The number 0.69789978997899789... is rational or irrational because it is the square root of a non-perfect square, it is a decimal that terminates, it is the square root of a perfect square, it is a decimal that repeats, it is a decimal that does not repeat or terminate.

Learn how to identify whether a number is rational or irrational based on its decimal form. Explore key concepts, including terminating, repeating, and non-repeating decimal expansions. This problem is suitable for students in Grades 8-10 and includes detailed explanations.

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