Is 24.52978156… rational or irrational 

The number \(24.52978156\ldots\) is **irrational**.

This is because the decimal does not appear to terminate (end) or repeat. A number is considered irrational if it cannot be expressed as a fraction \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\).

For a number to be rational, its decimal expansion must either terminate (come to an end after a certain number of digits) or repeat in a pattern. Since \(24.52978156\ldots\) shows no repeating pattern and continues indefinitely, it cannot be represented as a fraction of two integers, making it irrational.

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Here are 5 related questions:
1. What are the characteristics of an irrational number?
2. How can you determine whether a number with a long decimal expansion is rational or irrational?
3. What are some common examples of irrational numbers?
4. Can a number be irrational if its decimal expansion terminates?
5. How does the square root of a non-perfect square relate to irrational numbers?

**Tip:** To quickly determine if a decimal number is rational or irrational, look for either a repeating pattern or a terminating sequence. If neither is present, the number is likely irrational.

Explore whether the number 24.52978156... is rational or irrational with a detailed explanation. Learn about irrational numbers and why 24.52978156... does not terminate or repeat in its decimal expansion. Suitable for students in Grades 7-9 studying number theory and irrational numbers.

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