https://file.aiquickdraw.com/mathbot/file/1725405753241tz9ullnx.jpg

The problem in the image asks:

**"The numbers 2.888... and 2.999... are both rational numbers. What is an irrational number that is between the two rational numbers?"**

### Solution:

1. **Identify the given numbers:**
   - The first number, \( 2.888\ldots \), is a repeating decimal and can be represented as the rational number \( \frac{26}{9} \).
   - The second number, \( 2.999\ldots \), is equal to \( 3 \), which is a whole number and also rational.

2. **Determine an irrational number between them:**
   - An irrational number is a number that cannot be expressed as a simple fraction. It has non-repeating, non-terminating decimal digits.
   - One common irrational number between 2.888... and 3 is \( \sqrt{8.5} \), since \( \sqrt{8.5} \) is approximately 2.915, which lies between \( 2.888\ldots \) and \( 3 \).

### Final Answer:
An example of an irrational number between 2.888... and 3 is \( \sqrt{8.5} \).

Would you like more details on the steps, or do you have any questions?

### Further Related Questions:
1. How can you determine if a number is rational or irrational?
2. What is the difference between a repeating decimal and a non-repeating decimal?
3. How can you convert a repeating decimal to a fraction?
4. What are some other examples of irrational numbers?
5. How do irrational numbers relate to the number line?

**Tip:** Irrational numbers often appear when dealing with square roots, especially when the radicand (the number under the square root) is not a perfect square.

The numbers 2.888... and 2.999... are both rational numbers. What is an irrational number that is between the two rational numbers?

Explore how to find an irrational number between the rational numbers 2.888... and 2.999.... This problem involves understanding the properties of rational and irrational numbers, converting repeating decimals to fractions, and using the number line for visualization. Suitable for students in Grades 7-9.

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