https://file.aiquickdraw.com/mathbot/file/1725902880865p1bom5ef.jpg

Let's analyze each number to determine whether it is a **rational number**. A **rational number** can be expressed as a fraction \( \frac{a}{b} \), where \(a\) and \(b\) are integers, and \(b \neq 0\).

Here is the analysis for each number in the image:

1. **0.25**: This is a rational number since \( 0.25 = \frac{1}{4} \), which is a fraction.
   
2. **\(\sqrt{89}\)**: This is not a rational number because \(\sqrt{89}\) is an **irrational** number; it cannot be expressed as a simple fraction, and the square root of 89 is not a perfect square.

3. **3.14159...**: This represents **pi** (\(\pi\)), which is an irrational number because it cannot be expressed as a fraction and has infinite, non-repeating decimal places.

4. **95**: This is a rational number because it is an integer and can be expressed as \(\frac{95}{1}\).

5. **4.080080008...**: This is not a rational number because it is a **non-repeating, non-terminating decimal**, which is characteristic of an irrational number.

6. **\(\sqrt{0.64}\)**: This is a rational number because \(\sqrt{0.64} = 0.8\), and \(0.8 = \frac{4}{5}\), which is a fraction.

7. **10.84**: This is a rational number because it is a terminating decimal and can be expressed as \(\frac{1084}{100}\).

8. **\(\frac{2}{5}\)**: This is a rational number because it is already expressed as a fraction of two integers.

### Rational Numbers in the List:
- 0.25
- 95
- \(\sqrt{0.64}\)
- 10.84
- \(\frac{2}{5}\)

Would you like a more detailed explanation of any specific number, or do you have any questions?

### Relative Questions:
1. What is the difference between a rational and irrational number?
2. How can you tell if a square root is rational or irrational?
3. Why is pi (\(\pi\)) considered irrational?
4. Can repeating decimals always be considered rational?
5. What are some real-life applications of rational numbers?

### Tip:
Remember, all integers are rational numbers since they can be expressed as a fraction with denominator 1.

Select all the numbers below which are rational numbers.

Learn how to identify rational numbers from a list of given values, including decimals, fractions, and square roots. This problem covers key mathematical concepts such as rational and irrational numbers, square roots, and their properties, suitable for students in Grades 6-8.

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