https://file.aiquickdraw.com/mathbot/file/1726154462118k75svkjv.jpg

Let's analyze the list of numbers provided in the image and answer both parts of the question.

The list of numbers is:
\[
-9, \sqrt{8}, 3.0, \frac{2}{5}, 2.42, \pi
\]

### a. Which numbers are rational?

A **rational number** is a number that can be expressed as a ratio of two integers (i.e., \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q \neq 0\)).

- **-9**: This is a rational number because it can be written as \(\frac{-9}{1}\).
- **\(\sqrt{8}\)**: This is an **irrational number** because it cannot be expressed as a fraction of two integers.
- **3.0**: This is a rational number because it can be written as \(\frac{3}{1}\).
- **\(\frac{2}{5}\)**: This is a rational number because it is already in the form of a fraction.
- **2.42**: This is a rational number because it is a terminating decimal, which can be expressed as \(\frac{242}{100}\).
- **\(\pi\)**: This is an irrational number because it cannot be expressed as a fraction.

### Rational Numbers: 
\[
-9, 3.0, \frac{2}{5}, 2.42
\]

### b. Which numbers are irrational?

An **irrational number** is a number that cannot be written as a ratio of two integers. It has a non-repeating, non-terminating decimal expansion.

- **\(\sqrt{8}\)**: This is an irrational number because \(\sqrt{8} = 2.828...\), a non-repeating, non-terminating decimal.
- **\(\pi\)**: This is an irrational number because \(\pi = 3.14159...\), which is also non-repeating and non-terminating.

### Irrational Numbers:
\[
\sqrt{8}, \pi
\]

### Summary:
- **Rational numbers**: \(-9, 3.0, \frac{2}{5}, 2.42\)
- **Irrational numbers**: \(\sqrt{8}, \pi\)

Would you like further details or have any questions about this? 

Here are 5 follow-up questions you might consider:
1. What is the difference between terminating and repeating decimals?
2. Can every square root be classified as irrational?
3. How do you determine if a fraction represents a rational number?
4. Why is \(\pi\) classified as an irrational number?
5. Are all negative numbers considered rational?

**Tip**: To determine if a decimal is rational, check if it terminates or repeats. If it does, it's a rational number!

Keisha writes the following list of numbers: -9, √8, 3.0, 2/5, 2.42, π. a) Which numbers are rational? b) Which numbers are irrational?

Learn how to classify numbers as rational or irrational. This example analyzes numbers like -9, √8, 3.0, and π, focusing on key number theory concepts for students in Grades 6-8.

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