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!