Let's classify the numbers as rational or irrational based on the provided image:

1. 2: This is a rational number because it can be expressed as the fraction $\frac{2}{1}$, which is a ratio of two integers.

2. $\pi$: This is an irrational number. $\pi$ cannot be expressed as a fraction of two integers and its decimal expansion is non-terminating and non-repeating.

3. $2 + \pi$: This is an irrational number. The sum of a rational number (2) and an irrational number ($\pi$) is always irrational.

4. $2 \cdot \pi$: This is also an irrational number. The product of a rational number (2) and an irrational number ($\pi$) is irrational.

Final Classification:

• Rational numbers: 2
• Irrational numbers: $\pi$, $2 + \pi$, $2 \cdot \pi$

Would you like further details on any of these concepts?

Here are 5 questions to explore this topic further:

1. What are the key differences between rational and irrational numbers?
2. How can we prove that $\pi$ is irrational?
3. Is the product of two irrational numbers always irrational?
4. Can irrational numbers be written as exact decimals?
5. Why do we consider sums involving irrational numbers irrational?

Tip: A rational number is any number that can be written as a simple fraction (ratio), while irrational numbers cannot be written this way.