To identify the irrational numbers from the list provided, let's analyze each option:

1. $\frac{2}{3}$: This is a fraction of two integers, which makes it a rational number.

2. $\sqrt{20}$: The square root of 20 cannot be simplified to a whole number or a fraction. It is an irrational number because it results in a non-repeating, non-terminating decimal.

3. $0.245653256312 \ldots$: This number appears to be a non-repeating, non-terminating decimal. Since it does not terminate or repeat, it is an irrational number.

4. $-4.9$: This is a terminating decimal and can be expressed as $\frac{-49}{10}$, so it is a rational number.

5. $5.11111\ldots$: This number is a repeating decimal and can be expressed as a fraction, making it a rational number.

Therefore, the irrational numbers in this list are:

• $\sqrt{20}$
• $0.245653256312 \ldots$

Would you like more details on any of these points, or do you have any questions?

Related Questions:

1. What is the definition of an irrational number?
2. How can you determine if a square root is irrational?
3. What makes a repeating decimal a rational number?
4. Can the sum of two irrational numbers be rational?
5. How can you express a repeating decimal as a fraction?

Tip:

When identifying irrational numbers, look for non-repeating, non-terminating decimals or roots that cannot be simplified to a fraction.