1. The problem asks to identify which statements about rational and irrational numbers are true. 2. Recall definitions: - A rational number can be expressed as a ratio of two integers $\frac{a}{b}$ where $b \neq 0$. - An irrational number cannot be expressed as such a ratio. - Terminating decimals and repeating decimals represent rational numbers. - Integers are rational because they can be written as $\frac{n}{1}$. - Square roots of non-perfect squares are irrational. 3. Evaluate each statement: - $\frac{12}{10}$ is a ratio of two integers, so it is rational, not irrational. Statement is false. - $\sqrt{10}$ is the square root of a non-perfect square, so it is irrational. Statement is true. - $8.1$ is a terminating decimal, so it is rational. Statement is true. - $2.51\overline{51}$ is a repeating decimal, so it is rational, not irrational. Statement is false. - $-8$ is an integer and can be written as $\frac{-8}{1}$, so it is rational. Statement is true. 4. Conclusion: The true statements are the second, third, and fifth. Final answer: The true statements are: - Since 10 is not a perfect square, $\sqrt{10}$ is irrational. - Since it is a terminating decimal, 8.1 is rational. - Since it is an integer, -8 is rational.