To solve the task, we need to identify the rational numbers from the provided list. Here's how to determine which numbers are rational:

• Rational numbers are numbers that can be expressed as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers, and $b \neq 0$.

Let’s go through each option:

1. $\frac{1}{3}$ - This is a fraction, so it is a rational number.
2. $0.\overline{9}$ (repeating decimal) - This is equivalent to $1$, so it is also a rational number.
3. $\sin x$ - This represents a trigonometric function, which is not always rational for arbitrary $x$. So, not rational.
4. $\frac{2}{5}$ - This is a fraction, so it is a rational number.
5. $3 \cdot 10^{16}$ - This is a large integer, and integers are always rational numbers.
6. $-1$ - This is an integer, and integers are rational numbers.
7. $\pi$ - This is an irrational number (it cannot be written as a fraction), so it is not rational.
8. $i$ - This is an imaginary number, so it is not rational.

Correct answers:

• $\frac{1}{3}$ (checked)
• $0.\overline{9}$ (should be checked)
• $\frac{2}{5}$ (checked)
• $3 \cdot 10^{16}$ (should be checked)
• $-1$ (checked)

The correct selections should be:

• $\frac{1}{3}$
• $0.\overline{9}$
• $\frac{2}{5}$
• $3 \cdot 10^{16}$
• $-1$

Do you have any questions or need further details?

Here are 5 related questions to expand the concept:

1. What is the difference between rational and irrational numbers?
2. Can $\sin x$ ever be a rational number?
3. Why is $\pi$ considered an irrational number?
4. How can repeating decimals be converted into fractions?
5. Are all integers rational numbers?

Tip: Every integer can be written as a fraction with denominator 1, which makes it a rational number.