The base-3 number system, also known as ternary, uses three digits: 0, 1, and 2. Each digit's position represents a power of 3, similar to how the base-10 system uses powers of 10. For example, the number 210 in base-3 represents 2 \times 3^2 + 1 \times 3^1 + 0 \times 3^0, which equals 18 in decimal. Base-3 is useful in various fields, including computer science and mathematics, for simplifying certain calculations and algorithms. It can also be applied in ternary logic, which is a form of logic that uses three truth values instead of the traditional two.