To convert $21$ from base-ten (decimal) to base-three:

1. Find the largest power of 3 less than or equal to $21$.

$3^2 = 9 \quad (\text{since } 3^3 = 27 \text{ is too large})$

2. Divide $21$ by $9$:

$21 \div 9 = 2 \quad (\text{remainder } 3)$

3. Now divide the remainder $3$ by $3^1 = 3$:

$3 \div 3 = 1 \quad (\text{remainder } 0)$

4. Finally, for $3^0 = 1$, the remainder is already $0$, so no further division is needed.

So, $21$ in base-three is written as $210_3$.

Would you like more details on the conversion process or any other questions?

Here are 5 related questions:

1. How do you convert larger numbers to base-three?
2. What is the base-three representation of $45$?
3. How do you convert a base-three number back to base-ten?
4. What is the base-three equivalent of the decimal number $100$?
5. How do you perform addition in the base-three system?

Tip: To check your conversion from decimal to another base, convert it back to decimal to verify your answer!