### Instruction: What is $441_{10}$ in base $7$?### Response: To convert a number from base $10$ to base $7$, I need to repeatedly divide it by $7$ and write down the remainders.
The remainders will form the digits of the base $7$ number, starting from the rightmost one.
So, I start by dividing $441$ by $7$, which gives me a quotient of $63$ and a remainder of $0$.
This means that the rightmost digit of the base $7$ number is $0$.
Next, I divide $63$ by $7$, which gives me a quotient of $9$ and a remainder of $0$.
This means that the next digit of the base $7$ number is also $0$.
Then, I divide $9$ by $7$, which gives me a quotient of $1$ and a remainder of $2$.
This means that the next digit of the base $7$ number is $2$.
Finally, I divide $1$ by $7$, which gives me a quotient of $0$ and a remainder of $1$.
This means that the leftmost digit of the base $7$ number is $1$.
Therefore, the base $7$ number is $1200_7$.