### Instruction: What is the first digit (from left to right) of the base $8$ representation of $473_{10}$?### Response: I need to convert $473_{10}$ from base $10$ to base $8$.
One way to do this is to repeatedly divide by $8$ and write down the remainders.
So, $473 \div 8 = 59$ with a remainder of $1$.
Then, $59 \div 8 = 7$ with a remainder of $3$.
Finally, $7 \div 8 = 0$ with a remainder of $7$.
So, the base $8$ representation of $473_{10}$ is $731_8$, where the subscripts indicate the base.
The first digit of this representation is $7$.