### Instruction: Convert $2014_{10}$ to base 9.### Response: To convert a number from base 10 to another base, I can repeatedly divide the number by the base and write down the remainders.
For example, dividing 2014 by 9 gives 223 with a remainder of 7, so the rightmost digit in base 9 is 7.
Then I repeat the process with 223, which gives 24 with a remainder of 7, so the next digit is also 7.
Continuing with 24, I get 2 with a remainder of 6, so the third digit is 6.
Finally, 2 divided by 9 is 0 with a remainder of 2, so the leftmost digit is 2.
Therefore, the base 9 representation of 2014 is 2677.