### Instruction: Convert $2014_{10}$ to base 9.### Response: To convert a decimal number to another base, I can use repeated division and write down the remainders from right to left.
I start by dividing 2014 by 9, which gives me 223 with a remainder of 7.
So the rightmost digit of the base 9 representation is 7.
Then I divide 223 by 9, which gives me 24 with a remainder of 7.
So the next digit is also 7.
I continue dividing by 9 until the quotient is 0.
I get 24 / 9 = 2 with a remainder of 6, and 2 / 9 = 0 with a remainder of 2.
So the base 9 representation is 2677, reading the remainders from right to left.