### Instruction: What is the base-10 integer 515 when expressed in base 6?### Response: To convert a base-10 integer to another base, I can use repeated division by the base and look at the remainders.
So, I start by dividing 515 by 6 and finding the quotient and remainder.
515 / 6 = 85 with a remainder of 5.
This means that the last digit of the base-6 representation is 5.
Next, I divide the quotient 85 by 6 and find the new quotient and remainder.
85 / 6 = 14 with a remainder of 1.
This means that the second-to-last digit of the base-6 representation is 1.
I repeat this process until the quotient is zero.
14 / 6 = 2 with a remainder of 2.
2 / 6 = 0 with a remainder of 2.
So, the base-6 representation of 515 is 2215.