### Instruction: What is the base-10 integer 515 when expressed in base 6?### Response: To convert a number from base 10 to base 6, I need to repeatedly divide it by 6 and write down the remainders, until the quotient becomes 0.
The remainders will form the digits of the base-6 number, starting from the rightmost one.
So let me start dividing 515 by 6.
The first division gives me a quotient of 85 and a remainder of 5.
So the rightmost digit of the base-6 number is 5.
The next division gives me a quotient of 14 and a remainder of 1.
So the next digit is 1.
The next division gives me a quotient of 2 and a remainder of 2.
So the next digit is 2.
The final division gives me a quotient of 0 and a remainder of 2.
So the leftmost digit is 2.
Therefore, the base-6 number is 2215.