When the base 10 integer 269 is converted to base 5, what is the sum of the digits?
To convert from base 10 to base 5, I need to repeatedly divide 269 by 5 and write down the remainders. The remainders will be the digits of the base 5 number, starting from the rightmost one. So let me start dividing: 269 divided by 5 gives 53 with a remainder of 4. So the rightmost digit is 4. Then I divide 53 by 5 and get 10 with a remainder of 3. So the next digit is 3. Then I divide 10 by 5 and get 2 with a remainder of 0. So the next digit is 0. And finally I divide 2 by 5 and get 0 with a remainder of 2. So the leftmost digit is 2. So the base 5 number is 2034. To find the sum of the digits, I just add them up: 2 + 0 + 3 + 4 = 9. 