Math
posted by Heather on .
How do you convert a number to whatever base it indicates? For example: convert 252 base six to base five. I have tried posting for my teacher to help me, but he doesn't seem to get what I am asking. Can someone please explain the process and not just the answer? Thanks!!

Most of the time, you would convert numbers from "foreign" bases to base 10, then convert to the target base by division.
From a number in base n, we recognize that each digit from the right represents n^x, where x is the position from the right.
So 252_{6}
= 2*6² + 5*6¹ + 2*6^0
= 72 + 30 + 2
= 104_{10}
To convert 102_{10} to base 5, we divide by 5 successively and collect the remainders as digits from the right.
102/5=20R4
20/5=4R0
4/5=0R4
So 102_{10} = 404_{5} 
Thanks. How did it change from 104 base 10 to 102?

102ten to base 5 is not 404five it is 402five
102/5=20 r 2
20/5=4 r 0
4/5 =0 r 4
so that gives you 402five