which of the following is the base-five representation of the number 41 base 4? I know the answer is 32 base 5 but how do you solve it? I don't get it, help please!

Question

anonymous · Answer

(41) base 4 is 4 times 4 added to 1 times 1
converting the above number to decimal number system we get 4 times 4 is 16 and 1 times 1 is 1 together added to be 17
repeatedly divide the number 17 until you get a remainder less than 5

anonymous · Answer

"Base" is essentially telling you what the 10's place means. In base 10, 10 is just 10. However in base 4, the digits 10 represent the number 4. So 41 base 4 = 4*4 + 1 = 17 base 10 = 1*10 + 7. You can see that this is the same as 32 base 5 = 3*5 + 2 = 17 base 10.

There are different ways to convert bases. You can see that 17/4 = 4 with remainder 1, or 41 base 4. 17/5 = 3 with remainder 2, or 32 base 5.

anonymous · Answer

oh ok I think I'm getting it

anonymous · Answer

so what happens if you have 120 base 8?

anonymous · Answer

100 base 10 = 10*10 = 10^2. 
Likewise, 100 base 8 = 8*8 = 8^2 = 64.
20 base 8 = 2*8 = 16
0 base 8 = 0.

So: 120 base 8 = 1*8^2 + 2*8^1 + 0*8^0 = 64 + 16 + 0 = 80 base 10.

In particular, notice how you can write out a number as a sum of integer powers of the base, where the digits are coefficients.

anonymous · Answer

oh ok I think I get it, so 120 base 8 will equal 80 oh I get its not that hard! thank you! :)