Converting 4312 from Base 10 to Base 6: A Homework Solution

[um0123]

Homework Statement

The number 4312 in base ten is (4*10^3) + (3*10^2) + (1*10^1) + (2*10^0)

4312 in base six is (4*6^3) + (3*6^2) + (1*6^1) + (2*6^0) which is 980

therefore 4312 in base six is equal to 980 in base 10

QUESTIONS:

a) does 124 in base 5 represent an odd number?

b) how can you tell if a number is odd in base 10 by looking t its base 5 representation

Homework Equations

none

The Attempt at a Solution

i figured out that 124 in base five is 39 in base 10 and that means the answer to question a) is yes.

But i have no idea how to answer question b).

 

[um0123]

i have a guess.

If you add the digits together and it is an odd number, then that number in base five is odd when turned into base ten.

for instance, 124 = 1+2+4 = 7, which is odd, so when you make 124 base 5 into base 10 it must be odd.

please tell me if that is incorrect.

 

[OmCheeto]

i have a guess.

If you add the digits together and it is an odd number, then that number in base five is odd when turned into base ten.

for instance, 124 = 1+2+4 = 7, which is odd, so when you make 124 base 5 into base 10 it must be odd.

please tell me if that is incorrect.

Yes. You are correct.