# Math Help - decimals

1. ## decimals

i want decimal expansion of 1/13 in base 12

i have tried the "normal" algorithm but i got nowhere
eg: 1/13 in base 10 is .076923076
so if i want it in base 12 i go
.076923076=a/12 + b/144 + c/1728+ . . .
then mulitiply by the 12
.923076923=a + b/144 + c/1728 + . .
this would tell us the first digit after the decimal would be 0 but when i try to repeat the process
11.07692308 = a + b + c/1728 + . . .
I dont like that 11 is two decimal spaces.. or is it okay since im in base 12??

2. $11$ is correct! you just need to remember that we set $10 = A , \; 11 = B ...$ to give one digit representations.

3. By those three steps you wrote out, you should see you get a repeating fraction here.

$\frac{1}{13} = .0B0B0B0B0B..._{12}$

4. ## An alternate method

I like to write:
1 = 0.9999999...
in base 10.

So I get 1/11 by dividing the RHS by 11 to get
1/11 = 0.0909090909 etc.

In the same fashion, for base B+1
1 = 0.BBBBBBBB
So 1/(11 in base B+1)
1 = 0.0B0B0B....

5. okay i think i get it except im still not sure how im actually supposed to write it .. would my final answer be 1/13=0b0b0b0b.. or do i subsititute b in??
I get that its a repeating decimal since the order is 2.

6. im working on a similar problem 1/14 base 12

the period is 10.

would i do this the same way?