Converting to base 3

A tricimal is like decimal, except the digits represent fractions with powers of 3 instead of 10. For example, 16/27 = 1/3 + 2/9 + 1/27 = 0.121 as a tricimal.

I know that 16 in base 3 is 121 and 27 in base 3 is 123 and so the denominators are probably 3^1, 3^2 and 3^3, but I'm not so sure about the process to get from 16 to 121 and from 27 to 123. Please show me how to get it step by step-- I already read about converting to base n and when I tried it, it didn't really work out.

Define div as like division except you list the quotient and the remainder. For example,
18 div 7 = 2 remainder 4
because 7 goes into 18 2 times with a remainder of 4.

First of all 27(base 10) = 1000(base 3).

27 div 3 = 9 remainder 0
9 div 3 = 3 remainder 0
3 div 3 = 1 remainder 0
1 div 3 = 0 remainder 1

16(base 10) = 121(base 3)

16 div 3 = 5 remainder 1
5 div 3 = 1 remainder 2
1 div 3 = 0 remainder 1

Just for another example, 123(base 10) = 11120(base 3)

123 div 3 = 41 remainder 0
41 div 3 = 13 remainder 2
13 div 3 = 4 remainder 1
4 div 3 = 1 remainder 1
1 div 3 = 0 remainder 1

3 ---- 16
3 ----- 5 --- 1
3 ----- 1 --- 2
3 ----- 0 ----1

= 121 base 3.

first column is base to which you want to convert. second column is number which you want to convert.
In each step divide number with base and put the quotient in next line second column and reminder in next line 3 rd column. ie, 16/3 = 5 and reminder 1.

repeat this process untill you get quotient 0. then take the remainders from bottom to top to form the required number.

There is no 3 in base 3 (just as there is no digit for 10 in base 10) so NO number is 123 in base 3

27(base 10) = 1000(base3)