jmc

Rewrite all of the terms in base 3. Since the numbers are sums of distinct powers of 3, in base 3 each number is a sequence of 1s and 0s (if there is a 2, then it is no longer the sum of distinct powers of 3). Therefore, we can recast this into base 2 (binary) in order to determine the 100th number. $100$ is equal to $64+32+4$, so in binary form we get $1100100$. However, we must change it back to base 10 for the answer, which is $3^6+3^5+3^2=729+243+9=\boxed{981}$.