Find the one hundredth positive integer that can be written using no digits other than digits 0 and 1 in base 3. Express your answer as a ba

Hey superman!

 

The goal is to count in base 3 using only binary digits.

 

The \(100^{\text{th}}\) smallest positive binary integer is \(100 = 1100100_2,\) 

 

so the \(100^{\text{th}}\) smallest positive integer that can be written with only the binary digits is

 

 \(1100100_3 = \boxed{981}\).

 

I hope this helped,

 

Gavin.