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 base 10 integer.

 May 31, 2018

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,



 Jun 1, 2018

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