If you moved the 3 at the end of a certain large number to the beginning, it would be the same as multiplying it by 3. What is the number?
Denote our number 10*a+3
Given 3*( 10*a+3 )=3*10^n+a
Let see when we get an integer -
and then 10*a+3 is our number.
Personally I'm too lazy to do it- maybe later.
for now I leave it to other, more curious people