Sorry if this is not the right question for this channel, I just need to know and there is no good place to ask.
It is said the Fine Structure Constant α is one of the most fundamental constants in nature. Unlike the likes of the speed of light, α is dimensionless. I have heard an argument that when we encounter intelligent aliens sending the α at them is the best way to let them know how much we know. It was said that we should of course send the constant in the binary numeral system.
My question is: how do you communicate a fraction (α = roughly 1/137) in binary so that even aliens can decode it?