what fraction of energy on average actually reaches the earth's surface?

Answer 1

What is the source of energy in the question?
Let's say you consider the Sun as the source.
The total energy the Sun generates per second is Es
The Sun is Rs km away from the Earth.
The Earth effective surface area Ae is Ae=pi Re^2 (approximately)
Let As be area of a sphere in generated Rs distance away.

Then total energy Et=(Es/As)
and Total energy the Earth receives per second is
Ete=Et(Ae) =(Es/As)Ae

Ete=(Es/(4pi Rs ^2)) pi Re^2
Ete=(Es/(4 Rs ^2)) Re^2
Just plug the numbers in

and
Fraction =Ete/Es
;-)