Scientific notation is really just a shorthand version of writing really
big or really small numbers. No working scientist uses scientific notation for
every number -- numbers like 1,000 or 0.01 are small enough and simple enough
to write that they would be written just like that. But a working scientist
would certainly not write out 40,700,000,000,000 kilometers in a paper -- it's
just too long! Instead, she would write the number as 
kilometers -- which is easier to write. (In fact, she'd probably write
km, since ``km'' is the abbreviation for kilometers.)
Similarly, she wouldn't write out 0.000000000000000002356; again, it's just too
long. She would instead write out 
, which again is
easier on everyone. And scientific notation can make some kinds of math
problems more manageable. Doing arithmetic on really big or really small
numbers is much simpler, once you know how to use scientific notation.