I'm studing floating point representation of binary numbers, and it made me notice something.
Well, actually, I noticed it before of course, but it never occurred to me to ask about it up until now:
There are some numbers, rational numbers, that can be presented in a finite decimal floating-point representation,
but some cannot, like:
My question is why?
what distinguish "infinite decimal floating-point representation" from the ones that can be written in a finite form?
I also noticed (and correct me if I'm wrong) that when it comes to binary floating-point representation, the "problem" is much bigger:
There are considerably much more fractions that cannot be represented in a finite series of digits, then the ones that can.
Why does that happen?
Thank you in advance.