Ok so the real question is, if the Floating Points have some limitation in accuracy, how do Supercomputers Handle that?

By not using floats when high precision matters.

@Root how ? I mean you can interpret floating points number with real/integers number?

@wowotek
There are quite a lot arbitary-precision-integer library's out there, for almost all languages.

one workaround could be to use floating point numbers with the base 10, sacrificing performance for accuracy

There are so many different approaches I don't even want to list them, but here are a couple:

1) long long plus a decimal place tracker. Add a power tracker for insanely large numbers.

2) string math (perfect accuracy, range limited only by memory, slow as beans)

As @metamourge said, there are libraries out there for every language. Read them!

@metamourge @Root i just read those description. And as mindblown as i am, my brain is just happy. Thabks !

Well, supercomputers are not special. They treat floating numbers in the same way common computers do. When more precision than what is available in a float or a double is required other more complex types are used. I'm sure that there are some specific libraries for some particular systems but I expect it to be just a matter of getting better performance and the actual representation of the number not to be very different.

You use numerical stable algorithms or an iterative approach to get a solution that is accurate (e.g. when adding up numbers starting with the smallest number).
Also some PowerPC CPUs supports quad precision natively

@StopMotionCuber how can a computer support a quad precision floating point with a 64-bit processor?

@StopMotionCuber interesting. Could you point us to an example?

@wowotek
I'm not a CPU engineer but there is also AVX which supports 256/512 bit operations on a 64 bit processor.

@StopMotionCuber oh shit this thing will make me can't sleep