Representation of real numbers as floating points is a matter of trade-offs and economics. When we need super precise numbers, we buy a different computer or write slower software. Most computers have at least two forms of floating point numbers: one short (single precision) and another long (double precision). Some computers even give you the choice of how large of an exponent to store. Many real-world and engineering applications do not require enormously precise values.

The IEEE 754 standard, used by many vendors and programming languages like Java, is a document that specifies a way to represent floating point numbers in a computer. Here are its limits given in decimal:

                  # bits     # decimal
     type           total      digits            exponent range
-----------------------------------------------------------------
single precision     32          6          10-38 to 10+38
double precision     64         19          10-308 to 10+308