IEEE double precision (used by Excel) uses 64 bits to represent floating
point numbers. 52 bits (effectively 53 bits for numbers > 1E-307 in
magnitude) go to repesenting the value (the rest go to the exponent and
sign). This is sufficient to approximate 15 decimal digit numbers, but
requires 17 decimal digits to uniquely identify the binary represention.
Excel's documented 15 decimal digit limitation is a design decision to avoid
explaining why some 17 decimal digit numbers would otherwise change value
immediately on input. Some other IEEE compliant packages will allow you to
see and directly manipulate the full 17 decimal digits.
Jerry