Mathematica supports arbitrary precision and exact numbers, but it can also operate using normal machine-precision floating point numbers of the kind used in Excel and many other programs. When using machine-precision numbers, all the usual issues around floating-point arithmetic apply, including the possibility that precision might decline in certain calculations.
N, the function that turns exact numbers (
Realnumbers. Converts numbers at any position in an expression thus it works on vectors and matrices too.
- Tutorial on numerical precision covering among other things
NumberFormchanges the displayed version of the number without actually changing its underlying precision or accuracy.