For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.
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.
- David Goldberg, What Every Computer Scientist Should Know About Floating-Point Arithmetic, ACM Computing Surveys 23(1) March 1991.