> 100!; 933262154439441526816992388562667004907159682643816214685929638952175999932299\ 156089414639761565182862536979208272237582511852109168640000000000000000000000\ 00All 158 digits of 100! are returned, and the answer is exact. (The backslashes mean that the line breaks have been artificially introduced in order to make the answer fit on screen, and they are not part of the answer.)

Likewise, Maple fractions have numerator and denominator of arbitrary precision, so in theory any given rational number can be exactly represented by Maple (subject only to the size of your computer's memory!).

Most results in Maple are exact. Even irrational numbers are returned in terms of their definition, and not as truncated decimal expansions:

> arctan(1); 1/4 Pi > sqrt(2); 1/2 2Sometimes you may want to know the answer in floating-point form. The function

> sqrt(2); 1/2 2 > evalf("); 1.414213562

The precision of the answer (number of significant digits) is 10 by
default, but you can request a floating point approximation of any precision
by giving a second argument to `evalf()`:

> sqrt(2); 1/2 2 > evalf(", 30); 1.41421356237309504880168872421As an extreme example, try

The built-in variable `Digits` holds the default precision for floating
point approximations, initially 10. You can change the default precision to 40
by assigning `Digits := 40` for example.

Maple often gives an answer in partly unevaluated form, either because certain of the
quantities are variables whose value is not known, or because Maple couldn't
find a closed form answer. On occasion, you may want to ask Maple to evaluate
such an expression and give a numeric approximation. `evalf()` can
do this too. For example:

> int( exp(x^x), x=0..1); 1 / | x | exp(x ) dx | / 0 > evalf("); 2.197544438Maple had a hard time simplifying the integral, so it returned a symbolic expression--the unevaluated integral.

`evalf()` does the best it can, however if there are symbols in the expression
whose value is unknown or non-numeric, then the result will still depend on
these symbols:

> evalf(Pi + cos(t)); 3.141592654 + cos(t)

Keith Orpen, who is still writing this, would like to hear your comments and suggestions.