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Scheme numbers are either *exact* or *inexact*. A number is
exact if it was written as an exact constant or was derived from
exact numbers using only exact operations. A number is
inexact if it was written as an inexact constant,
if it was
derived using inexact ingredients, or if it was derived using
inexact operations. Thus inexactness is a contagious
property of a number.

If two implementations produce exact results for a computation that did not involve inexact intermediate results, the two ultimate results will be mathematically equivalent. This is generally not true of computations involving inexact numbers since approximate methods such as floating point arithmetic may be used, but it is the duty of each implementation to make the result as close as practical to the mathematically ideal result.

Rational operations such as ‘`+`’ should always produce
exact results when given exact arguments.
If the operation is unable to produce an exact result,
then it may either report the violation of an implementation restriction
or it may silently coerce its
result to an inexact value.
See section Implementation restrictions.

With the exception of `inexact->exact`

, the operations described in
this section must generally return inexact results when given any inexact
arguments. An operation may, however, return an exact result if it can
prove that the value of the result is unaffected by the inexactness of its
arguments. For example, multiplication of any number by an exact zero
may produce an exact zero result, even if the other argument is
inexact.

Next: Implementation restrictions, Previous: Numerical types, Up: Numbers [Contents][Index]