Scientific Computing

This module demonstrates the effect of different rules for rounding a
given decimal number to a smaller number of digits. If a given real
number is not exactly representable as a floating-point number, then it
must be approximated by some nearby floating-point number, a process
called *rounding*. Two commonly used rounding rules are

*chop*, in which the base-*β*expansion is truncated after the( digit, where*p*−1)st*p*is the precision of the target system, and*round to nearest*, in which the nearest floating-point number is chosen as the approximate value.

Round to nearest is the more accurate of the two, and is the default rounding mode in IEEE floating-point arithmetic.

The user selects values for the input and output precisions, and then either enters explicitly or chooses randomly a value to be rounded. The chosen number is then rounded by clicking the button for the desired rounding rule.

**Reference:** Michael T. Heath,
*Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 1.3.4, especially Example 1.10.

**Developers:** Nicholas Exner and Michael Heath