AS 2706:2003 Numerical values一Rounding and interpretation of limiting values
3.4 ROUNDING OF NUMBERS IN COMPUTERS AND CALCULATORS
The procedures employed in computers and calculators to produce ’rounded’ numbers in the display or print out vary. The more common procedures round to one unit in the last place retained and are as follows:
(a) Truncation That is, simply removing the unwanted figures with no adjustment to the last figure of the ’rounded’ number.
(b) A/ways rounding up When the discarded figures fall exactly midway between two successive round values.
(c) Variable This appears to be a feature of some computers that store numbers in binary form. It is often evident as a dependency on the figure before the last place to be relained as well as on the figure afiter. Moreover, the changeover from rounding up to rounding down can occur elsewhere than at the midway position between two successive round values.
NOTE: In any intermediate stages in the course of the computation of a value that is finally to be rounded, it falls within the discretion of the operator to ignore such figures as would have no influence on the last selected place of the value to be rounded. The number of figures to be carried depends largely on the nature of the work and for some purposes it is inadvisable to discard figures at an intermediate stage. All rounding implics loss of information, and the effect of the accumulation of such losses in a lengthy calculation has to be estimated, even if roughly. This applies particularly to calculations in the course of which large numbers not differing widely are subtracted from one another. It is helpful in the intermediate stages to use a + or – sign after a final 5 to indicate whether a subsequent rounding should be up or down.
The user should check a computer’s or calculator’ s rounding procedure (by direct experiment if there is no published information) before accepting any rounded values displayed or printed out. In many cases, it may well be preferable to display or print out numbers with extra figures and to do rounding manually.