


Appendix A

Operating Limits


Accuracy


The accuracy of the HP65 depends upon the operation being performed. Also. in the case of transcendental functions,
it is impractical to predict the performance for all arguments alike. Thus, the accuracy statement is not to be
interpreted strictly, but rather as a general guide to the calculator’s performance. The accuracy limits are
presented here as a guide which. to the best of our knowledge. defines the maximum error for the respective
functions.


The elementary operations +, –, ×, ÷, g1/x, f , f^{1} D.MS
have a maximum error of
±1 count in the 10th (least significant) digit. Errors in these
elementary operations are caused by rounding answers to the 10th digit.


An example of roundoff error is seen when evaluating (√5)2. Rounding √5 to 10 significant
digits gives 2.236067977. Squaring this number gives the 19digit product 4.999999997764872529. Rounding the
square to 10 digits gives 4.999999998. If the next largest approximation (2.236067978) is squared, the result is 5.000000002237008484. Rounding this number to 10 significant digits gives 5.000000002. There simply is no 10digit number whose square when rounded to 10digits is 5.000000000.


Factorial function (gn!) is accurate to ±1 count in the ninth digit. Values converted to
degreesminutesseconds f D.MS are correct to ±1 second, as are the results of fD.MS+ and f^{1}D.MS+.


The accuracy of the remaining operations (trigonometric, logarithmic, and exponential) depends upon the
argument. The answer that is displayed will be the correct answer for an input



