HP HP-65 - Appendix A Operating Limits; Accuracy

Appendix A
Operating Limits
Accuracy
The accuracy of the HP-65 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 , @ , 7 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 (1/3)2
Rounding /5 to 10 significant digits gives 2.236067977. Squar-
ing this number gives the 19-digit product 4.999999997764872-
529. 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 signifi-
cant digits gives 5.000000002. There simply is no 10-digit num-
ber whose square when rounded to 10-digits is 5.000000000.
When subtracting numbers having 10 significant digits, the an-
swer is correct to =1 count in the 10th (least significant) digit of
the algebraically larger operand.
Factorial function ([8] [n1]) is accurate to =1 count in the ninth
digit. Values converted to degrees-minutes-seconds [
are correct to =1 second, as are the results of [ and
@ (oms+ |-
The accuracy of the remaining operations (trigonometric, loga-
rithmic, and exponential) depends upon the argument. The an-
swer that is displayed will be the correct answer for an input
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