# 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 +  ,   , ×  , ÷  , g   1/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 19-digit 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 10-digit number whose square when rounded to 10-digits is 5.000000000.
Factorial function (  g   n!  ) is accurate to ±1 count in the ninth digit. Values converted to degrees-minutes-seconds f   D.MS are correct to ±1 second, as are the results of f   D.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
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