HP 15c Scientific relative, absolute, =0.5×10−n+m( x)

Appendix E: A Detailed Look at f 247

format to i n or ^ n, where n is an integer,* implies that the uncertainty in the function’s values is

δ(x) = 0.5×10−n ×10m( x)

=0.5×10−n+m( x)

In this formula, n is the number of digits specified in the display format and m(x) is the exponent of the function's value at x that would appear if the value were displayed in idisplay format.

The uncertainty is proportional to the factor 10m(x), which represents the magnitude of the function's value at x. Therefore, i and ^ display formats imply an uncertainty in the function that is relative to the function's magnitude.

Similarly, if a function value is display in • n, the rounding of the display implies that the uncertainty in the function's values is

δ(x) = 0.5×10−n.

Since this uncertainty is independent of the function's magnitude, • display format implies an uncertainty that is absolute.

Each time the f algorithm samples the function at a value of x, it also derives a sample of δ(x), the uncertainty of the function's value at x. This is calculated using the number of digits n currently specified in the display format and (if the display format is set to i or ^) the magnitude m(x) of the function's value at x. The number Δ, the uncertainty of the approximation to the desired integral, is the integral δ (x):

*Although i 8 or 9 generally results in the same display as i 7, it will result in a smaller uncertainty of a calculated integral. (The same is true for the ^format.) A negative value for n (which can be set by using the Index register) will also affect the uncertainty of an fcalculation. The minimum value for n that will affect uncertainty is -6. A number in RI less than -6 will be interpreted as -6.