Uncertainty and the display format – HP 15c User Manual
Page 246
246 Appendix E: A Detailed Look at
f
)
(
δ
)
(
)
(
2
x
x
f
x
F
,
where δ
2
(x) is the uncertainty associated with f(x) that is caused by the
approximation to the actual physical situation.
Since
)
(
δ
)
(
ˆ
)
(
1
x
x
f
x
f
, the function you want to integrate is
)
(
δ
)
(
δ
)
(
ˆ
)
(
2
1
x
x
x
f
x
F
or
)
(
δ
)
(
ˆ
)
(
x
x
f
x
F
,
where δ(x) is the net uncertainty associated with f(x).
Therefore, the integral you want is
dx
x
x
f
dx
x
F
b
a
b
a
)]
(
δ
)
(
ˆ
[
)
(
b
a
b
a
dx
x
dx
x
f
)
(
)
(
ˆ
I
where I is the approximation to
b
a
dx
x
F
)
(
and ∆ is the uncertainty
associated with the approximation. The f algorithm places the number I
in the X-register and the number ∆ in the Y-register.
The uncertainty δ(x) of
)
(
ˆ x
f
, the function calculated by your subroutine, is
determined as follows. Suppose you consider three significant digits of the
function's values to be accurate, so you set the display format to i 2.
The display would then show only the accurate digits in the mantissa of a
function's values: for example, 1.23 –04.
Since the display format rounds the number in the X-register to the
number displayed, this implies that the uncertainty in the function's values
is ± 0.005Ч10
–4
= ± 0.5Ч10
–2
Ч10
–4
= ± 0.5Ч10
-6
. Thus, setting the display