HP -15C Advanced Functions Handbook page 176

174 Appendix: Accuracy of Numerical Calculations
Example 4: A Bridge Too Short. The lengths in meters of three
sections of a cantilever bridge are designed to be
^ = 333.76 y = 195.07 2 = 333.76.
The measured lengths turn out to be respectively
X= 333.69 Y= 195.00 Z= 333.72.
The discrepancy in total length is
z)-(X+Y+Z) = 862.59 - 862.41 = 0.18 .
Ed, the engineer, compares the discrepancy d with the total length
(x + y + z) and considers the relative discrepancy
d/(x + y + z) = 0.0002 = 2 parts in 10,000
to be tolerably small. But Rhonda, the riveter, considers the
absolute discrepancy d\ 0.18 meters (about 7 inches) much too
large for her liking; some powerful stretching will be needed to line
up the bridge girders before she can rivet them together. Both see
the same discrepancy d, but what looks neglibible to one person
can seem awfully big to another.
Whether large or small, errors must have sources which, if
understood, usually permit us to compensate for the errors or to
circumvent them altogether. To understand the distortions in the
girders of a bridge, we should learn about structural engineering
and the theory of elasticity. To understand the errors introduced by
the very act of computation, we should learn how our calculating
instruments work and what are their limitations. These are details
most of us want not to know, especially since a well-designed
calculator's rounding errors are always nearly minimal and
therefore appear insignificant when they are introduced. But when
on rare occasions they conspire to send a computation awry, they
must be reclassified as "significant" after all.