Fear is a powerful motivator, Dennis. Mine express concern about
rounding off too much in the final answer. I suspect that the larger
number of digits bolsters their confidence in the accuracy of their
answers. Ironically, they will round off prematurely in their chains of
calculation.
A recent "bug" has arisen with calculators that "float" a number to some
stated number of decimal places. If the student goes on and uses the
stored number for further calculations then all is well and good. But if
they write it down and then reinsert it, disaster can occur. For
example, the default value for "float" seems to be 3 decimal places. So,
"the period of a 156 Hz tone is 0.006 s and the period of a 153 Hz tone
is 0.007 s". Then, "one hears 167 cycles of a 156 Hz tone in one second
or 143 cycles of a 154 Hz tone in one second". The "sharp" student would
round of those two answers to "2 x 10^2 cycles and 1 x 10^2 cycles,
respectively"! Notice that even if 154 and 156 were both rounded to one
significant figure, the result would be 2 x 10^2. Of course, the
students are throwing away precision by premature rounding. I've even
seen them let the calculator round a very small number to 0 and then to
null out anything they multiply by that intermediate value!
I have gotten to the point where I usually remind my students to make
sure that they don't have their calculator set to "float 3" or some
similarly small value at the start of each test.
Jim
Dennis Brownridge wrote:
>
> Yes, clearly the area should have been given as 8000 km2. Probably the
> single most common mathematical mistake that people make is failure to round
> off to an appropriate precision. Often this happens in converting from
> wombat to SI, but that doesn't seem to be the case here. Unfortunately, high
> school math courses DO NOT teach significant digits and the rounding rules.
> If students learn that at all, they learn it in science courses. In middle
> school, students learn a little about rounding, but they are taught that
> it's used for "estimating" or "approximating." The concepts of precision and
> accuracy are not taught in math, nor is the notion that ALL measurements are
> approximate. Unless they hear about it in chemistry or physics, they are
> unlikely to hear about it at all. Even our best students insist on
> expressing too many digits in their answers. You can tell them to round off
> a hundred times and still they resist.
>
> > -----Original Message-----
> > From: Duncan Bath
> > >
> > Globe & Mail [A3], Mar 08:
> > "What's killing Mexico's Monarchs: .."
> >
> > In this article, by a "science reporter", reference is made to ".. a
> > 795,000-hectare model ..". This raises two questions re the rational use
> > of numbers:
> >
> > a) with areas this large, why not refer to 7,950 square kilometres -
> > this is easily envisaged by all but the most profoundly numerically
> > challenged as (say) about 80 km by 100 km
> >
> > b) using high-school math teachings concerning 'significant
> > digits', why
> > not refer to 8,000 square kilometres. This "rounding" process involves a
> > discrepancy of well less than 1% and should be entirely appropriate in
> > this context.
> >
> > Duncan
> > DT Bath, 861 Kensington Dr., Peterborough ON K9J 6J8
> > (705)743-4297
> >
> >
--
Metric Methods(SM) "Don't be late to metricate!"
James R. Frysinger, CAMS http://www.metricmethods.com/
10 Captiva Row e-mail: [EMAIL PROTECTED]
Charleston, SC 29407 phone/FAX: 843.225.6789
