Experiment
Design:
Design
an experiment to test each hypothesis. Make a
stepbystep list of what you will do to answer
each question. This list is called an experimental
procedure. For an experiment to give answers you
can trust, it must have a "control." A
control is an additional experimental trial or
run. It is a separate experiment, done exactly
like the others. The only difference is that no
experimental variables are changed. A control is a
neutral "reference point" for comparison
that allows you to see what changing a variable
does by comparing it to not changing anything.
Dependable controls are sometimes very hard to
develop. They can be the hardest part of a
project. Without a control you cannot be sure that
changing the variable causes your observations. A
series of experiments that includes a control is
called a "controlled experiment."
Scientific
(programmable) calculators should be accurate!
Here are a few ways to determine their accuracy
and some results. Naturally, if you test a
calculator not mentioned here, I am eager to learn
the results you get: Please email.
One way to test
the accuracy of a scientific calculator is to
perform the following formula and see when the
answer turns out to be ONE (1).
Y
=lim ( X / sin X) where X descends to zero.
If Y is 1 upon X
= 0.01 then the accuracy will be classified ´low´.
Simular with X =
0.001, accuracy will be ´below normal´.
With X = 0.0001,
accuracy ´normal´. X = 0.00001, accuracy ´good´.
X = 0.000001, accuracy ´very good´. X =
0.0000001 or smaller, accuracy ´extremely good´.
A few examples of
calculators I have that are still in working
order: The TI57 and TI25 score NORMAL. The
TI58, HP33E, FX502P and FX6000G score GOOD.
The HP48SX scores VERY GOOD and the TI92 scores
EXTREMELY GOOD.
Another way to
test the accuracy is to see how many digits will
be correct (or give a correct rounded result) for
the following calculations:
Cos
0.184 (rad) = 0.983119705665017
Sin
3.8° (deg) = 0.066273900400000
Atn
0.445 (rad) = 0.418688151438
The TI57 scores
7, 7, 7 digits.
The FX6000G
scores 10, 10, 10 digits.
The HP33E scores
10, 11, 10 digits.
The FX502P
scores 11, 11, 11 digits.
The TI58 scores
12, 10, 12 digits.
The HP48SX
scores 12, 11, 12 digits.
The TI92 scores
14, 14, 12 digits.
Of
course the number of accurate digits never exceeds
the number of digits used by the calculator
internally. Digits that are not shown by the
display can be made visible by subtracting the
visible result. For example: The TI92 gives the
following result for Cos 0.184 (rad):
0.983119705665. If we subtract 0.983119705665 from
this answer we will see the remaining digits: 2 E
14. Put together the result is 0.98311970566502,
which is a correct (be it rounded) result for all
14 digits.
(Of
course, on the TI92 there is an easier way to see
the full 14 digits of the result, but that is
beside the point here.)
A Simple
Accuracy Test for Calculators
Back in the early
days of handheld calculators the 'Commodore' test
was a simple demonstration of trigonometric
accuracy. It was invented by the Commodore
Business Machines (CBM) marketing department to
highlight the accuracy of their machines.
Althought it only tests a few functions, over the
years it has proven a useful way to get a 'feel'
for the overall accuracy of calculators.
At the time the
test appeared in CBM adverts good machines would
return values a few thousands of a percentage out
while there were some machines on the market which
would be a few percent in error. (Yes, I
owned a Sinclair Oxford 300!) Nowadays it is
unusual to find a machine that is more than a
billionth of percent in error.
To test a
calculator set it to work in degrees and then
enter the following calculation:
asin(acos(atan(tan(cos(sin(29))))))
which should
return a value of '29'. To get the percentage
error carry out the following calculation:
(asin(acos(atan(tan(cos(sin(29))))))29)/29*100
