currency at the half cent

[Alex-Jordan]

Sometimes when using contextCurrency.pl, there is algebra that leads to a perl decimal version of an answer, and then you pass that decimal to the Currency() constructor to create an answer where students must use a dollar sign.

Sometimes, you are creating an answer like this one: Currency(12.345). And sometimes (depending on what produced that decimal value and whatever machine rounding error may be in play) the correct answer displays as $12.35, but neither $12.35 nor $12.34 will be accepted as correct when a student enters them, using the default tolerance. They are just at the cusp of the decimal tolerance. Also a student may not enter something like $12.345 with the default flags.

Perhaps the problem author should be aware of all this and round their decimals before passing them to the Currency() constructor. But maybe not, since maybe the Currency() object is supposed to retain deeper decimal precision if it gets used in further calculations. So I'm wondering if we could address this by tweaking the cmp method for a Currency object. What I'm thinking is, if the context disallows entering more than two decimal places, the correct answer should be rounded to two decimal places before it is actually compared to the student answer. Would that idea raise any objections? Of course this is something where I'm interested to hear from @dpvc.

[dpvc]

This issue is discussed in the POD documentation at the top of the file, which says:

The default tolerance of .005 works properly only if your original
monetary values have no more than 2 decimal places. If you were to do

$m = Currency(34.125);

for example, then $m would print as $34.12, but neither a student
answer of $34.12 nor of $34.13 would be marked correct. That is
because neither of these are less than .5 away from the correct answer
of $34.125. If you create currency values that have more decimal
places than the usual two, you may want to round or truncate them.
Currency objects have two methods for accomplishing this: round() and
truncate(), which produce rounded or truncated copies of the original
Currency object:

$m = Currency(34.127)->round;    # produces $34.13
$m = Currency(34.127)->truncate; # produces $34.12

so in that sense, this is something the authors should be aware of.

In the case where students are only allowed to enter 2 decimal places, I'm wondering if using a tolerance of something like .005001 or something like that might be an easier solution?

I'm not sure if it is really necessary to keep the extra digits, and this is such an old context (2006 as I recall), I no longer remember the reason that they were not rounded or truncated originally. My current gut feeling is that keeping the extra digits was probably a mistake, and they should be reduced when the currency object is created (there could be a flag to control whether they are rounded or truncated). I suspect that the rounding may be a bit touchy with the .xy5 values, but Peter Staab and I did some work with rounding for his Significant Figures context that might be useful here.

If you want to keep the extra digits for computational purposes, then your suggestion of rounding (or truncating) for comparisons is a reasonable one, but it should probably be done in the compare() method, not cmp().