I have something I need to get off my
chest. As math teachers, it is so
important to us to have our students (and the general population) see that math
is useful. Anytime math is in the media or in anything mainstream, we want to
jump up and down, and shout, “See! See! This is important!” (And I mean other
than March 14th, when people everywhere bake delicious pies and post
in their statuses “Happy Pi Day!” even though any other of their math-related
posts involve the phrase FML. Don’t ask me what that means, I’ve checked, and
it’s not the formula for anything). But
we’re math teachers, we don’t jump up and down, we just push our glasses up our
noses and try not to sigh audibly as the attendant counts out the wrong change.
Beginning
with the announcement of plans to scrap the Canadian penny last year, and the
fruition of these plans in February of this year, an age-old mathematical
process has been brought into the limelight. That’s right, I’m talking about
rounding.
This
concept, introduced in Ontario in Grade 3, is supposed to be used obtain a
value that is easier to write and to handle than the original. But the removal of the penny, and the
subsequent need for monetary amounts to exist in five cent increments, have
created an uproar from sea-to-sea in our beautiful True North, strong and free. And I think it basically boils down to the
fact that people just don’t understand the concept of rounding.
Listening
to a cross-Canada call in radio show (CBC’s Cross-Country check-up), or reading
the comment sections of related news articles, and you see the comment so
often, “Why do I get feeling there's
going to be a lot more rounding up than rounding down?”.
Mr.
Anonymous Internet Commenter does not realize that rounding is not an arbitrary
thing where the merchants (or worse, the Government!) get to decide whether the
total gets rounded up or rounded down. It is a mathematical process with a set
of rules. And I feel as though I need to explain. If the final value we need to obtain has two
numbers after the decimal (i.e. hundredths), and the hundredths need to be in
increments of 5, then there is a specific way to get there. Zero and five stay zero and five,
respectively. One and two round down to
zero, three and four round up to five, six and seven round down to five, and
eight and nine round up to ten (zero in hundredths column). That means there are two numbers that don’t
change, four that round up, and four that round down. There is an equal mathematical probability of
getting to any of these numbers. The
rounding is only applied to after-tax amounts, and there is no way for a store
strategically plan their prices in order to dictate that you will always end up
with a 3, 4, 8, 9 (and thus, have to round up).
Prices all vary in amounts in the tenths and hundredths (for a while it
was always .99, but it seems as though .97 is the new .99, and go to Wal-Mart
and you will find prices ending in everything from .49 to .74 to .82, but shop
at MEC and everything ends in .00 or .50).
A store has no control over the number of items you purchase at a time,
and therefore has no way to predict what the combination of prices will add up
to be. Tax also varies – there is no tax
on food, some things have only the 5% GST, and some have the full harmonized
13% (“harmonized” – talk about a euphemism!), and that is only in Ontario –
other provinces have different PST amounts.
This all to say, there is absolutely no way to use prices in stores to
guarantee that tallies will fall more frequently into the ranges that get
rounded up. One day you win, one day you
lose, but on a whole, the probabilities will be equal.
If
you think the penny’s exodus and this rounding “dilemma” is part of some
bigger, more sinister conspiracy, or can poke holes in my mathematical
reasoning, please, by all means, weigh-in.
After all, this is only my two cents worth, and we all know that rounds
down to nothing anyway.
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