I’ve had many students who tell me that they’re happy in
math classes as long as someone tells them
exactly what the procedure is, gives some examples, and then the homework and
test problems are just
like those examples. Those students typically don’t like word problems much,
because each one seems
so different and it ’s hard to pick out the relevant information.
So, the bad news here is that using mathematics in the real world – and in the
biotechnology real world –
is mostly word problems. The good news is that we’ll spend quite a lot of time
looking at those word
problems and helping you find the critical ideas in each one, so that you can
see the patterns and become
confident in using math in biotechnology situations.
We don’t have much time in this short course to do this, so we need you to do
some work on your own.
In particular, you’ll need to review some standard math techniques, like laws of
exponents , scientific
notation, measurement conversions, solving linear equations, and solving
proportion problems. Our book
has excellent overall summaries of these , with problems and solutions . I will
give you guidance on what
to review and how to review it. Our class discussions will focus on a few
mathematical topics that you
may not have seen before and, mostly, on how to use these techniques to solve a
variety of biotechnology
problems.
Here’s an idea to think about to start. How big is a typical virus? Don’t
just quote a number, but be
able to talk about how big that is in comparison to other things you’re familiar
with.
So what’s some math to help us? Answer: The idea of orders of magnitude .
Consider this example: Here’s a meter stick (like a yard stick, but a meter
instead.) I’ll use it to measure
myself. Notice that I’m about 1.5 meters tall. (We could measure more
accurately, but for this purpose,
we don’t need to.) Now let’s think of how we’d measure the length of an ant.
Remembering how small
they are, and looking at these measures, I think that it might be about 2
millimeters long.
To compare these numbers, we could either subtract them or divide them to get a
comparison. Of course,
to get a meaningful answer from either subtraction or division, we have to write
them in the same units.
Subtracting these two numbers isn ’t very satisfactory, since the difference is
about 1.5 meters. We’d have
to measure my height a lot more precisely to get anything interesting here. That
isn’t surprising – it is
usually the case when comparing measured numbers of things which are very
different in size.
So we will compare them by dividing. Now, of course, the measurements we did
here aren’t very precise,
so that could cause a big difference in the resulting ratio – particularly if
the one in the denominator isn’t
very precise. So we often don’t want to give the ratio very precisely. People
handle that by just
rounding it off to the nearest power of ten . We call that the order of magnitude
of the number. When
thinking of the order of magnitude, we divide, and then round it off to the
nearest power of ten.
So here, 1.5 meters / 2 mm = 1500 mm/ 2 mm = 750. When we round to the nearest
power of ten, that’s
10^3= 1000. So the order of magnitude of the ratio is 3. Or, another way of
wording it is that the height
of a person is 3 orders of magnitude more than the length of an ant.
It is also fairly common to just round off each of the measurements to a power
of ten in the first place
(before dividing) and then divide those, which, because of the laws of
exponents , is the same as
subtracting the exponents.
If we wanted to discuss the comparison of weights, the answer wouldn’t
necessarily be the same as this.
Can you see why that might be true?
So here’s a fun question for you to answer for tomorrow.
How big is a virus? How many orders of
magnitude different from an ant? From a person? Here think of “length,” not
weight or volume or
another measure.
A hint: Search the Internet for “Orders of magnitude” and see if you can quickly
find something that
tells you the size of a virus to use here. (When I did a Google search I found
several sites with this
information.) Spend no more than 5 minutes on this. Second question: “Why is
it reasonable to
believe that the site you found is giving accurate information?”
