Significant Figures
·
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practice worksheets
One
of the most baffling subjects for students is frequently significant
figures. The reason for this is
simple: Nobody ever seems to know what
they’re supposed to be used for. Why
should I care if “100” has one significant figure or “100.0” has four?
Fortunately,
your friend Mr. Guch is here to help.
Let’s take a look at the joyous excitement produced by significant
figures:
Why do we need
significant figures?
For
some reason, teachers never really tell students why significant figures are
important (note to any teachers who are reading this: I’m not talking about you. I’m talking about those
other teachers).
Significant
figures are important because they tell us how good the data we are using
are. (Incidentially, the word “data” is
plural for “datum”, so even though it seems weird saying that “data are
[something]”, it’s grammatically correct.)
For example, let’s consider the following three numbers:
100
grams
100.
grams
100.00
grams
In
short, when you plug these three numbers into your calculator, there’s no
difference in how the calculator will manipulate them – your calculator neither
knows nor cares about how good the numbers it’s working with are. However, to you, the taker of data, these
three numbers tell you whether or not your data is good enough to pay attention
to.
How do we find
the correct number of significant figures?
Right
now you’re thinking to yourself, “Mr. Guch, my teacher never mentioned anything
you talked about above, but for some reason just likes to ask me a bunch of
questions in which I need to figure out how many significant figures a number
has. What should I do?”
What
you should do is march
right on down to your teacher and tell them that they’ve been wasting your
time, teaching you something that’s totally irrelevant (because as I mentioned,
significant figures are completely irrelevant if you don’t understand why they’re important). Of course, your teacher will laugh at you,
call your parents, and make you stay after school, so this probably isn’t a
great idea.
What
you’ll probably end up doing is just learning how to figure out the rules for
measuring significant figures. However,
make sure that you tell your friends why significant figures are handy so they
know why they’re bothering with all of this.
Rule
1: Any number that isn’t zero is
significant. Any zero that’s between two
numbers that aren’t zeros is significant.
Rule
2: Any zero that’s before all of the
nonzero digits is insignificant, NO MATTER WHAT.
Rule
3: Any zero that’s after all of the
nonzero digits is significant only if you see a
decimal point. If you don’t actually see
a little dot somewhere in the number, these digits are not significant.
Rule
4: When you write numbers in scientific
notation, only the part before the “x” is counted in the significant
figures. (Example, 2.39 x 104
has three significant figures because we only worry about the “2.39” part).
How about some
practice problems?
Knock
yourself out. Click HERE for a
practice worksheet.
© 2006 Ian Guch – All rights reserved.