Significant Figures

 

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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.

 

 

 

 

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