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Topic: Significant Figures  (Read 11270 times)

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Offline Vette Freak

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Significant Figures
« on: March 14, 2006, 06:00:08 PM »
I know I shouldn't be having problems with this as a senior in college, but I've never come across such a problem before.  My data for a biochemistry lab consists of absorbance readings taken at 10 second intervals for two minutes.  My data set starts with .000 absorbance at time 0.  Other readings are .032 at t=10s, .144 at t=50, and 1.024 at t=120.  I need to determine the slope of the linear regression for this data.  By what I know, .000 technically has no significant figures, .032 has 2, .144 has 3 and 1.024 has 4.  So ignoring the significant figures for time, how many significant figures would I use for my absorbance values and therefore for my calculation of slope (obviously, zero is incorrect)?
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Offline hmx9123

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Re:Significant Figures
« Reply #1 on: March 14, 2006, 11:19:46 PM »
You have come across the problem with significant figures.  That is, your instrument reads and gives you useful numbers to a certain decimal place.  No matter if it's 0.000 or 0.989, it still gives only SF to the 3rd decimal place.  I used to work in an analytical lab, and we used to laugh at Sig Figs, because we never used them.  The true measure of sig figs is the limit of accuracy of your instrument, and the real measure of accuracy is error analysis (the tolerances on your measurements).  Here's how I would handle this:

Take all your numbers, plug them into a linear regression algorithm and then get a number out of it.  Round the number to 3 decimal places since your figures were taken with 3 decimal places of accuracy.

You could think of the idea of drawing a line over the significant digits in the zero value, but it still is a problem that you have 4 SFs from the value that's over 1.  Personally, I think the whole SF issue is really lame.

If you have an idea of what the tolerances are for your material, then you can use error analysis (i.e., additive and multiplicative error) to determine the final error in your answer, which may be a more fair assesment.
« Last Edit: March 15, 2006, 02:04:24 AM by hmx9123 »

Offline Vette Freak

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Re: Significant Figures
« Reply #2 on: April 21, 2006, 09:49:32 AM »
I forgot I made that post, but I do thank you for your response. I was thinking the exact same thing at the time and putting way too much thought into it.  After carrying sig figs thru the statistical method of calculating the linear regression, I concluded that 3 sig figs should be sufficient.  If it wasn't I'd have a lot of complaining to do to my professor.  I made a good educated guess and didn't any points taken off this time for sig figs.  Its insane how chemistry professors are so obsessed with sig figs in college and how many points you lose for not having the right sig figs in your correct answer.  Who came up with this crap? LOL  Thanks again!
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Offline xiankai

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Re: Significant Figures
« Reply #3 on: April 21, 2006, 07:15:38 PM »
i prefer to use decimal points instead of significant figures, which are a more accurate way when collecting measurements since it ensures the last digits of the same measurement are correlated.

about significant figures however, i agree that the hype about this is crazy; i always had a problem when calculating with sig. figs, because using the rounded number and the number with actual amount of decimal places often gave me 2 different answers, so i had to fall back on the number with actual amount of decimal places. :p
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