Significant Digits (Please Help!)

[astrife]

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I have a huge problem applying significant digits correctly to long computation problems in my chemistry class. The fundamentals of division/multiplication and adding/subtraction are exceedingly simply, but despite this when applying this to long computation problems there is so much room for error and wasted time it seems. I was going to try and give a simple example, but it's really hard to relate without going into an in depth chemistry problem which is hard to relate on an internet forum.

To these long computation problems I have to go through the whole problem and use all the exact calculations I get not adjusting for sig figs until the end as this would make my answer off. So at the end of the problem I go back and basically do the problem again only this time applying sig fig rules to each calculation. When I get my 2nd answer (where each step has correct sig figs) I then use the amount of sig figs in it and apply it to the more exact answer first answer.

From my ch. 1 text that explain all this horribly and from all the internet sites I've found that go into this, this is the correct way to do it. In high school my teachers taught sig figs, but didn't really apply it to our work, and now that I'm really learning how to actually use them it is seeming rather tedious and making me go much slower on problems I should be whizzing through.

My chem 1 professor says adjust for sig figs on all her quizzes thus far, but even she did a horrible job explaining how to really apply them in long computations, and I'm feeling like I'm the only one in my class who is really caring to get this skill down. Do most professors ignore sig figs once you get into the nitty gritty problems of chem or are they sticklers for it? Does anyone else feel the same way I do about sig figs? Any suggestions for how to go about sig figs better? Tell me I'm not alone.

I feel so dumb asking about a topic I feel should be easy.

 

[NapeSpikes]

When I was brand new to science, it was confusing for me, too. Now it's second nature. So for now, struggle through it, learn the rules, practice. No profs will care too much after--but by then, it'll be easy as pie for you anyway.

 

[adam64897]

Yeah my Chem 1 and 2 lab instructor (same lab instructor) was real anal about the sig. figs. good thing my TA wasn't though or else a ton of my answers would have been "technically wrong" as he liked to say even though you've done the entire problem correctly. I would be willing to bet those that make you report sig. figs. accurately suffer from O.C.D. because in the long run it really doesn't matter if you use 1.0000001 g of glucose or 1.00000001 g of glucose...the whole idea of sig. figs. is just stupid and we really shouldn't have to learn that stuff.

 

[Knickerbocker]

When I get my 2nd answer (where each step has correct sig figs) I then use the amount of sig figs in it and apply it to the more exact answer first answer.

Between each step your number of sig figs can change. You are limited by measurements in each step, and the "exact value" you get for your first answer is incorrect as it makes false claims on precision.

I think it is important to understand what exactly those significant figures are...

They are a claim of how accurate your measurements are. If I say I have 1.5g of a substance, I claim to be accurate to tenths of a gram. However, the real measurement could be 1.50001 or 1.533228383 or anything else that rounds to 1.5.

Let's say that you know that the formula weight is 32.151 grams per mol and you want to know the number of moles in your 1.5 g. If you divide 1.5 by 32.151 and say that it is 0.046654 mol, you falsified results. Since 1.5 might be something different, the number of moles has a huge range. To be honest about what you do know, you follow the rules and get 0.047 mol. Though it is rounded, you are not claiming more precision than your least precise measurement. If you kept with five sig figs for each part of the problem, you're potentially falsifying precision at each step.

 

[Knickerbocker]

Yeah my Chem 1 and 2 lab instructor (same lab instructor) was real anal about the sig. figs. good thing my TA wasn't though or else a ton of my answers would have been "technically wrong" as he liked to say even though you've done the entire problem correctly. I would be willing to bet those that make you report sig. figs. accurately suffer from O.C.D. because in the long run it really doesn't matter if you use 1.0000001 g of glucose or 1.00000001 g of glucose...the whole idea of sig. figs. is just stupid and we really shouldn't have to learn that stuff.

In your extreme case it might not really matter, but read my previous post. Btw, that's not a good learning attitude.

 

[MinnyGophers]

lol the way i do it is that the number in the problem with the less sig figs gives me the the number of sig figs in my answer.

Meaning that if you have numbers such as 0.3, 0.03, and 0.0003 in your problem, your answer will be two sig figs. Technically, it's not really correct, but it works well for me and it usually ends up being right 😎

Otherwise it's pretty easy once you get used to it:

If you have an addition/substraction, then your answer cannot have more decimal places than the least accurate measurement.

Ex: 15.74 + 3.2= 18.9 and not 18.94

If you have a division/multiplication:
Your answer cannot have more sig figs than your least accurate measurement.

Ex: 15.07 * 5.01 = 75.5 and not 75.50.

The best way is to keep track of your sig figs DURING each calculations. This way, you'll know for sure you'll end up with the correct amount of sig figs in your final answer.

Hope that helps.

 

[DoctorPardi]

What I have done is carry extra digits throughout the computation until I get to the end, where I figure the significant digits at that point. So if the numbers involved are 137, 3,349 , and 4,400. Then say I needed to add all these numbers together I would get.

137 + 3,349 = 3486 + 4,400 = 7,886 = 7,886

Using significant digits my final answer would be 7,900.

137 = 3 S.D., 3,349 = 4 S.D., 4,400= 2 S.D.

 

[adam64897]

In your extreme case it might not really matter, but read my previous post. Btw, that's not a good learning attitude.

oh come on now...I was joking.

 

[Dr. Pepper]

In my book it says that if you have a decimal after a group of zeroes, all of the zeroes are sig figures:

ex. 5300 Liters = 2 SF....5300. Liters = 4 SF.

For the most part it's fine, but there are some real tricky examples.
-Dr. P.

 

[astrife]

Everyone seems to have their own method. How the hell is this accepted science? I guess I'll just ask my prof what she wants me to do since she is the one who gives me my grades.

This article has some rather interesting comments about significant digits.

http://en.wikipedia.org/wiki/Significance_arithmetic

It says that the simple rules we all follow do not account for the accumulation of errors in multi-step calculations.

 

[MinnyGophers]

Everyone seems to have their own method. How the hell is this accepted science? I guess I'll just ask my prof what she wants me to do since she is the one who gives me my grades.

This article has some rather interesting comments about significant digits.

http://en.wikipedia.org/wiki/Significance_arithmetic

It says that the simple rules we all follow do not account for the accumulation of errors in multi-step calculations.

Obviously, because if you keep track of sig figs at during each calculations, you're basically rounding off your answers, which will lead to an inaccurate yet correct final answer. Sig figs is basically rounding off.

Everyone has their own method, but most of them are not the correct method. The two rules in my previous posts are the real method. Most people just don't use them and have their way at going at it that is not totally correct.

 

[Haemulon]

This is not really a pre-allo topic. 😕

 

[astrife]

Yes it is. We all must take chemistry as a pre-allo and this is an essential skill for that class.

 

[astrife]

Obviously, because if you keep track of sig figs at during each calculations, you're basically rounding off your answers, which will lead to an inaccurate yet correct final answer. Sig figs is basically rounding off.

Everyone has their own method, but most of them are not the correct method. The two rules in my previous posts are the real method. Most people just don't use them and have their way at going at it that is not totally correct.

My chem book disagrees with your method.

 

[Knickerbocker]

Everyone seems to have their own method. How the hell is this accepted science? I guess I'll just ask my prof what she wants me to do since she is the one who gives me my grades.

Reread my post. At this level, that is how you should be doing it. Other people have given you a lazy method that will work most of the time. But you are right, the real answer is to ask what your professor wants.

 

[Haemulon]

Yes it is. We all must take chemistry as a pre-allo and this is an essential skill for that class.

Well, I don't really care that much, so i'll go with the flow. I just think that if this forum got taken over with discussions of course material and working out problems for physics and stuff like that, then it would be a lot more difficult to get timely info about the application process, interviews, secondaries, and such. But hey, I suppose your right, we all need chemistry to go to med school. And physics, and biology, and calculus for some schools, and even humanities courses for others, so we can make threads talking about all those too. Plus we all need to take the MCAT, so lets lump that in with pre-allo too. Oh yeh, and we should lump in how to choose your undergraduate college too, because we all need to go to college to be pre-allo. And since we are choosing undergrad schools, how about those undergrad application essays and SAT requirements? Which electives should we take in highschool to get into a good school for the best chemistry class to meet the requirements for med school? Does it hurt my chances if I had to take my chemistry SOL's twice in my sophomore year of highschool? I got this one D in chemistry one time on my report card when I was 16 because I could not understand stoichiometry, can we have a thread here to practice stoich. problems?

I know ... i'm being grouchy. Must be the anxiety of waiting for news (and this crummy cold I have now). Someone give me some chicken soup. I have started some pretty unrelated threads on here before too.

 

[astrife]

Well, I don't really care that much, so i'll go with the flow. I just think that if this forum got taken over with discussions of course material and working out problems for physics and stuff like that, then it would be a lot more difficult to get timely info about the application process, interviews, secondaries, and such. But hey, I suppose your right, we all need chemistry to go to med school. And physics, and biology, and calculus for some schools, and even humanities courses for others, so we can make threads talking about all those too. Plus we all need to take the MCAT, so lets lump that in with pre-allo too. Oh yeh, and we should lump in how to choose your undergraduate college too, because we all need to go to college to be pre-allo. And since we are choosing undergrad schools, how about those undergrad application essays and SAT requirements? Which electives should we take in highschool to get into a good school for the best chemistry class to meet the requirements for med school? Does it hurt my chances if I had to take my chemistry SOL's twice in my sophomore year of highschool? I got this one D in chemistry one time on my report card when I was 16 because I could not understand stoichiometry, can we have a thread here to practice stoich. problems?

I know ... i'm being grouchy. Must be the anxiety of waiting for news (and this crummy cold I have now). Someone give me some chicken soup. I have started some pretty unrelated threads on here before too.

As far as I'm concerned the name of this forum is "Pre-Allopathic [MD]" under the section Premedical Forums. It doesn't say "Pre-Allopathic [MD] Students in The Process of Applying", therefore, just because the the forum is dominated by those applying doesn't mean their issues are the exclusive content that can be discussed here.

Sorry just being anal...

 

[MinnyGophers]

My chem book disagrees with your method.

That is how I was taught at my school. So my chem book + prof disagrees with your chem book 😉

I'm sure though that there are different ways of going at it, but you still end up with the same result.

 

[starflower]

Just work out the entire problem without rounding, and write your final answer. After you get your final answer, decide how many sig figs it needs (read the question again) and round your final answer.

 

[MollyMalone]

As far as I'm concerned the name of this forum is "Pre-Allopathic [MD]" under the section Premedical Forums. It doesn't say "Pre-Allopathic [MD] Students in The Process of Applying", therefore, just because the the forum is dominated by those applying doesn't mean their issues are the exclusive content that can be discussed here.

Sorry just being anal...

Actually, technically speaking, Haemulon is correct and this thread is really not appropriate for pre-allo for exactly the reasons cited. This thread in the study question subforum of the MCAT forum would have been the correct place to ask this or any other questions of this nature, and I would ask that in the future you post your questions there.

Thanks!