Is My Physics Teacher Being Inconsistent with Significant Figures?

[Ba]

I just got done taking a test, and one question really was bothering me. My teacher had one problem where there was 20 m/s^2, this is one signifigant digit? Right? Yet last time I gave my answer in one signifigant figure, I got a lecture and told he'ld let me get away with it this time. I ended up not doing it on this test but it really is bothering me. Should I have just done it anyways? I can justify it with the textbook we use and probally somebodies notes of him as well. :grumpy: As it is I circled it, wrote a note, and underlined it darkly several times.

 

[Chi Meson]

A techincality here. Was the quantity written as "20 m/s^2" or "20. m/s^2" (Note the decimal in the second example). The first quantity is ambiguous (could be one or two sigs). The second example has definitely two sigs.

If it was the first way, then your teacher is in error for insisting that there are two sigs. He should have either put the decimal ofter the zero, OR put a line over the zero OR written it as 2 x 10^1 m/s^2.

 

[DaveC426913]

Hm. No that's 2 sigdigs.

1 sigdig would be $$2*10^1$$.

It's the left-side zeros that don't count towards sig digs.

 

[Ba]

No, the zeros behind the decimal places are what doesn't count. Take some long time say 500 million years, this is one signifigant figure.

And yes I know it's a technicality, but it really does bother me. There was no decimal point behind the twenty, I checked. The last time when I got the lecture it was 100 kg, once again no decimal point or indication that all figures were signifigant.

 

[Gza]

I find the whole obsession with sig figs in introductory physics classes to be pretty stupid, IMHO.

 

[franznietzsche]

No, the zeros behind the decimal places are what doesn't count.

That's not correct. 500.00 is 5 sig figs. Behind the decimal place counts. Leading zeros do not count. 500 is technically one sig fig, because there is no decimal.


And yes, the whole idea is idiocy incarnate.

 

[mathlete]

I find the whole obsession with sig figs in introductory physics classes to be pretty stupid, IMHO.

I couldn't agree more. For about 5 years straight we'd start every year off with something on sig-figs. I'm just glad I'm way past that point now. At least I didn't have any professors who were obsessive with it, because I know a lot of them would mark poitns off if your answers were the wrong number of sig-figs which is pretty stupid imo.

 

[JasonRox]

Tell the prof to go **** himself.

 

[cepheid]

Yeah, that's a good idea. Should really help your grade out...

 

[JasonRox]

Yeah, that's a good idea. Should really help your grade out...

That's what I would do.

I'm really close to saying it right now. I'm actually really pissed off at the school right now.

 

[cepheid]

That doesn't mean you should go swear at your prof...cool it man.

 

[BLUE_CHIP]

You think that's obsessive,

My applied teacher requires:

Non-recycled paper
Lined paper
Blue margin
Only two holes punched in the margin
No double banking in your answers (i.e. only 1 ' = ' on each line)
Must be in fountain pen with blue ink
No ink eradicator or erasing fluid

If one of the criteria isn't met then you get ZERO

a wee bit obsessive


(P.S. all answers should be given to 3 significant figures too :tongue2:)

 

[ZapperZ]

I find the whole obsession with sig figs in introductory physics classes to be pretty stupid, IMHO.

It actually isn't THAT stupid if you consider that students tend to cite the whole 10 digit (or more) number that they read off their calculators. The whole pedagogical reason for emphasizing significant figures is to make sure the students are aware of the scale of things and how accurate things are. I have seen even college kids still rattling off a 12-digit number they read off their calculators. This shows a complete lack of "perspective" in knowing the accuracy of things and to what extent certain values can be accepted with confidence.

So yes, these things can appear to be very tedious and rudimentary at this level. But the implication of not emphasizing such things can be hysterical especially when it transcends just physics and into real life applications.

Zz.

 

[Moonbear]

:uhh: Please tell me that's a joke Blue_Chip.

Ba, hopefully your note on the test will be sufficient to show you understand the concept of significant figures. As others have pointed out, at best, the way the number was written leaves ambiguity as to the number of significant digits. If your teacher expects you to be careful of significant digits in your answer, then he/she must be careful in using them to write the question. The best way to eliminate ambiguity is to use scientific notation, as Chi Meson pointed out. That way, it is clear whether the number is meant to be 2 x 10^1 or 2.0 x 10^1.

There's no reason to swear at your profs. They will be more inclined to listen to you and be sympathetic if you talk to them calmly and explain your reasoning showing them the same respect you'd like them to show you. If students come to me to question the way an answer was graded, what I'm really determining is whether they honestly do understand the question and answer and can defend their answer, or if they are just quibbling for points any way they can get them.

 

[cronxeh]

Sig figs are important.

20 m/s is 1 sig fig
20. m/s is 2 sig figs
20.0 is 3 sig figs
20.00 is 4 sig figs
and so on

Sig figs become significant when you start doing calculations
((20 + 30.2) / 4.1) + ((4.56 + 2.1)/5.124) = you'd think answer is 13.54 but it isnt

 

[BLUE_CHIP]

:uhh: Please tell me that's a joke Blue_Chip.

Its about as funny as having to use 4 different colours minimum in a diagram (not felt-tip pens) also a wrong answer immediatly voids all method marks... so by effect one can get the answer right and get the wrong method and get more marks than getting the method right and the answer wrong...

 

[Moonbear]

The whole pedagogical reason for emphasizing significant figures is to make sure the students are aware of the scale of things and how accurate things are.

I just want to lend my support to this explanation. I'm not going to give an example in physics, because I'd probably bungle it, though those experiments probably work more often close to tolerance limits where accounting for the degree of accuracy in your calculations can be the difference between success and disaster.

Instead, I'm going to give an example of why significant digits would be important in another application, so the students can see that it's not just important in physics.

Let's assume you're working in quality control for a pharmaceutical company. That company manufactures a pill that is supposed to contain 200 mg of a drug. Your job is to collect samples of each batch of pills off the assembly line and test them to make sure everything is working correctly and the pills do indeed contain 200 mg of the drug. (Yes, this is a real job that people do, and critical to complying with regulatory agencies to keep pharmaceuticals safe). What degree of accuracy would be acceptable to you in your measurements? If all of your instruments are only accurate to one significant figure and you determine that your batch of pills contains 200 mg of the drug, how confident are you in that dose of drug?

With accuracy to only one significant figure, you might have anywhere between 150 to 250 mg of drug in that pill. That's quite a dose difference. However, if your instruments are all accurate to 3 significant figures, you will have more confidence in that dose being closer to 200 mg (a range of 199.5 to 200.5 mg).

On the other end, as instruments increase in their degree of precision and accuracy, they get more expensive to buy, because they are harder to make. So, if a range of 199.5 to 200.5 mg is sufficiently within safety margins for the drug and you don't need to be accurate to 5 or 10 significant digits, knowing this allows you to purchase equipment that meets your needs without spending an excessive amount on equipment that far exceeds what you need in terms of accuracy.

 

[Norman]

Sig figs are important.

20 m/s is 1 sig fig
20. m/s is 2 sig figs
20.0 is 3 sig figs
20.00 is 4 sig figs
and so on

Sig figs become significant when you start doing calculations
((20 + 30.2) / 4.1) + ((4.56 + 2.1)/5.124) = you'd think answer is 13.54 but it isnt

I know this is pedantic, but couldn't 20 be considered exact since there is no decimal place?

 

[JasonRox]

There's no reason to swear at your profs. They will be more inclined to listen to you and be sympathetic if you talk to them calmly and explain your reasoning showing them the same respect you'd like them to show you. If students come to me to question the way an answer was graded, what I'm really determining is whether they honestly do understand the question and answer and can defend their answer, or if they are just quibbling for points any way they can get them.

My anger is not related to marks on a test. It is because I got dropped from a class (computer program) and might not even get back in because of some damn computer. They also told me that this happens every year, but yet they do **** about it.

Also, I took Calculus II, and so far it feels like Physics. If I wanted Phyiscs, I would have taken Phyiscs. Teach me math dammit.

I'm really angry at the school. Even more angry because they have been dumbing down the courses so bad it's not even funny. They used to teah Spivak's Calculus to first year math majors, but dropped that a few years ago. They used to have Calculus based Introductory Physics, but dropped it 2 years ago. They are currently make changes to the courses to this date, and I wouldn't be surprised if they dumbed it down even more.

Note: The chair knows I have thought about changing school's, and tried to talk to me out of it, but another prof offered a letter of recommendation to avoid doing classes over again (transfer credits).

Note: I have decided to stay for monetary reasons, but I wouldn't be surprised if I stirred up **** in a year or two. They need to clean up their act if they want to get this school somewhere academically.

 

[Moonbear]

My anger is not related to marks on a test. It is because I got dropped from a class (computer program) and might not even get back in because of some damn computer. They also told me that this happens every year, but yet they do **** about it.

That's a problem with administration, not something the profs have control over. Don't blame the prof. There ought to be a way around it though, if you find the right person...sweet talking someone in the registrar's office can often work wonders at resolving such problems (somebody, somewhere must have a way to override computer glitches, it's just a matter of finding that person). My undergrad school used to run into problems like that related to delayed financial aid; the computer would hit a certain date and if the tuition wasn't paid by then, the student got the boot. But, there was always a way to override it, it just took some footwork to get documentation from the financial aid office to the registrar's office, and when all else failed, an appointment with the dean of academic affairs usually got it straightened out with just a phone call or two (I think most people were afraid to mess with her...she came across pretty gruff, though she was actually really helpful). Well, I spent a lot of time in her office anyway, getting over-rides to exceed the maximum credit load, and resolving conflicts between my three different academic advisors (for a while I had four advisors, and all four would give conflicting advice about what to take and what not to take...oh, the fond memories of trying to put together a course schedule ).

Anyway, there's always a way to resolve problems, it just sometimes requires a bit of legwork and staying calm when talking to the right people.

 

[BobG]

You think that's obsessive,

My applied teacher requires:

Non-recycled paper
Lined paper
Blue margin
Only two holes punched in the margin
No double banking in your answers (i.e. only 1 ' = ' on each line)
Must be in fountain pen with blue ink
No ink eradicator or erasing fluid

If one of the criteria isn't met then you get ZERO

a wee bit obsessive


(P.S. all answers should be given to 3 significant figures too :tongue2:)

That's really old school. Quill pens or are mechanical fountain pens acceptable? :rofl:

In the old days, numbers and answers were always given to 3 significant figures, so you didn't have to worry about it.

 

[KingNothing]

Wow, I didn't think such an elementary discussion of sigdigs could appear on this forum.

 

[Moonbear]

I can understand requesting lined paper, no double banking in answers, and no erasing fluid. All of those help keep the work neat and legible. However, I'm having a really hard time with non-recycled paper (geez, let's force students to be irresponsible about the environment), only two holes punched in the margin (I don't think I've ever even seen paper like that), and blue margin (all the lined paper I've seen has blue rulings, but pink margin lines), and why must it be blue ink? I could see requesting blue or black ink, or forbidding red or green, because it gets confusing if you grade with a red ink pen and some nitwit student hands in the assignment done in red ink (then again, when they do that, I just use some even more hideous color for grading...I have an assortment of pens in purple, pink, lime green, etc., just to find the one that clashes most with any strange colors the students wrote in; you really have to try to have some fun with grading).

How would they know if you used a fountain pen? As far as I can tell, fountain pen ink and roller ball ink and gel pen ink all look pretty much the same on paper. Then again, I have a nice calligraphy pen I can loan you...the kind with a nub on the end and you have to keep dipping in ink. Makes for fun blobs and smears to prove you're following the rules. :rofl:

 

[JasonRox]

That's a problem with administration, not something the profs have control over. Don't blame the prof. There ought to be a way around it though, if you find the right person...sweet talking someone in the registrar's office can often work ...

I know and you're right.

It just doesn't end there. Also, my one prof is the chair of the math department. I'm sure he plays a role on what is being taught in the classroom, which isn't math.

He's a pretty good prof overall. I just hate how they sit around and do nothing about it.

Note: I also have another prof who I truly respect and does a lot for the students. He's one of the reasons I am choosing to stay.

Note: I apologize for my attitude because I shouldn't be so rude, but sometimes I just have to let it out.

Note: I also apologize for the poor writing and "typos" in my last post. I try to keep it neat, but the computer at school was really slow and couldn't keep up with my typing. I do not blame the school for this because they have good computers, but that wasn't one of them.

 

[Bartholomew]

Use of sig figs makes for an estimator that is either biased or inefficient.

 

[Moonbear]

Note: I apologize for my attitude because I shouldn't be so rude, but sometimes I just have to let it out.

That's what happens when you forget to use your [rant] tags. It's okay to vent, just try to warn us when that's what you're doing.

Here's the silver lining in case you didn't know there was one. If you learn now how to find the right person to correct problems and learn how to talk to them persuasively so they really help you out, you've learned a valuable lesson in how to deal with people and get things done for when you're out in the working world, where you're going to run into even more incompetent people.

 

[Bartholomew]

Sig figs are stupid, it's like interval estimation only far less reliable.

 

[cepheid]

I know this is pedantic, but couldn't 20 be considered exact since there is no decimal place?

Not if "20" is a measurement that arose from some experiment etc. That's the whole point...you definitely don't know for sure that it is exactly 20...your instruments have some limited precision.

If, on the other hand, it is just the number 20, then fine.

btw...cronxeh...never heard of that convention that: '20' is one sig fig and '20.' is two sig figs. I always thought that '20' was just ambiguous. Never seen '20.' before. hmm...interesting.

 

[misogynisticfeminist]

I find the whole obsession with sig figs in introductory physics classes to be pretty stupid, IMHO.

Taking note of sig. figs. is something like brushing your teeth. A simple task which you can teach any adult. But getting that into HABIT is another matter, and should be taught from young.

But also, i sometimes tend to write all 12 digits from my calculator in any computation (esp. in physics) in all my workings because i find them easier to type than saving them in the memory bank of the calculator. But of course, answers are in the appropriate amt. of sig figs.

 

[cronxeh]

Not if "20" is a measurement that arose from some experiment etc. That's the whole point...you definitely don't know for sure that it is exactly 20...your instruments have some limited precision.

If, on the other hand, it is just the number 20, then fine.

btw...cronxeh...never heard of that convention that: '20' is one sig fig and '20.' is two sig figs. I always thought that '20' was just ambiguous. Never seen '20.' before. hmm...interesting.

True but it brings home the point

It could be 20.1 or 20.2 or 20.3 or 20.4 or it could be 19.5 or 19.6 or 19.7 or 19.8 or 19.9 - all rounded from some other calculation, or even worse - by a program that student writes. Then there is a problem - we can't say if its 19.5 or 20.4 - it just says '20' and not '20.'

 

[BLUE_CHIP]

How would they know if you used a fountain pen? As far as I can tell, fountain pen ink and roller ball ink and gel pen ink all look pretty much the same on paper. Then again, I have a nice calligraphy pen I can loan you...the kind with a nub on the end and you have to keep dipping in ink. Makes for fun blobs and smears to prove you're following the rules. :rofl:

After having done his MSci. in maths, he went on a 2 year calligraphy course... HE KNOWS when you don't follow the creiteria

Ill see if i can get a picture :P

 

[Kamataat]

Also, the number of sigfigs depends on the given tolerance. 20m/s^2 could be one or two (or more sigfigs)...

(20 +/- 10)m/s^2 is 1 sigfig, since the zero only tells you the magnitude of the number and only the first digit contains "relevant data" about the measurement
(20 +/- 1)m/s^2 is 2 sigfigs, since the outcome of the measurement is indicated by both digits, so you need to keep track of both in calculations

- Kamataat

 

[Imparcticle]

Non-recycled paper

wow. my physics teacher is the best environmentalist I've ever seen. He will not let you in his classroom with a disposable cup or disposable anything; he insists it has to be reusable so fewer trees are used. Also, to decrease the number of trees that have to be used to make paper, he makes us e-mail our homework. The only time we use paper in his class is for notes (in which case we must use both sides of paper) which are two or 3 pages long and quizes and tests.

 

[ShawnD]

Your environmentalist teacher is insane. Trees, like corn, are grown on farms. If you need more trees, you simply grow more. Wasting lots of paper is like throwing out a whole ear of corn, of course it's bad, but forcing students to always use both sides is as crazy as eating the corn cob.
Sorry but I had corn on the cob for supper

As for a number like 100, I would interpret that as 3 digits. The general rule is that everything is done for a reason. If you write 5.00, it's because just 5 is not the same. If you write 100, it's because 1x10^2 is not the same.

 

[DaveC426913]

Your environmentalist teacher is insane. Trees, like corn, are grown on farms. If you need more trees, you simply grow more.

Yes, Shawn D is correct. If you need more paper, you just use more land, more equipment, more bleach for processing the paper, dump more toxic byproducts in the water, creating higher banks of foam (ever been within ten miles of a paper mill?) and create more waste heat and toxic gasses.

And when all that runs out - well, they're finding new planets every day!

As for a number like 100, I would interpret that as 3 digits. The general rule is that everything is done for a reason. If you write 5.00, it's because just 5 is not the same. If you write 100, it's because 1x10^2 is not the same.

Yeah, I think that's how most things are handled in the science of mathematics: it's all a matter of interpretation - you know, common sense.