Does a vernier caliper have doubtful figures?

[Yoseph Santoso]

In measurements, significant figures have certain figures and first doubtful figure. I looked for whether vernier caliper (with 0.01 cm accuracy) have doubtful figure or not, then I found two opinions about it.

The first opinion tells that vernier caliper reading doesn't have doubtful figure because it has vernier scale so we don't need to estimate the next digit after vernier scale. Example : 1.23 cm.

The second, tells that vernier caliper reading must include doubtful figure. If the vernier scale marking line up with main scale marking, the doubtful figure is 0 (Example : 1.230 cm). If the vernier scale doesn't exactly line up with any of the markings (change "phase" between two successive main scale markings), we have to estimate the doubtful figure such as 5 or the other (Example : 1.225 cm).

Please help me explain which opinion is right, the first or the second?

 

[sophiecentaur]

With care you can do better than just looking at the 'nearest' division on the sliding scale. When there is not actually complete coincidence you can estimate where you are, between the two nearest coincidences - e.g half way in between two will give you +0.005 etc.
This all depends on scale linearity, of course.
There is uncertainty involved rather than "accuracy" and there is an awful lot written about it. Your first figure of 1.23cm refers to the nearest coincidence of divisions. There would be extra useful information if you quoted "(+0,+ 0.005)" for instance, when it's definitely one side of coincidence. That's a bit like an extra 1/2bit accuracy for a digital meter when there's jitter.

 

[Yoseph Santoso]

With care you can do better than just looking at the 'nearest' division on the sliding scale. When there is not actually complete coincidence you can estimate where you are, between the two nearest coincidences - e.g half way in between two will give you +0.005 etc.
This all depends on scale linearity, of course.
There is uncertainty involved rather than "accuracy" and there is an awful lot written about it. Your first figure of 1.23cm refers to the nearest coincidence of divisions. There would be extra useful information if you quoted "(+0,+ 0.005)" for instance, when it's definitely one side of coincidence. That's a bit like an extra 1/2bit accuracy for a digital meter when there's jitter.

I would like to say thank you for your response.

I know about uncertainty of measurements. But if the reading of vernier caliper written without uncertainty so how many significant figures of the reading? If we write in 1.23 cm, it has 3 significant figures. If we write in 1.230 cm, it has 4 significant figures. Which one is correct?

 

[phinds]

If we write in 1.23 cm, it has 3 significant figures. If we write in 1.230 cm, it has 4 significant figures. Which one is correct?

Both are correct, but that is terminology and not necessarily a reflection of how accurate a physical device is.

EDIT: To expand on that just a bit, if a device actually has accuracy to 4 significant digits and reads "exactly" 1.2 then it is correctly stated as 1.200 because both zeros ARE significant digits. If a device has only two significant digits of accuracy and reads 1.2 then writing it as 1.200 would imply something that is not true.

 

[sophiecentaur]

IMO, if you read 1.23 then (implied) there is no uncertainty that the value lies between 1.225 and 1.2349. That is the accepted terminology(?). Where the uncertainty is different, I would say that it should be specified with the “+_” notation. In the case of a vernier scale, I’d say an experienced operator could give reliable data that’s tighter than just a specified ‘sig fig’.
Engineering parts can be sorted into bands of all sorts of percentage widths. So no right or wrong - just appropriate.

 

[Cutter Ketch]

I think this can be over complicated. You as the experimenter are telling us what you think you know. If when taking a measurement you look at the scale and you think you can discern the position to something better than what the scale shows, for example even halfway between the markings would count, then your error is less then the last marked digit. You take a guess and write the extra digit. If you really don't feel comfortable that you can tell any more than what the scale says (because perhaps the scale is tiny and your eyes aren't what they used to be) then don't guess an extra digit.

Of course, if you really want to know what your precision is, you should make many independent measurements and see how much your answers vary.

 

[Yoseph Santoso]

Okay thanks for all of your explanations.

Actually my question comes from the Final Test for senior high school in my country (Indonesia). The multiple choices question is :

From the image in attachment, the vernier caliper reading in significant figures rules is ...
A. 4.3 cm
B. 4.30 cm
C. 4.35 cm
D. 4.350 cm
E. 4.3500 cm

I'm confused to choose whether the answer is C or D. Or is it a kind of strange question?

 

[BvU]

the image in attachment

of horrible quality -- partly from the jpg compression, but I suspect the original is poor too. Funny enough the center vertical line is quite sharp and perfectly aligned. From that I deduce your exercise composer expects D to be the correct answer.

The vernier scale as shown is 10 divisions over 9 mm, so alignment occurs every 0.1 mm. But here the aligment is so perfect there is no room for more than 0.02 mm deviation.

Better calipers have 19 mm vernier in 20 divisions, so alignment every 0.05 mm. And the first picture here is even better: 0.02 mm (and they claim it's the normal vernier constant: 99 mm in 50 divisions).

At least their pictures have equal thickness tick marks ...

 

[sophiecentaur]

I'm confused to choose whether the answer is C or D. Or is it a kind of strange question?

I could agree with @BvU but adding a whole extra significant figure implies that you could actually distinguish between 4.350 and 4.351 or any other number of 0.001steps. The gaps between the lines (including the line thickness) are not regular so, despite the theoretical idea of estimating the relative gap sizes as the slider moves from 4.35 to 4.36 might suggest that you could work to another sig fig, you would really need to establish that the scale linearity is at least as good as that suggests.
For a multiple choice question with no discussion, the answer could well be D because you should always be able to do better than the 'nearest / smallest gap'. However, I remember being told, at school, to go for the nearest and take that as the answer as it gives you a reliable extra sig fig to the unaided reading. I would have to ask you what level of discussion have you had in your lessons about this sort of measurement and if it actually relates to using machine tools. I taught A Level Physics (UK) and, with the limited amount of practical experience the students got, I am sure they would find it a real challenge to work to better than the 'nearest' i.e. Answer C

 

[sophiecentaur]

@BvU It looks as though the question could be a dodgy one unless the OP can give us some context about the course he / she is studying. Exam questions are so often of poor quality.

 

[Mister T]

From the image in attachment, the vernier caliper reading in significant figures rules is ...
A. 4.3 cm
B. 4.30 cm
C. 4.35 cm
D. 4.350 cm
E. 4.3500 cm

I'll wager that the exam authors are claiming that D is the right answer.

There's no doubt the reading is between 4.349 and 4.351, and it's closer to 4.350 than it is to either 4.349 or 4.351.

 

[Yoseph Santoso]

First of all, forgive me if my question is lacking in detail.

Allow me to confirm what I have learned from this thread.

Because the poor of the question and we are forced to choose one answer, if the line of main scale and vernier scale is perfectly aligned, the answer should be D. If the vernier scale line "seen" aligned with one main scale line, we "forced" to choose C as the answer because we can't guarantee the 0.001 cm steps (no doubtful figure).

Is my understanding correct?

 

[Cutter Ketch]

First of all, forgive me if my question is lacking in detail.

Allow me to confirm what I have learned from this thread.

Because the poor of the question and we are forced to choose one answer, if the line of main scale and vernier scale is perfectly aligned, the answer should be D. If the vernier scale line "seen" aligned with one main scale line, we "forced" to choose C as the answer because we can't guarantee the 0.001 cm steps (no doubtful figure).

Is my understanding correct?

Just to be clear, being perfectly aligned does not affect the precision of the measurement or whether or not you should guess an extra digit.

I believe what others are saying is that being perfectly aligned is a clue as to what the person who constructed this problem had in mind. The perfect alignment suggests that they may not have even considered the possibility that you could tell when a vernier is aligned between readings and so could justify guessing an extra digit. I’m pretty sure they expect you to answer C.

 

[sophiecentaur]

they may not have even considered the possibility

Haha - dead right!

 

[Yoseph Santoso]

Okay, let me confirm again. Since there is no uncertainty in the multiple choice, so the safest answer is C. But the better answer is (4.350 +- 0.005) cm. Am I correct?

 

[sophiecentaur]

Okay, let me confirm again. Since there is no uncertainty in the multiple choice, so the safest answer is C. But the better answer is (4.350 +- 0.005) cm. Am I correct?

Nearer a best answer (somewhere between C and D, I reckon) but not one of the options, I'm afraid. At least we can say that you have been forced to think about this problem - so it's been a worthwhile exercise for you, whatever.

 

[Mister T]

The thing about a test is that to earn credit you have to provide the answer that the test authors say is correct. They don't always get it right, and many times the question itself is poorly written. I would say that in this case they did a poor job of drawing the figure.

I'm sticking with what I said in Post #11.

 

[gmax137]

I would unhesitatingly put down "C" (4.35 cm). I don't guess at in between values, but that may be because I am used to inch scale verniers, where the marks are closer together, and read down to 0.001 inch (0.0025 cm). Measurements with calipers are unlikely to be more accurate than that, due to variation in angle between the blades and the object, variation in applied pressure, parallax in reading the marks, etc.

Even so, the comments about interpreting what the test author was thinking are valid. Has the class material previous to the test discussed verniers, how they work and how to use them? If not, then this is a crappy test question.

 

[Yoseph Santoso]

significant figures have certain figures and first doubtful figure.

Okay, from this thread I learned to be careful in applying definition of significant figures, to estimate extra digit as doubtful figure we must include uncertainty. Is it right?

 

[Mister T]

Okay, from this thread I learned to be careful in applying definition of significant figures, to estimate extra digit as doubtful figure we must include uncertainty. Is it right?

The extra digit that you estimate can be stated without including the uncertainty, but when you do that you are leaving out some useful information. On the other hand, when you do state the uncertainty you provide extra information that can be useful.

 

[Cutter Ketch]

Okay, from this thread I learned to be careful in applying definition of significant figures, to estimate extra digit as doubtful figure we must include uncertainty. Is it right?

That extra digit by its inclusion makes a statement about your uncertainty. You are saying that you at least know something more than the last indicated digit. How much more is unclear unless you also state an uncertainty.

However, that situation is not unique to doubtful digits. The whole concept of significant figures is a loose imprecise way to state and propagate uncertainty. The least significant digit says your uncertainty is greater than one and less than 10 in that digit. It’s a very rough statement of uncertainty, but it’s better than nothing.

 

[Yoseph Santoso]

Okay, now allow me to reconfirm my early post:

Does a vernier caliper have doubtful figure?
My answer is yes, but written or not depends on the condition.

The first opinion tells that vernier caliper reading doesn't have doubtful figure because it has vernier scale so we don't need to estimate the next digit after vernier scale. Example : 1.23 cm.

The second, tells that vernier caliper reading must include doubtful figure. If the vernier scale marking line up with main scale marking, the doubtful figure is 0 (Example : 1.230 cm). If the vernier scale doesn't exactly line up with any of the markings, we have to estimate the doubtful figure (Example : 1.225 cm).

Either first or second opinion above become a kind of method that can be used depends on the condition.

 

[Cutter Ketch]

Okay, now allow me to reconfirm my early post:

Does a vernier caliper have doubtful figure?
My answer is yes, but written or not depends on the condition.
Either first or second opinion above become a kind of method that can be used depends on the condition.

I think you’ve got it. I wouldn’t necessarily say it depends on the condition. If you can tell better than the vernier scale (and you almost always can) then really you should write another digit. When I say C is probably the right answer I’m trying to get inside the head of the person who wrote the question, and I’m guessing they weren’t considering the possibility of an extra digit and didn’t think about it as carefully as you are.

 

[Yoseph Santoso]

Okay, thank you physics teachers forum who has patiently taught me

 

[Merlin3189]

Just two points:
Disagree with "correct answer". In my experience exams want the "best answer", aka "least worst answer".
(May not help here, since people say c or d is best. I say c because it's the tightest answer I'm sure of and d is only maybe.)

The second point is just my personal, cynical view on measurements in general.

Don't try to do better than maker claims (here 4.35) then ask, how reliable is that and maybe downgrade it!
If the instruction is to read the third figure by noting which vernier division mark lines up closest, then they're allowing for play/backlash/error (which must exist) so long as users don't try to get smart.
Then wonder about temperature sensitivity, or how long since it was last checked, or does it make a difference if there's a big steel chassis on the bench next to me,etc.
Digital instruments with 4 digits, claiming +/- 0.5% +/- 2 counts makes the last digit almost superfluous. Is it worth guessing an extra digit when it flickers? What is the tolerance on components inside 6 digit devices?

You can invent or imagine more figures, but are they, or even the ones you didn't have to guess, significant and do you have confidence in them?