Significant Figures

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  • #26
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Re-read what you have written about n and see if there is any sense to be made of it.
There is sense. I just did not say it formally. It is a simple idea. No need to be pedantic.
 
  • #27
Svein
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That is right. So the number of sig figures do not represent the precision, they just add to the precision.
No, they do not add to the precision.

If the larger mass is measured with 12 significant figures - a precision of one part in 1012, I would like to see the measuring device!
 
  • #28
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No, they do not add to the precision.

If the larger mass is measured with 12 significant figures - a precision of one part in 1012, I would like to see the measuring device!
So. In a book it says:
"The uncertainty is just an estimate and it should not be stated with too much precision. For example, instead of saying g = 9.82 +/- 0.02385 m/s2, we should say g = 9.82 +/- 0.02 m/s2 because you cannot know the uncertainty to four significant figures. As a rule, experimental uncertainties should almost always be rounded to one significant figure"

So observe that the author talks about precision and significant figures as they are related and I too believe that. Many authors seem to play with this word precision while talking about significant figures.

What I am asking here is what is the connection between them two more precisely. I know that the precision refers to the repeatability of a measurement. For example, if I measure 4.54, 4.56, 4.55, etc, then I can say that I have a precision of 0.01. And the number of significant figures is 3. If the precision were to be 0.001 then the number of significant figures would have been 4.

It seems to me that the significant figures add to the precision of a measurement. Or I can say that the precision represents the number of significant figures in the decimal places. Exception can be like 0.005, 0.004, etc There is only one significant figure here while the precision is 0.001. But if the precision increases then the number of sign figures also increases. So I can safely say that the significant figures add to the precision of a measurement and just that.

Am I wrong?
 
  • #29
jbriggs444
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Significant figures do not add to precision. They express the precision in a different way.
 
  • #30
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Significant figures do not add to precision. They express the precision in a different way.
I am not saying 'add' in the way that I actually add the number of significant figures with the precision. I'm saying it in a figuratively way.
The more significant figures you have in the decimal places, the more precision you have.

Or is this wrong?
 
  • #31
Svein
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I am not saying 'add' in the way that I actually add the number of significant figures with the precision. I'm saying it in a figuratively way.
The more significant figures you have in the decimal places, the more precision you have.

Or is this wrong?
If the person doing the measurements knows what he/she is doing, the number of significant figures given represents the precision of the measurement. If not (see my earlier anecdote about introducing a lot of figures when converting from one standard to another), the number of "significant" figures are neither significant nor bear any relation to the measurement precision.
 
  • #32
jbriggs444
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I am not saying 'add' in the way that I actually add the number of significant figures with the precision. I'm saying it in a figuratively way.
The more significant figures you have in the decimal places, the more precision you have.

Or is this wrong?
That idea is correct. A better word choice might be "related".
 
  • #33
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Significant figures do not add to precision. They express the precision in a different way.
Ok. I finally understood it. (with the help of the book introduction to error analysis by Taylor)

A measured value with n significant figures means an uncertainty of one unit in the nth significant figure. Sometimes it means a bigger uncertainty, sometimes it means a smaller uncertainty, depending on the situation. But we adopt a middle of the road definition that it is one unit.

An uncertainty of one unit in the nth significant figure means some variable precision depending on the number (here precision is defined as uncertainty/measured value). So for 10, the precision is 10%, while for 99 the precision is 1%. We can say that the precision is roughly 50%.

In general for n sign figures, the precision can vary from 10^(-n+3)% to 10^(-n+2)%.

Thus, there is an approximate correspondence between the number of significant figures (as we defined them) and the precision (as we defined it) given by:
roughly precision [%] = 10^(-n+3)/2 %

PS: Also we adopted the convention that all trailing zeros are significant.
 
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