Significant figures in practical investigation report

  • #1
winkyinky146
2
0

Homework Statement


I am writing a prac report regarding Hooke's Law, and am uncertain how many significant figures I should write my results in in my results table. I have heard that in my prac report, I must keep my significant figures consistent, that is, all data measured by the same device should have the same number of significant figures.
My masses were pre-measured and inscribed on the weights themselves. The spring extension was measured with a centimeter ruler, and 1mm was the smallest increment.

Homework Equations


I have data similar to this:
Mass (g)__Ave. Extension (cm) ___Uncertainty (cm)
50________2.1_________________0.05
100_______6.8_________________0.2
150 _____ 11.8________________ etc.
200 ______16.7_________________

The Attempt at a Solution


As shown above, the significant figures are inconsistent, but I'm not sure how to make them consistent. For the masses for example, I can't just add a ".0" to the end of "50" for example, to make "50.0" in order to make the number of significant figures 3, in line with the rest of the masses, as that would increase the accuracy of the measurement. Like wise with the extension, the smallest increment was 1mm, so I can't just add a "0" to "2.1" to make "2.10" for the number of significant figures to fit with "11.8" and "16.7". As for the uncertainty, I have no idea what to do with it. I was taught that uncertainty for analogue devices was plus or minus half the smallest increment. So for the ruler it would be 0.05cm. This only has one significant figure however, do I need to change this at all?
Thanks! Any help would really be appreciated!
 

Answers and Replies

  • #2
Janosh89
61
19
In Physics experiments, it is usual to give readings taken to decimal places. If you want to give Extension ( in cm ??)
to 2 decimal places - I would suggest truncating/ rounding down to 1 dec. place - you have to have read extension to 3
decimal places, which you haven't
Mass / Kg _ Average extension/m _Uncertainty/m
0.0500 _________0.0205 ___________+/- 0.0005
 
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  • #3
winkyinky146
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In Physics experiments, it is usual to give readings taken to decimal places. If you want to give Extension ( in cm ??)
to 2 decimal places - I would suggest truncating/ rounding down to 1 dec. place - you have to have read extension to 3
decimal places, which you haven't
Mass / Kg _ Average extension/m _Uncertainty/m
0.0500 _________0.0205 ___________+/- 0.0005
So basically I don't need to keep the significant figures consistent, but I should keep the decimal places consistent? And also I should use SI units?
 
  • #4
36,167
13,154
I must keep my significant figures consistent, that is, all data measured by the same device should have the same number of significant figures.
That would be wrong. Your ruler can't measure 5 mm with more than one significant figure, but it certainly can do so for 50 mm. The absolute uncertainty is the same, the relative uncertainty is not.
I was taught that uncertainty for analogue devices was plus or minus half the smallest increment. So for the ruler it would be 0.05cm.
That is usually a reasonable estimate.
This only has one significant figure however
It is the uncertainty. More than one significant figure for an uncertainty rarely makes sense.

Don't focus on significant figures here. Look at the absolute uncertainties, that is much more useful.
 
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  • #5
Janosh89
61
19
I auto-corrected the extension - of course, the extension could have been 2.15cm!
 

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