Sig. Figs. and Averaging: How Many Decimal Places Should I Keep?

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Discussion Overview

The discussion revolves around the appropriate number of significant figures to retain when averaging measurements of pendulum swings taken over three trials. Participants explore the implications of significant figures in the context of experimental measurements, particularly focusing on the precision of counting methods and the representation of uncertainty.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the need to keep decimal places when averaging swing counts, suggesting that the number of swings should be an integer.
  • Another participant argues that the counting method may need to be adjusted, proposing that measuring the time for a fixed number of swings could yield more precise data.
  • Several participants emphasize that significant figures are meant to represent the uncertainty in measurements, with one noting that if the PASCO counter only reports whole numbers, reporting decimals would misrepresent the certainty of the measurement.
  • One participant suggests keeping the average as a recurring decimal or fraction until further calculations are made, proposing to round to two significant figures afterward.
  • There is a discussion about the differing practices between physics and chemistry regarding the use of significant figures, with some participants noting that physicists may prioritize rigorous accuracy over strict adherence to significant figures.
  • Another participant proposes that while the average count can include decimal points, the final results for cycles and period should be reported with specific significant figures based on the context of the measurements.

Areas of Agreement / Disagreement

Participants express differing views on the treatment of significant figures in averaged measurements, with no consensus reached regarding the appropriate number of decimal places to retain. The discussion remains unresolved with multiple competing perspectives on the matter.

Contextual Notes

Participants highlight the importance of understanding the precision of the measuring instrument and the context in which measurements are taken, indicating that the discussion is influenced by the specific characteristics of the PASCO counter and the nature of the measurements being averaged.

eurekameh
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So in lab, I've measured the number of times it takes for a pendulum to swing in 60 seconds. I do this three trials for every change of length. Now, I want to take the average of these numbers, which is the value I get adding them all up and dividing by three. I get a decimal. How many sig. figs. should I keep? It doesn't make sense to keep even one decimal point, but I'm not sure.
 
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why is it not worth keeping decimal places? Are you under the impression that the number of times a pendulum swings in 60 seconds has to always be an integer number? 'cause it isn't ...it's just that you are having a hard time counting the fraction that is there...

maybe you should change the way you are counting...

...instead of counting the number of swings in 60 seconds...maybe you should count, say, 60 swings and record how long it took...THEN, take an average of those times.
 
The lab procedure instructed us to record the number of swings in 60 seconds using a PASCO counter. We did this for three trials. Let's say that I recorded 80, 81, and 80 swings. I want to take the average number of swings. (80+81+80)/3. How many sig. figs do I keep?
 
eurekameh said:
The lab procedure instructed us to record the number of swings in 60 seconds using a PASCO counter. We did this for three trials. Let's say that I recorded 80, 81, and 80 swings. I want to take the average number of swings. (80+81+80)/3. How many sig. figs do I keep?

The whole point of sig figs is to represent the uncertainty in measured values. What's the precision of a "PASCO counter?" If it only reports counts to the nearest whole number, then obviously it makes no sense to report any decimal places, since you would be over-representing the certainty of your measurement.
 
Personally, I would keep it as a recurring decimal or fraction until you actually work out the time period or frequency of the swing, then round it to 2 sig fig.
 
Are you instructed to use significant figures? In my experience they are much more often used in chemistry (and even then mostly in HS), physicists tend to use much more rigorous approach to accuracy of their results.
 
cepheid said:
The whole point of sig figs is to represent the uncertainty in measured values. What's the precision of a "PASCO counter?" If it only reports counts to the nearest whole number, then obviously it makes no sense to report any decimal places, since you would be over-representing the certainty of your measurement.

I think the question was not about expressing the integer result that comes from the counter, but the averaged value from the several trials - if so, decimal points are perfectly OK, as the result should be reported as average±sigma.

Or am I wrong?
 
Borek said:
I think the question was not about expressing the integer result that comes from the counter, but the averaged value from the several trials - if so, decimal points are perfectly OK, as the result should be reported as average±sigma.

Or am I wrong?

I think that I will keep the sig. figs for when I calculate the number of cycles N in 60 seconds, and the period T of the oscillating pendulum, but tabulate the number of average counts C = (C1+C2+C3)/3 and the number of cycles N = (C - 1)/2 to the nearest whole number, but the period T to 4 decimal places, since T = 60.00 / N? Does this make sense?
 

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