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

[eurekameh]

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.

 

[gsal]

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.

 

[eurekameh]

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?

 

[cepheid]

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.

 

[jetwaterluffy]

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.

 

[Borek]

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.

 

[Borek]

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?

 

[eurekameh]

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?