Help with uncertainties

[Conspicuous]

I did a Physics lab in which I measured the height of the first bounce of a ball. I used a motion sensor to calculate it, so the uncertainty was really small: the smallest value it could measure was 0.0001, so the uncertainty would be 0.0001/2 = ±0.00005 (<--that's 5 decimal places). However, the values I got are, for example, 0.6798 (<--- that's 4 decimal places).

In order to get a good mark in the 'data collection & processing' criteria, the values cannot have less or more d.p than the uncertainties. So how do I manage those uncertainties? For example, I can't write down '0.6798 ± 0.00005' because the decimal places don't match.

I thought maybe about using scientific notation, but in a table it would look weird. For example, 0.6798 ± 5.0000 x 10^-4, because it still needs the same amount of decimal places.

Any help is very much appreciated. Thank you in advance!

[Keel]

I did a Physics lab in which I measured the height of the first bounce of a ball. I used a motion sensor to calculate it, so the uncertainty was really small: the smallest value it could measure was 0.0001, so the uncertainty would be 0.0001/2 = ±0.00005 (<--that's 5 decimal places). However, the values I got are, for example, 0.6798 (<--- that's 4 decimal places).

In order to get a good mark in the 'data collection & processing' criteria, the values cannot have less or more d.p than the uncertainties. So how do I manage those uncertainties? For example, I can't write down '0.6798 ± 0.00005' because the decimal places don't match.

I thought maybe about using scientific notation, but in a table it would look weird. For example, 0.6798 ± 5.0000 x 10^-4, because it still needs the same amount of decimal places.

Any help is very much appreciated. Thank you in advance!

'0.67980 ± 0.00005' would be correct notation.

Have a look at the uncertainties section for more info:

[Chronofox]

After using a motion sensor to acquire the velocity-time graph of a cart, I opened up the graph in logger pro and saw that the uncertainty of each value of velocity was ± 0.001 (three significant digits). However, after linearizing the graph, the slope had an uncertainty of ± 0.0001 (four significant digits) which as presented by loggerpro. So in this case, do I put acceleration down as having ± 0.001 uncertainty or ± 0.0001?

Edited November 5, 2011 by Chronofox

[Ezeh]

That's very strange... If that's what it gives you - then use that and possibly mention it somewhere in your write up. Alternatively you can calculate the individual uncertainties of each data point by adding the percentage uncertainties of the time and velocity.

[DeBrogliez]

Well, as far as I know, when using a digital device, the uncertainty would be the smallest value it could measure (without dividing by two!).

However, if you are using a ruler or anything that has to be measured normally, then the uncertainty is the smallest division over two.

Therefore, in this case, you don't have to divide 0.0001 by two; since you are using a motion sensor which is digital. Meaning that you can write 0.6798 ± 0.0001, and there you have consistent decimals.

[Sabs44]

You can use this tool, I find it amazing

http://ibsurvival.com/uncertainties/index.php