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Help with Calculating Uncertainties

1. Homework Statement

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).

2. Homework Equations

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.

3. The Attempt at a Solution

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!
 

PeterO

Homework Helper
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1. Homework Statement

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).

2. Homework Equations

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.

3. The Attempt at a Solution

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!
While not actually solving the problem you see ....
I presume that you bounced the ball more than once - did more than one trial.

The uncertainty in a measured result usually include an instrument error [to what precision does the instrument work] plus a "reapeatability" uncertainty - how much variation did you get when you measured the same event several times.
Indeed, you may choose to repeat the experiment 10 times, then "ignore" the outliers as perhaps influenced the falling ball on release unexpectedly.
I would expect your repeatability error to be far larger than the precision of the instrument you were using.

While the instrument may measure to ±0.0005, the repeatability error may be as bad as ±0.03.
 

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