AS Physics ISA: Decimal Places Watch

Chris250
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I have to measure the height of a bouncing tennis ball on a horizontal surface, when I record the values, how many decimal places (or significant figures) should I put my initial height to, and how many decimal places should I write my bounce height to?

In my notes, it says two decimal places but I want to confirm that first

EDIT: The height is in metres
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jaroc
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(Original post by Chris250)
I have to measure the height of a bouncing tennis ball on a horizontal surface, when I record the values, how many decimal places (or significant figures) should I put my initial height to, and how many decimal places should I write my bounce height to?

In my notes, it says two decimal places but I want to confirm that first

EDIT: The height is in metres
It depends on your uncertainty. You probably could measure the initial height no more accurately than to 0.5\mathrm{\ cm} and your bounce height up to 1\mathrm{\ cm} (You can estimate the uncertainties to be different).

With the uncertainties proposed above, you could write measured values like this:

h_0=0.810\mathrm{\ m} or h_0=0.815\mathrm{\ m} (if your uncertainty is 0.005\mathrm{\ m}, it's impossible to measure anything between those two values. Which means that in this case you have to write down your measurement with either {0} or 5 as the last figure);

h_n=0.57\mathrm{\ m} There's no point in giving further figures, because the centimeters' place is already not quite certain.
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mmmegan_x
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I did this ISA and we were told to measure to the uncertainty of the ruler, not half the uncertainty because the rules changed.
So we were told to measure the uncertainty to +0.0005m originally but then told only to +0.001m... when you're doing the experiment though it's pretty impossible to figure out where the ball got to anyway let alone measuring to +0.0005m...
So when you're measuring, just write down as many decimal places to the last mm... but ask your teacher before the ISA, as your rules might be different. Good luck!
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Stonebridge
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With a reading taken on a meter rule, the precision of the instrument is usually quoted as either
*the smallest division on the scale (±1mm or ±0.001m)
*half the smallest division on the scale (±0.5mm or ±0.0005m)
depending on which book you read and which examining board you use.
The important point is that ultimately it is your decision as to how clearly you can read the scale with confidence.
For the initial height of the ball, if you are holding it steadily against the ruler before letting go, you can probably measure this to the nearest mm. This is no problem if the height of the ball is around 50cm up to 1m as it represents a % uncertainty of 1mm in 500mm and is going to be 0.2% or less. This is extremely low and will not contribute significantly (if at all) to the errors in the experiment.

Far more critical is the bounce height. If you are doing this by guessing the height using your own eyes, then you cannot measure this height to that level of certainty. You have to estimate with a moving object.
I would put the uncertainty here to be around ±1cm, maybe more. If the bounce height is around 50cm this represents an uncertainty of about 2%.
It is by far the most uncertain measurement and is the one that needs careful consideration.
You should either
*find a more accurate way of measuring it (eg light gates or using photography maybe)
*repeat the measurement 6 or 7 times and find the average and spread of results.

By the way, a 2% uncertainty is not that large.
If you are plotting a graph, then draw error bars representing the uncertainty in the bounce height, and use these to find the spread of best and worst gradient.
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