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lucaz
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#1
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Hi, I was wondering if anyone could give me some help on how to work out percentage errors, how to work out how many sif. figs to put, uncertanties etc. Thanks. BTW I have my exam in 2 days times so as much help as possible would be apprechiated!!!
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Goddess
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When physical quantities are added or substracted, errors of observation are always added.
Eg:
L = 10.64 +/- 0.01 cm
b = 4.46 +/- 0.01 cm
t = 1.98 +/- 0.01 cm
L + b + t = (10.64 + 4.46 + 1.98) cm +/- 0.03 cm = 17.08 +/-0.03 cm
L - b + t = (10.64 - 4.46 + 1.98) cm +/- 0.03 cm = 8.16 +/-0.03 cm

When physical quantities are multiplyed or devided, percentage errors of measured are added.
Eg:
L = 10.64 +/- 0.01 cm
b = 4.46 +/- 0.01 cm
t = 1.98 +/- 0.01 cm
Percentage uncertainty of L = (0.01/10.64) x 100 = 0.09%
Percentage uncertainty of b = (0.01/4.46) x 100 = 0.22%
Percentage uncertainty of L = (0.01/1.98) x 100 = 0.50%
L x b x t = (10.64 x 4.46 x 1.98) cm3 +/-(0.09 + 0.22 + 0.50)% = 93.96 cm3 +/-0.81% = 93.96 cm3 +/-0.76cm3
L / (b x t) = 10.64 /(4.46 x 1.98) cm-1 +/-(0.09 + 0.22 + 0.50)% = 1.20 cm-1 +/-0.81% = 1.20 cm-1 +/-0.0097cm-1

When physical quantities are squared, cubed, ..... etc, percentage errors of measured quantities are doubled, trebled, ..... etc.
Eg:
I'm sorry I can't give an example because I can't type powers. If you need more clarification, PM me.
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Tindo
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You can type powers by 3^2 meaning 3 squared.
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nepali_babu
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yea do it dat way..bt wteva uve already done is greatly appreciated. thnx man!!!
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Taxy
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#5
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(Original post by Goddess)
When physical quantities are added or substracted, errors of observation are always added.
Eg:
L = 10.64 +/- 0.01 cm
b = 4.46 +/- 0.01 cm
t = 1.98 +/- 0.01 cm
L + b + t = (10.64 + 4.46 + 1.98) cm +/- 0.03 cm = 17.08 +/-0.03 cm
L - b + t = (10.64 - 4.46 + 1.98) cm +/- 0.03 cm = 8.16 +/-0.03 cm

When physical quantities are multiplyed or devided, percentage errors of measured are added.
Eg:
L = 10.64 +/- 0.01 cm
b = 4.46 +/- 0.01 cm
t = 1.98 +/- 0.01 cm
Percentage uncertainty of L = (0.01/10.64) x 100 = 0.09%
Percentage uncertainty of b = (0.01/4.46) x 100 = 0.22%
Percentage uncertainty of L = (0.01/1.98) x 100 = 0.50%
L x b x t = (10.64 x 4.46 x 1.98) cm3 +/-(0.09 + 0.22 + 0.50)% = 93.96 cm3 +/-0.81% = 93.96 cm3 +/-0.76cm3
L / (b x t) = 10.64 /(4.46 x 1.98) cm-1 +/-(0.09 + 0.22 + 0.50)% = 1.20 cm-1 +/-0.81% = 1.20 cm-1 +/-0.0097cm-1

When physical quantities are squared, cubed, ..... etc, percentage errors of measured quantities are doubled, trebled, ..... etc.
Eg:
I'm sorry I can't give an example because I can't type powers. If you need more clarification, PM me.
Wow that's a lot of work! Must have taken you a lot of time to type.
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Goddess
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This is what the NAS AS and A2 Revision Guide (for Edexcel) says about percentage uncertainties:

* Only work out uncertainties if and where the question tells you to do so, therefore for most of your measurements you won't have to bother with uncertainties.

* For a single measurement take the smallest division of the instrument as its uncertainty e.g. a length might be 19 + 1 mm using a meter rule and 18.8 + 0.1 mmusing vernier callipers.

* Practice finding percentage uncertainties (equation given in test); e.g. 5.3% and 0.53% for above lengths.

* For a set of repeated readings take half the spread of the readings as the uncertainty of the average value e.g. 1.25, 1.29, 1.28, and 1.26 mm giving a spread of 0.04 mm so average value = 1.27 + 0.02 mm with a percentage uncertainty of 1.6%.

* For measurements, such as starting and stopping a timer, where your own error adds significantly to the uncertainty, always take several measurements and use their range to get the uncertainty.

* Add the uncertainties of any measurements that are either added or substracted.

* Add the percentage uncertainties of any measurements that are multiplyed or devided.

* Multiply the percentage uncertainty by any powers to which the measurement is raised e.g. percentage error in r^3 is 3 x percentage uncertainty in r.

* Use 100 x difference/average value to calculate the percentage difference between two values.
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mackin boi
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#7
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Sfteeeeeee
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Economist
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#8
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For those taking the A2 edexcel practical tomorrow this is from the specification:

'Candidates should take repeat readings whenever it is reasonable to do so, in which case the
percentage uncertainty should be based on the spread of the readings. The estimated uncertainty
is then half the spread.
If it only possible to take one reading, then the percentage uncertainty should be based on the
precision with which the scale can be read. The estimated uncertainty in this case is half of one
scale division.'
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