The Student Room Group

Percentage uncertainties question

I was wondering if I could please have some help with the following question:
A student has a diffraction grating that is marked 3.5 × 10^(-3)
lines per m.
(a) Calculate the percentage uncertainty in the number of lines per metre suggested by this
marking.

The answer is: 2.9%

But according to this answer, the absolute uncertainty is 0.1x10^(-3), however I thought it would be 0.05x10^(-3) because if the number of lines was 3.56x10^(-3), it would have been rounded to 3.6x10^(-3). So was wondering why this is the case. Thanks in advance!
Reply 1
Original post by Felix'sfreckles
I was wondering if I could please have some help with the following question:
A student has a diffraction grating that is marked 3.5 × 10^(-3)
lines per m.
(a) Calculate the percentage uncertainty in the number of lines per metre suggested by this
marking.

The answer is: 2.9%

But according to this answer, the absolute uncertainty is 0.1x10^(-3), however I thought it would be 0.05x10^(-3) because if the number of lines was 3.56x10^(-3), it would have been rounded to 3.6x10^(-3). So was wondering why this is the case. Thanks in advance!


The reason is because when measuring this value, you’d need to use something like a ruler. The nature of rulers and similar instruments is that you’d need to read off two points on the ruler to identify a measurement. Hence, this means you’ve made two readings. Each reading has its own uncertainty (which is what is 0.05 x 10^(-3)) but since there’s two, you add them together and you remain with 0.1 x 10^(-3).
Original post by Haneul_Sol
The reason is because when measuring this value, you’d need to use something like a ruler. The nature of rulers and similar instruments is that you’d need to read off two points on the ruler to identify a measurement. Hence, this means you’ve made two readings. Each reading has its own uncertainty (which is what is 0.05 x 10^(-3)) but since there’s two, you add them together and you remain with 0.1 x 10^(-3).

That makes sense, thank you very much!
Reply 3
Original post by Felix'sfreckles
That makes sense, thank you very much!


No worries!

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