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# Percentage Uncertainty Watch

1. There's a question of a Physics past paper that makes no sense to me. The worst part is it's the very first question.

"A diffraction grating has 0.0035 lines per metre. Calculate the percentage uncertainty."

I've looked at the mark scheme and worked it out backwards. The way to do it is (100/0.0035)x100, giving 0.29 (the answer on the mark scheme). The thing I'm confused about is where the first 100 comes from. It's either 1 metre, or 1000 millimetres. So why 100??

The only way I've ever been taught to work out uncertainty is to use the resolution of the measuring instrument, but there is no measuring instrument involved.

I know this probably sounds stupid but I really have no idea. Thanks in advance!
2. The grating is defined as having 3.5x10^3 lines per meter so it has a potential error of 0.1x10^3 lines per meter. As it is defined to one decimal place, if it was less than 3.45x10^3 it would have been written as 3.4x10^3 and if was more than 3.55x10^3 it would have been written as 3.6x10^3. So, the measurement can vary between 3.45x10^3 and 3.55x10^3 i.e 0.1x10^3 lines per meter.

The percentage uncertainty is worked out as 0.1x10^3 divided by 3.5x10^3 which would give you 0.029 i.e 3%
3. (Original post by Teenie2)
The grating is defined as having 3.5x10^3 lines per meter so it has a potential error of 0.1x10^3 lines per meter. As it is defined to one decimal place, if it was less than 3.45x10^3 it would have been written as 3.4x10^3 and if was more than 3.55x10^3 it would have been written as 3.6x10^3. So, the measurement can vary between 3.45x10^3 and 3.55x10^3 i.e 0.1x10^3 lines per meter.

The percentage uncertainty is worked out as 0.1x10^3 divided by 3.5x10^3 which would give you 0.029 i.e 3%
Thank you! I knew it would seem obvious once someone mentioned it, I just really couldn't think of it.
This really helped

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