How do you calculate percentage uncertainty?

Answer 1

If the uncertainty is not written on the measuring instrument then you must estimate it yourself.

Take half of the final certainty to which you can read the instrument. If you can read the instrument to 12.5 mm then the uncertainty is 0.25 mm. However, it makes no sense to have 0.25 as a two decimal point uncertainty, so in this case the uncertainty would be taken as 0.3 mm.

Length = 12.5 ± 0.3 mm

Answer 2

Resistivity is given by measuring the resistance (R) of your material, multiplied by its cross-sectional area (A) and divided by its length (L).

Your uncertainty is mostly due to how well you can measure (A), (L) and (R). For example, if your multimeter can only measure resistance to an accuracy of 1 decimal place, then your systematic uncertainty of (R) will be +/- 0.1 (eg. if you measured R =10.2 Ohms, you don't really know if it was 10.2Ω, 10.23Ω or 10.29999Ω)

The same is true for your length and area measurements. You have to know how accurately you are able to measure with the tools you have.

Additionally, the measurement of the resistance, no matter how accurate, has experimental uncertainties. The temperature of the material will change its resistance. So you must include an experimental uncertainty on this effect.

Typically, you will then quote your systematic uncertainties in quadrature (syst uncertainty = sqrt( (+/-R) ^2 + (+/- A)^2 + (+/-L)^2), and your experimental uncertainties separately and also in quadrature.

You can often reduce some of your uncertainties by making many measurements on 'as close to identical' samples as possible, reducing what it called 'statistical uncertainty'.

Answer 3

It's just the uncertainty over the actual number multiplied by 100

36.1 (+/- 0.1)

Percentage of uncertainty here is 0.1 / 36.1 x 100= 0.3%

Answer 4

Its hard to write down but here it is.

Delta X delta P is equal to or greater than the Planck's constant over 2.

see Heisenberg's Uncertainty Principle.