here i needed help in this to work out the unceertainty step by step
There are at least 2 methods of computing it.
Method 1:
uncertainty = ½ × (maximum value – minimum value)
This is a method that will work for A level physics and you should know. I say it will work provided that you do thing correctly.
Δ(L1)=21×(L−ΔL1−L+ΔL1)
For example, when L = (54.5 ± 0.5) × 10-2 m,
Δ(L1)=21×((54.5−0.5)×10−21−(54.5+0.5)×10−21)
Δ(L1)=0.0168
Method 2: Assume that you know the following rule:
c=ba
cΔc=aΔa+bΔb
Let a = 1 and b = L in c=ba,
cΔc=1Δ1+LΔL
cΔc=0+LΔL
cΔc=LΔL
Note that c=L1,
Δc=LΔL×c
Δc=LΔL×L1
Δ(L1)=L2ΔL
Using method 2 for when L = (54.5 ± 0.5) × 10-2 m,
Δ(L1)=(54.5×10−2)20.5×10−2
Δ(L1)=0.0168
I did not round to the correct significant figures for the uncertainty. Rounding to how many significant figures for the uncertainty is something you should know.
Both methods give the same answer for the uncertainty. Note that you can use a more sophisticated method and the uncertainty may be smaller but it is ok.