Measured physical quantities are always approximate and cannot be expressed in exact numbers; the difference between the true and the measured values of a quantity is known as error. Error can be negative or positive.
If there is an error ΔL in measurement of any physical value L, then ΔL/L is known as fraction error and ΔL/L*100 is called percentage error.
Combination of Errors
(i) Sum and difference of quantities: x = a ± b
Δx = (Δa + Δb)
(ii) Products and quotients of quantities: x = a * b, x = a/b
For both,Δx/x=(Δa/a+Δb/b)
(iii) Powers of quantities: x =an/bm
=> Inx = nIna - mInb
differentiating dx/x = (nda/a - mdb/b)
For errors, Maximum fractional error in x,Δx/x = n(Δa/a) + m(Δb/b)
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