Description:

Consider a quantity A = a b where a and b have standard errors σa and σb, then

As subtraction is simply addition with the signs changed, the above also holds for the error in a difference:

Equation should not be confused with equation (2.4) which refers to the mean, not the sum as above.

Uncertainty of a product:

Consider A = (a × b × c) where a, b and c have standard errors σa, σb and σc. The variance

The terms in brackets may be regarded as the relative errors Ra, Rb, Rc giving

Uncertainty of a quotient

Consider A = a/b, then the variance

Uncertainty of powers and roots:
The case for the power of a number must not be confused with the case for multiplication, for example
a³ = a × a × a, with each term being exactly the same.

Thus if A = aⁿ, then the variance

Similarly for roots, if the function is A = a1/n, then the variance

The same approach is adapted to general forms which are combinations of the above.

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