Suppose I measure the length and width of a rectangle, and get L = 4 +/- 1 m and W = 10 +/- 2m. What is the uncertainty (not fractional uncertainty!) in the area of the rectangle? (recall A = LW)

Step-by-step explanation:

fractional uncertainty, to quantify the precision of a measurement for L and W is

ΔL/L = 1/4 = 0.25 = 25%

ΔW/W = 2/10 = 2/5 = 0.4 = 40%

Now the area of triangle A = L*W = 4*10 = 40m^2

The rules for propagation of error state that when two quantities are multiplied, their fractional uncertainties are added:

So,

ΔA/A = ΔL/L + ΔW/W = 0.25+0.4 = 0.65 =65%

Now we can compute uncertainty in the area, which is

ΔA = A * (ΔA/A) = 40*0.65 = 26%

Finally, we can write the area of the rectangle together with its uncertainty:

A = 40m^2 ± 26%

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