Question

A rectangular plate has a length of (22.4 ± 0.2) cm and a width of (8.4 ± 0.1) cm. Calculate the area of the plate, including its uncertainty.

Answer 1

Area of the rectangle = Length x Width
We will calculate the percentage of uncertainties.
For a length: p 1 = ( 0.2 · 100 ) : 22.4 = 20 : 22.4 = 0.893
For a width: p 2 = ( 0.1 · 100 ) : 8.4 = 10 : 8.4 = 1.190
p 1 + p 2 = 0.893 + 1.190 = 2.083 %
A = 22.4 · 8.4 = 188.16 +/- 2.083 %
Uncertainty: 188.16 · 0.02083 = 3.92
A = 188.16 +/- 3.92 cm²