Expert: Ahmed Salami - 5/13/2009

Question
The following data resulted from measurements on a rectangle: width = 28 ± 0.5 cm, breadth = 33 ± 0.5 cm. Calculate the area of the rectangle and its uncertainty in cm2:
924 ± 30.5 cm2

hi can you please tell me if my answer is coorect as seen above. And also
Convert 7.1 g/cm3 to kg/m3.
I got 0.71 is this corret?

thanks very much for your help


Answer
Hi Susan,
The area, A = wb
The relative error of A, ΔA is gotten using average errors from
ΔA/A = Δw/w + Δb/b
ΔA = A(Δw/w + Δb/b)
  = b.Δw + w.Δb
  = (33)(0.5) + (28)(0.5)
  = 30.5
A = 28 x 33 = 924
And so your value for A is correct.
A = 924 ± 30.5 cm²


1g = (1/1000)kg
1cm = (1/100)m
1cm^3 = (1/100)m . (1/100)m . (1/100)m
     = (1/1000000)m^3
Therefore,
7.1 g/cm^3 = 7.1 x (1/1000)kg/(1/1000000)m^3
          = 7.1 x 1000kg/m^3
          = 7100 kg/m^3

Regards