Question

Assume that the uncertainty of each number is +-1 in its last decimal place. Use propagation of error to find the uncertainty of each result.

Please show calculations.

A.) 4.591+0.2309+67.1=71.9219 or 71.9

B.) 313-273.15=39.85=39.8

C.)712x8.6=6123.2=6.1x10^3

D.) 1.43/0.026=55.00 or 55

E.) (8.314x298)/96485=0.02567 or 2.57x10^-2

Answer 1

As the uncertainty of each number is +-1.

A) 4.591+0.2309+67.1=71.9219 or 71.9

      x +y+z = w

where x = 4.591+-1

y =0.2309+-1 , z = 67.1+-1

Using simpler average errors

Dw = Dx + Dy + Dz = 1 + 1 + 1 = 3

w = 71.9+-3

Using standard deviations

w = 71.9+-1.73

B.) 313-273.15=39.85=39.8

      x-y = w

where x = 313+-1

y =273.15+-1

Using simpler average errors

Dw = Dx + Dy = 1 + 1= 2

w = 39.8+-2

Using standard deviations

w = 39.8+-1.4

C) 712x8.6=6123.2=6.1x10^3

     x*y = z

where x =712+-1, y =8.6+-1

Using simpler average errors

z = 6.1x10^3 +-720.6

Using standard deviations

z = 6.1x10^3 +-712.1

D) 1.43/0.026=55.00 or 55

x/y =z

where x =1.43+-1, y =0.026+-1

Using simpler average errors

z = 55+-55

Using standard deviations

z = 55+-2115