A rectangular piece of aluminum is cm long and wide. (a) Find the area of the rectangle and the uncertainty in the area. (b) Verify that the fractional un-certainty in the area is equal to the sum of the fractional uncertainties in the length and in the width. (This is a general result.)

Solution 58P Step 1 : We need to find the area of the rectangle Given Length l = 7.60 ± 0.01 cm Width w = 1.90 ± 0.01 cm Area of rectangle is given by a = l × w Substituting the values we get a = 7.60 cm × 1.90 cm = 14.44 cm a1= 7.61cm × 1.91 cm = 14.5351 cm a2= 7.59cm × 1.89 cm = 14.3451 cm The uncertainty in the area of rectangle is 0.095