One way to measure the water content of a soil is to weigh the soil both before and after drying it in an oven. The water content is W = (M₁ − M₂)/M₁, where M₁ is the mass before drying and M₂ is the mass after drying. Assume that M₁ = 1.32 ± 0.01 kg and M₂ = 1.04 ± 0.01 kg.

a. Estimate W, and find the uncertainty in the estimate.

b. Which would provide a greater reduction in the uncertainty in W: reducing the uncertainty in M₁ to 0.005 kg or reducing the uncertainty in M₂ to 0.005 kg?