Question

A well-known rule states that when two numbers are multiplied together, the answer will be reliable if rounded to the number of significant figures is the less precise of the original two numbers.(a) Using our rule (2.28) and that fact that significant figures correspond roughly to fractional uncertainties, prove that this rule is approximately valid. (To be definite, treat the case that the less precise number has two significant figures.) (b) show by example that the answer can actually be somewhat less precise than the "well-known" rule suggests. (esp true, several #s multiplied together)