Why do Multiplication and Addition Have Different Rules?
When you add two numbers, you add their uncertainties, more or less. If one of the numbers is smaller than the uncertainty of the other, it doesn’t make much of a difference to the value (and hence, uncertainty) of the final result. Thus it is the location of the digits, not the amount of digits that is important. When you multiply two numbers, you more or less multiply the uncertainties. Thus it is the percentage by which you are uncertain that is important — the uncertainty in the number divided by the number itself. This is given roughly by the number of digits, regardless of their placement in terms of powers of ten. Hence the number of digits is what is important. Which Digits are “Significant?” In order to figure out how many significant figures to put into your final answer you must figure out how many significant figures are in each of the numbers you are working with. The rules are best explained separately for fundamental constants, physical constants, numbers not ending in
