change units, then . m = . cm = mm = .004700 km Since the last number has trailing zero(s) in a number with no decimal, we would conclude erroneously from observation ( ) above that the number has two significant figures, while in fact, it has four significant figures and a mere change of units cannot change the number of significant figures. ( ) To remove such ambiguities in determining the number of significant figures, the best way is to report every measurement in scientific notation (in the power of ).
In this notation, every number is expressed as a × b , where a is a number between and , and b is any positive or negative exponent (or power) of . In order to get an approximate idea of the number, we may round off the number a to (for a ≤ ) and to (for < a ≤ ). Then the number can be expressed approximately as b in which the exponent (or power) b of is called order of magnitude of the physical quantity. When only an estimate is required, the quantity is of the order of b .
For example, the diameter of the earth ( . × m) is of the order of m with the order of magnitude . The diameter of hydrogen atom ( . × – m) is of the order of – m, with the order of magnitude – .
Thus, the diameter of the earth is orders of magnitude larger than the hydrogen atom. It is often customary to write the decimal after the first digit. Now the confusion mentioned in (a) above disappears : . m = .
× cm = . × mm = . × – km The power of is irrelevant to the determination of significant figures. However, all zeroes appearing in the base number in the scientific notation are significant.
Each number in this case has four significant figures. Thus, in the scientific notation, no confusion arises about the