There are other ways of expressing uncertainty besides significant figures. for example, suppose a quantity is known to have a value between 20.4 and 20.0 and our best estimate of the value is midrange at 20.2. we could write the number as 20.2 +/- 0.2 and say that the number has a 1% uncertainty. we would also say it has 3 significant figures. if we square a number with 1% uncertainty (i. e., 2 parts in about 200) and 3 significant figures, what results? 1 unlocks icon subscribe to course hero to unlock this document unlocks icon subscribe to course hero to unlock this document unlocks icon subscribe to course hero to unlock this document
The answer is : uncertainity is 2% and number of significant figures is 3.
The original number has an uncertainty of 1%
squaring a number is in other words multiplying it by itself.
in case of multiplication or division of two numbers, their PERCENTAGE uncertainties are added.
(this is not to be confused with addition or subtraction of numbers where ABSOLUTE uncertainties are added.)
so the uncertainty of the square will be:
(20*20) +/- (1+1)%= 400 +/- 2%
Also the number of significant figures in a product is the number of significant figures in the original figures. If the number of significant figures is different : 23.8 * 24.65; then the lesser number is the number of significant figures in the product; i.e. 3 in this case.