Significant and Insignificant Figures
Your instructors are not fanatic about significant figures, but we do agree on a few things:
1) Do not quote your answer with a zillion significant figures unless they really are significant. That is, if the problem is stated in quantities having only two significant figures, your answer ought not to have eight or nine significant figures. Two or three figures ought to do the job.
2) Never, never, never make the following error: 1.5 x 105 – 1.5 x 102 = 1.4985 x 105 . The correct value for that subtraction is 1.5 x 105.
3) DonÕt get carried away with the previous instruction. Suppose we consider the planet earth, whose radius is 4,000 miles. If an exploding asteroid deposits a 1-inch thick layer on the surface of the earth, it is true that the earthÕs radius is still 4,000 miles. However, if you are asked, ŌBy how much has the earthÕs volume increased?Ķ the answer is not zero. Rather, you need to find the volume of a spherical shell whose radius is 4,000 miles and whose thickness is one inch.
4) Carry enough (or more than enough) significant figures through your calculations. IÕve noticed a lot of students punching just one or two significant figures into their calculators, when they ought to be working with at least three. This sometimes happens because they have written down intermediate results and then re-entered (parts of ) those numbers, instead of using the numbers that are sitting in their calculatorsÕ memories. We especially donÕt want you to do this, and then to quote your answer to three significant figures.
5) ItÕs almost always best to figure out your final answer in symbolic terms before plugging the first number into your calculator. ItÕs amazing how often this requires many fewer calculations, thus reducing your chances of messing up and getting the wrong number.
6)
Finally, most of the time, you can use three significant
figures and keep us pretty happy.