STUDY GUIDE: Sig Figs
Background

Science often involves making detailed measurements. One way that scientists convey how accurate their measurements are is by using significant figures. If a research paper in material science quotes a value of 1.756543 meters for the width of a particular substance, the reader of that journal knows that that substance was measured with an accuracy of 7 significant figures.

Calculations are an every day occurence in science. A particular situation might involve (for example) calculating the area of a round object which involves using a value of П (pi).

For the sake of example, let's choose that item to have a radius of 10.0 meters (3 sig figs). However, to calculate the area of a circular area, we use the formula (pi x radius[squared]).

As you may remember, pi has no known ending value. Conceivably, we could use a value of pi with any number of decimal places. For this example, let's use a value of pi with 20 decimal places.

Squaring that number and multiplying by 10.0, our calculator shows us an answer with 20 (or even more perhaps) decimal place. However, the value we used for the radius contains only 3 sig figs, so showing an answer with 17 more places innaccurately indicates precision far beyond what actually exists.

How to recognize Sig Figs

Perhaps the hardest part to dealing with sig figs is recognizing when to start and when to stop counting numbers. Fortunately, we hav an ideal method to remember how that works. 

The whole thing starts by first examining the number and seeing if a period is either present or absent.  A great way to remember this is the 'Coming to America' method. Image that you can approach America from either the Atlantic or Pacific sides. 

Now substitute the map of America with the number you are working with:

Coming To America

Periods are Present
 
periods are Absent
Pacific===========>
<=========Atlantic
For Example
 
For Example
1.001 | 90.09 | .001| .00100 |
 
1000 | 99 | 1001 | 15,002
The Rule Is:
 
The Rule Is:

Start from the left and examine the first digit. If it is a 0 (zero), ignore it and continue to the first non-zero number.

Once you come to a non-zero number, count each and every digit thereafter, regardless of whether it is a zero or not.

 

Start from the right and examine each digit. If it is a 0 (zero) ignore it and continue to the first non-zero digit.

Once you come to a non-zero number, count each and every digit thereafter, regardless of whether it is a zero or not.

# of Sig Figs From the examples:
 
# of Sig Figs From the examples:
4, 4, 1, 3
 
1, 2, 4,5