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 (online practice is HERE)

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

Coming To America

Periods are Present
 
periods are Absent
Pacific===========>
map
<=========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 each digit. If it is a 0 (zero), ignore it. If it is not a 0, start counting digits until there aren't any left.   Start from the right and examine each digit. If it is a 0 (zero) ignore it. If it isn't a zero, count all the digits.
# of Sig Figs From the examples:
 
# of Sig Figs From the examples:
4, 4, 1, 3
 
1, 2, 4,5

ONLINE Sig Fig Practice is HERE