Estimation and Significant Figures

Dick Trent                               Elk Grove High School
                                         500 W. Elk Grove Blvd.
                                         Elk Grove Village, IL 60007
                                         708-439-4800

Objectives:

(This activity is intended for high school students)
This activity will aid the student in understanding the estimation of 
measurements and the use of significant figures in measurement and calculations. 

Materials needed (for each lab group):

Pieces of construction paper cut to various sizes 
     (possible lengths: 67mm, 27mm, 137mm, 47mm)
Ruler calibrated to millimeters
Ruler calibrated to centimeters
Ruler calibrated to decimeters

Strategy:

     This is a simple activity which is used in the beginning of the year.  It 
can be used in physical science, chemistry or lower level science and math 
classes.  Give each group a package consisting of a group of four pieces of 
paper.  Tell each group to measure the pieces of paper with each of their rulers 
and make a data table which shows paper number and ruler used.  Label this table 
"individual paper table".  The length of the paper should be rounded to the 
nearest marking on the ruler.  Then have the students lay the pieces of paper 
side by side and measure the length of the entire string with each of the rulers 
and make a table labeled "paper string table".  The students should add up the 
length of each individual piece to get a "theoretical" total length using the 
data from "individual paper table" for each separate ruler. 
     Discussion following this activity should focus on the comparison between 
the theoretical total length and the measured total length.  Questions which 
might be posed include "Did the papers change length?" and "When converted to 
meters, what is the relationship between the different rulers?"  The students 
should discuss the principles behind the need for significant figures in order 
to get accurate totals when using measuring devices with different calibrations. 
     An analogy that explains this concept is one with money.  If a person who 
only has dollar bills were to go into a store that does not give change and 
purchase an article that is priced at $0.75, the person would lose $0.25.  If 
the person did this four times, they would have paid $4 for articles worth $3.  
They would have lost a dollar.  This shows how rounding and estimation are 
important concepts to understand.  This also explains why stock prices are given 
to such precision.
     This type of project can be modified for younger students in order to 
display the same concepts of estimation, rounding and significant figures.  The 
rulers can be made out of laminated poster board or pre-made rulers with the 
markings taped over and remarked to the correct units.