In the Classroom

www.JCE.DivCHED.org • Vol. 82 No. 10 October 2005 • Journal of Chemical Education 1507

Understanding and properly manipulating significantfigures, while normally tackled early in a chemistry course,can present a lasting challenge. Many students will likely learnthe rules by rote, but not necessarily understand the ratio-nale and meaning. Some useful approaches have appeared inthis Journal to assist students with the uncertainty of mea-surements and the necessity of significant figures throughexercises (1) and activities (2). Herein is an alternative, re-quiring little preparation and no equipment, that allows stu-dents to intuitively discover and discuss the uncertainty ofmeasurements and conversion factors and the necessity of sig-nificant figures. By allowing students to study new conceptswith familiar topics such as age, they will be more comfort-able later applying these concepts to unfamiliar chemicalmeasurements.

The Activity

In class, students are simply asked about a particular fa-mous person and how many days old he or she is. The in-structor will need to prepare for class by calculating an accurateanswer. This is readily done by finding the Julian dates forthe current date and the birth date in question and subtract-ing. The Julian Day Count is a count of days since noon ofJanuary 1, 4713 BCE and is frequently used by those whoare interested in determining time spans for cyclic events. Thissystem avoids the confusion associated with months of dif-ferent numbers of days and leap years. The Julian date (JD)is available through Internet sources (3) or print materials (4).

The activity starts with no given information about theage of the person in question and progresses with increasinginformation leading to increasingly precise age estimations.Students will recognize that a person’s age is a measured value,and this estimation is only as precise as the measuring de-vice. They intuitively become aware of error in the estima-tion of the age in years as well as the conversion to age indays. As the age in years is known with increasing precision,

the calculated age in days may be expressed with increasingprecision.

Example and Discussion

A person who is familiar to everyone must be selectedto use as a class example. Using George W. Bush as an ex-ample in 2004, students might estimate based on his appear-ance that he is 60 years old. This immediately opens adiscussion of how many significant figures are in 60. My classwill generally agree that it is 1 significant figure, meaningthe actual value is between 50 and 70 years. Therefore, sig-nificant figure rules allow us to report the age in days to 1significant figure. This allows us to state that he is 20,000days old (60 years × 365.25 days�year = 21,915 days), orconfidently between 10,000 and 30,000 days old. Most stu-dents will agree that we can not state that he is definitelybetween 21,914 and 21,916 days old as the calculator an-swer might suggest.

George W. Bush was born on July 6, 1946, which wasapproximately Julian date 2,432,008.1 For a class discussionheld September 1, 2004 (JD 2,453,250), Mr. Bush wouldbe approximately 21,242 days old or 58.157 years. The in-structor could use this value to reveal an increasingly preciseage in years (i.e., one more decimal place for each successivecalculation) for Mr. Bush to allow students to calculate theage in days with increasing precision as outlined in Table 1.

I find that at some point the discussion will turn to theconversion factor relating days and years, thus opening up adiscussion of exact versus inexact values. The typical studentwill recognize that a leap day every fourth year will result inan average length of year of 365.25 days. Some students mayrecognize that there are exceptions whereby a particular“fourth year” does not have a leap day (such as the years 1700,1800, and 1900, which are common years and not leap years)resulting in a long term average of 365.24219 solar days pertropical year (5). Once one recognizes that every fourth year

Teaching Significant Figures Using Age ConversionsThomas D. CruteDepartment of Chemistry and Physics, Augusta State University, Augusta, GA 30904; tcrute@aug.edu

Applications and Analogiesedited by

Arthur M. LastUniversity College of the Fraser Valley

Abbotsford, BC, Canada

4002,1rebmetpeSnohsuB.WegroeGfoegA.1elbaTsraeYniseulaVesicerPylgnisaercnImorfsnoisrevnoCnodesaB

dedivorPnoitamrofnI syad/egAfoyalpsiDrotaluclaC syad/egAdetropeR tnacifingiSserugiF

01x6 1 )ecnaraeppanodesab(dlosraey 519,12=52.563x06 000,02 1

)6491ninrob(dlosraey85 5.481,12=52.563x85 000,12 2

)6491yluJninrob(dlosraey2.85 55.752,12=52.563x2.85 003,12 3

sraey61.85 49.242,12=52.563x61.85 042,12 4

sraey751.85 48.142,12=52.563x751.85 242,12 5

In the Classroom

1508 Journal of Chemical Education • Vol. 82 No. 10 October 2005 • www.JCE.DivCHED.org

of George W. Bush’s life has been a leap year, one can use365.25 days�year as a reasonable conversion.

Analysis of all the calculations in Table 1 reveals thatnone of them are wrong according to the precision reportedby significant figure rules. For instance a value of 58.2 yearsis provided to the students in the third entry of Table 1, andalthough Bush is not 21,300 days old, he is between 21,200and 21,400 days as implied by a three significant figure value.Extended discussions might underscore the propagation ofrounding errors such as using a value of 365 days�year as aconversion factor. Students might be asked how to determinesomeone’s age more exactly, including having students specu-late whether any two people can be exactly the same age. Thisdiscussion ought to lead to the conclusion that while twopeople might be born on the same date, they are not born atthe same instant once one considers the birth time to an ap-propriate number of significant figures.

Followup Activities

A useful assignment would have students select a famousperson, research the birth date, and perform their own seriesof calculations as was done in class. More sophisticated stu-dents might be asked to contemplate the limitations of sig-nificant figures by, for instance, calculating the percent errorfor the age in years versus the age in days. More specificallystudents can discover that the range suggested by 2 signifi-

cant figure value in years (58 years ±1 year is a 2-year range)is a smaller range than the range suggested by a 2 significantfigure value in days (21,000 days ±1000 days is a 2000 dayrange or greater than a 5-year range). This discussion willhelp highlight both the strengths and weaknesses of usingsignificant figure rules to express uncertainty.

Notes

1. Obviously greater precision of this Julian date is availablefrom knowing the hour of birth and thereby including fractionaldays in the Julian date.

Literature Cited

1. Pacer, R. A. J. Chem. Educ. 2000, 77, 1435.2. Kirksey, H. G. J. Chem. Educ. 1992, 69, 497.3. Julian Date Converter. http://aa.usno.navy.mil/data/docs/

JulianDate.html. Welch, Doug. Calendar Date to Julian DateCalculator. http://wwwmacho.mcmaster.ca/JAVA/JD.html. JulianDate Converters. http://onlineconverters.com/calendars.html (allaccessed Jun 2005).

4. The Astronomical Almanac for the Year 2003; U.S. GovernmentPrinting Office: Washington, DC, 2001; p B4.

5. CRC Handbook of Chemistry and Physics, 65th ed.; Weast, R.C., Astle, M. J., Beyer, W. H., Eds; CRC Press: Boca Raton,FL, 1984; p F-319.