dimensional analysis or the factor-label method

The previous blog posts discussed the Metric system, significant figures and reviewed scientific notation.  With this foundation, your students are ready to learn a very important skill, that of dimensional analysis (also known as the factor-label method). 
 
It is a skill the also gets students used to reading measurement units and recognizing the importance of the units to calculate the final answer of any situation -- this is important in the study of Chemistry, and Physics.

 I have viewed some videos showing this method, but I found them to be overly complicated.  I’m going to discuss the approach here and show a few examples.

 Dimensional analysis (or the factor-label method) is a way to convert measurements between systems, along with several unit changes.

A chart for reference is:

Given a value such as 51.8 ounces that need to be converted to grams, I instruct students to set up the initial conversion set-up:


51.8 ounces  x  __________________



where the line the beginning of the conversion factor.


Then enter the units first (the numbers will be entered later):  

51.8 ounce  x  __________gram __
                                        ounce

The values can then be entered, and the set-up can become on big fraction:

 
51.8 ounce  x  _____1____gram __
                                 0.035  ounce
  

And the “ounce” unit cancels and “gram” remains:

  
51.8 ounce  x  ______  1___gram __   =   1480 grams or 1.48 x 10 3 grams
                                 0.035  ounce

  
The conversion values are not considered to be limiting, so the answer would have the same number of significant figures as the beginning value (which has 3 sig figs).


The chart above also contains the equivalence 1 ounce = 28.349 grams,

so the conversion could be set up:  

 
51.8 ounce   x   28.349 grams     =   1470 or  1.47 x 10 3  grams
                                1 ounce

 

Note that the last significant figure is different by one number, and that is the value that is an estimate.

  A few worksheets for the introduction of this topic are:

 
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&sqi=2&ved=0CCMQFjAB&url=http%3A%2F%2Fwww.atlanta.k12.ga.us%2Fsite%2Fhandlers%2Ffiledownload.ashx%3Fmoduleinstanceid%3D9044%26dataid%3D44848%26FileName%3D6%2520Hwk%2520dimensional_analysis_worksheet.pdf&ei=ALoFVLuwCsaxggTpmICYCw&usg=AFQjCNHeRmLD1XWUkDLeO2f-FBkUW152aw&bvm=bv.74115972,d.aWw


http://teacherweb.com/LA/MandevilleHighSchool/Chausse/013.DimensionalAnalysisReview2.pdf


This is several pages, but has a handy description of the technique as well as problems:

http://www.flanaganhighschool.com/files/_gDDgM_/5c3bcc427e96a23b3745a49013852ec4/Dimensional_Anal_Worksheet_001.pdf

 
This worksheet contains some more difficult examples:

http://www.acschools.org/cms/lib07/PA01916405/Centricity/Domain/362/Dimensional%20Analysis%20Worksheet.pdf



One question that is more complicated follows:

1. The painter Raphaeleoeo is said to have worked  at the rate of 1.0 ft2/hour.  Using the factor-label method, calculate his rate expressed in cm2/century?  (10)  (Assume a standard year of 365 days; 100 years = 1 century)
   
   

 1.0 ft 2 x    12 in  x  12 in  x  1 cm            x           1 cm                  
   Hour           1 ft        1 ft        0.3937 in                  0.3937 in   

x  24 hours  x   365 days  x  100 year    =    8.1 x 10 8 cm 2                                            1 day          1 years         1 century            century


Another possibility for dimensional analysis practice is using conversion of currency to various denominations.  The following link contains several worksheets:

 http://www.wasatch.edu/cms/lib/UT01000315/Centricity/Domain/588/Currency%20Conversion%20Worksheets.pdf


You can purchase my lab book "Chemistry on a Budget" through  amazon.com and lulu.com for only $20!  The book contains 13 labs that require consumable materials you can purchase at local stores.
http://www.amazon.com/Chemistry-Budget-Marjorie-R-Heesemann/dp/0578129159/ref=sr_1_1?s=books&ie=UTF8&qid=1389410170&sr=1-1&keywords=chemistry+on+a+budget

Each lab is presented with two possible report formats -- both labs use the same procedure but each has a different conclusion -- one with 10 questions to be answered as a conclusion, the other with a full laboratory report required.  This gives the teacher the option of what type of report is desired.  Each version is designed to be just two pages.  This way the teacher can photocopy just one 2-sided page per student (saves paper).    

I hope your start of the school year is going well!  

I am changing the day of my new blog posts to Friday – this is to give you the entire weekend to read the new post.  My next post will be this Friday, September 5th.  

BTW, I'd love to hear from you with your questions or suggestions for blog topics.

Enjoy the rest of the week!