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:
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 __
The values can then be entered, and the set-up can become on big fraction:
51.8 ounce x _____1____gram __
And the “ounce” unit cancels and “gram” remains:
51.8 ounce x ______ 1___gram __ = 1480 grams or 1.48 x 10 3 grams
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
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:
This is several pages, but has a handy description of the technique as well as problems:
This worksheet contains some more difficult examples:
One question that is more complicated follows:
- 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)
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:
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.
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!