Chapter 6
Day 2
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Dimensional Analysis
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RM Math Dimensional Analysis
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HW: Wkst Dimensional Analysis
Pg. 133 #1 – 6 (Optional)
Algebra I
Chapter 6 Day 2
Dimensional Analysis
Name______________________
Period_____Date_____________
The unit factor or dimensional analysis method is a simple but powerful technique that can be applied to
a great variety of calculation problems. This method makes use of the units (labels) of the quantities involved
as a guide in setting up a calculation. The method is based on the use of conversion factors, and on the idea that
units or dimensions of various quantities can be handles algebraically in the same way as numbers are handled.
Conversion factors are constructed from equalities.
For instance:
2.54 centimeters = 1 inch
1000 grams = 1 kilogram
24 hours = 1 day
We can also write “2.54 cm per in.”
“1000 g / kg”
“24 hrs. /day”
Since the “per” can mean “divided by,” we can write conversion factors:
2.54 cm
1 in.
1000 g
1 kg
24 hr.
1 day
An hour divided by an hour is equal to one, and we say that the units cancel.
1 hr. = 1
1 hr.
Example: How many hours are in 5 days?
1. First write down in algebraic form what is being asked.
? hours = 5 days
2. Hours and days are related by the definition
24 hours = 1 day
3. This equality can be written as 24 hours
1 day
or
1 day
24 hours
4. We would use the first one since we would like the word “day” to “cancel.”
? hours = 5 days ∙ 24 hours
1 day
? hours =
5. If we would have used 1 day
24 hours
? hours = 5 days ∙
we would have had
1 day
24 hours
= 5 day2
24 hr.
The units would have been incorrect and tells us we have chosen the incorrect factor. With a little
patience, the correct conversion factor can be chosen every time. In this case, we want hours for the units of the
answer. Therefore, we put hours in the numerator of the conversion factor. Also, we want “days” to cancel out;
therefore, we put “days” in the denominator. Writing the “? hours” first, serves as a guide to remind you of
what units you want in the result.
When several steps are necessary to carry out the conversion, a “roadmap” is very helpful.
Example:
A football field has a length of 100 yards. What is its length in meters?
We know that 2.54 cm = 1 inch.
1.
2.
3.
4.
First convert the yards to inches,
then convert the inches to centimeters,
and then convert centimeters to meters.
Our roadmap or plan is yards
inches
cm
meters.
1 yd. = 36 in.
? meters = 100 yd. ∙ 36 in. ∙ 2.54 cm ∙ 1 m
1 yd.
1 in.
100cm
0.01 m = 1 cm
? meters =
Example:
Two chemistry classes, having 24 students per class are issued test tubes. If 7 test tubes per student are
given out, what is the number of test tubes issued?
Solution: We write the equivalences from which we construct our plan:
classes
students
tubes
number of test tubes
? no. of test tubes = 2 classes ∙ 24 students ∙ 7 test tubes
1 class
1 student
=
Steps to follow to solve dimensional analysis problems:
1) Write the units of the answer needed.
2) Set this equal to the quantity given with its units multiplied by some conversion factor (s).
3) Multiply the original quantity given by whatever factors are needed to convert its units to the unit
needed. Each factor will be a fraction in which the numerator is equivalent to the denominator.
Ex. #1 How many yards are in 6 feet?
Ex. #2 How many liters are there in 250 ml?
Ex. #3 If you are driving 60 miles / hr., how many feet do you travel in 1 second. ( that is feet/sec.)
Steps: 1) The units needed are feet/sec.
2) Units given are miles/hr.
3) Two conversions must be done
a. miles to feet
b. hrs. to sec.
That is (hrs. to min. to sec.) 3600 sec. = 1 hr.
Ex. #4 Change 6 miles to feet.
Ex. #5 Change 3 miles to inches
Ex. #6 Convert 50 in/sec to ft/hr
Ex #7 Change 30 in/day to ft/week
Ex #8 Change 55 mi/hr to feet/min
Ex #9 Convert 320 yd/hr to ft/min
Ex #10 Arvin wants to put a walkway around his garden made up of slate square tiles. Each side of the tile is 8
inches. The rectangular garden has a length of 12 feet and a width of 8 feet. How many tiles does she
need?
HW. Pg 133 #1 – 6 and worksheet on Dimensional Analysis