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Dimensional Analysis II
Beyond Simple Conversion Problems: Identifying the GIVEN andthe DESIREDin Word Problems
Basic Steps in Dimensional Analysis
• Identify the GIVEN value/quantity.
• Identify the DESIRED value/quantity.
• Identify the CONVERSION FACTOR(S).• Set up the problem with the GIVEN first and the DESIRED last--
this will just be a blank space with an attached unit or units.
• Put in “bridging” conversion factors which will cancel units UP/DOWN such that the DESIRED unit(s) will come through un-cancelled.
• Do the math: multiply factors together that are in the numerators and divide by factors that are in the denominators.
Identification Clues• The GIVEN is usually a number all by
itself with no implied equality with something else.
• The DESIRED has a question word associated with it: How many, How much, What is the total cost, etc.
• CONVERSION FACTORS are (1) a pair of numbers with explicit or implicit equality or (2) an explicit “something per something.”
Setting Up the Problem
GIVEN CONV. CONV. CONV. DESIRED
FACTOR
FACTOR
FACTOR
2.000 GALS.
4 QTS.1
LITER1000 mL
1 GAL.1.057 QTS.
LITER
7569 mL
Convert 2.000 gallons to milliliters.
Ruth wanted to raise sheep on 8.1 acres of property. If it takes 0.125 hectare to raise one sheep, how many sheep can be raised on the property. There is one hectare per 2.47 acres.
Given:
Desired:
Conversion(s)
8.1 acres
How many sheep?
0.125 hectare per sheep1.0 hectare per 2.47 acres
Given Conversion Factors Desired
8.1 ÷ 2.47 ÷ 0.125 = 26 sheep
8.1 acres hectare 1 sheep = sheep
2.47 acres
0.125 hectare
A fast food worker wraps 350 hamburgers every hour. He works 8 hours per day. He works 5 days a week. He gets paid every 2
weeks with a salary of $440.34 (after taxes). How many hamburgers will he have to wrap to
make his first one million dollars?
Given:
Desired:
Conversion(s)
$1,000,000
How many hamburgers?
$440.34 per 2 weeks5 days per week8 hours per day350 burgers per hour
Given Conversion(s) Desired
1,000,000 x 2 x 5 x 8 x 350 ÷ 440.34 =
63.6 million hamburgers wrapped
(63,600,000)
$1,000,000 2 wks. 5 days
8 hours
350 HB = HB
$440.34
wk day hour
How many ounces in 54 grams? (There are 16 ounces per 454 g).
16 ounces
454 g
Given:
Desired:
Conversion(s)
54 grams
How many ounces?
16 ounces per 454 g
Given Conversion(s)
Desired54 Grams 16 ounces = ounces
454 grams
54 x 16 ÷ 454 = 1.90 ounces
If you are going 50 miles per hour, how many feet per second are you traveling? (5280 feet per mile). In this problem, the GIVEN looks the same as a CONVERSION FACTOR. It makes it harder to identify!!
5280 Feet
Mile
Given:
Desired:
Conversion(s)
50 miles per hour
How many feet per sec?
5280 feet per mile, and you should know the ones for time.
Given Conversion(s) Desired
50 x 5280 ÷ 60 ÷ 60 = 73.3 Ft per Sec
50 Miles
5280 Ft. Hour Min = Feet
Hour Mile 60 Min 60 Sec Sec