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Dimensional Analysis
Converting
REMEMBER THAT:• ***This is a process…even if you
know how to do it another way…DON’T…I am teaching you the process!
• A conversion factor is ALWAYS equal to one
– (because when you divide something by another quantity that is equal to it, it is like dividing that number by itself, which always equals ONE)
Creating Conversion FactorsSTATEMENT EQUALITY CONVERSION FACTORS
There are 60 seconds in a minute. 1 min = 60 s 1 min and 60 s60 s 1 min
There are 100 pennies in a dollar. $1 = 100¢ $1 and 100¢100¢ $1
There are 16 cups in a gallon.
There are 1000 milliliters in a liter.
There are 5280 feet in a mile.
16 1
1 16
cups galand
gal cups
5280 1
1 5280
ft mileand
mile ft
16 cups = 1 gal
1000 mL = 1 L
5280 ft = 1 mile
1000 1
1 1000
mL Land
L mL
NOTICE:
• One of the #’s in the conversion is always 1• Can apply to metric units.• Bigger unit is going to be 1
STATEMENT EQUALITY CONVERSION FACTORS
km to m
g to cg 1g and 100cg100cg 1g
1 km and 1000m1000m 1 km
1 g = 100cg
1 km = 1000 m
Giga Mega kilo hecta deca deci centi milli micro nano
G M k h da d c m n
# MU 1 1 1 1 1 101 102 103 106 109
# base
109 106 103 102 101 1 1 1 1 1
How to use the conversion factors.
• Since conversion factors have a value of 1, when you multiply by them, although the number (and units) may change, the value stays the same, since you’re just multiplying by 1.
Rules
• Set up a grid. (with as many sections as you need)
Rules
• Place # and unit of what you are given in first space of grid.
#unit
Rules
• Place conversion factor with unit you are given on bottom of grid and unit of what you want on top in next space.
#unit conversion unit
facto
want
git nr veuni
Rules
• Repeat step 3 if needed.
# want want
giv
unit conversion unit conversion unit
factor unit factoen gii vr en t nu
Example
• 205 km = ____m
• 4 cg = ____g
STATEMENT EQUALITY CONVERSION FACTORS
km to m 1 km = 1000 m 1 km and 1000m1000m 1 km
g to cg 1 g = 100cg 1g and 100cg100cg 1g
205 1000
1
km m
km
4 1
100
cg g
cg
= 205 000 m
Don’t forget units!
= .04 gDon’t forget units!
Squared and Cubed Unit Conversions
• Sometimes it is necessary to create a conversion factor that involves a squared or cubed unit.
BarrelCubic inchesCubic feetCubic yardsMinimsDrops
Gallons, imperial gallons, quarts, pints, fluid ounces, pecks, bushels
1 gram defined as the mass of one cubic centimeter of water (or one milliliter [mL] of water_.
Liter from Litron:
Measure of capacity
One liter of water has a mass of one kilogram
Example 1: You need a conversion factor that relates square inches (in2) and square feet (ft2).
• How to create the conversion factor: (square the numbers and the units!)
Complex Unit Conversions
A complex unit is one that has both a numerator and a denominator.
To convert complex units, just tackle the units one at a time, but in the same problem.
Example 1: Convert 65 mi/hr to m/s.