The Factor-Label Method
At the conclusion of our time together, you should be able to:
1. Recognize a problem that can be solved with the factor label method
2. Transform a statement of equality into a conversion factor
3. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found

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A way to solve math problems in chemistry
Used to convert km to miles, m to km, mol to g, g to mol, etc.
To use this we need:
 1) given quantity
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2) desired quantity
3) conversion factors
Conversion factors are valid relationships or equalities expressed as a fraction and equal to one!

Conversion Factors
Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units.
Example: 1 in. = 2.54 cm
Factors: 1 in. and 2.54 cm
2.54 cm 1 in.

Conversion factors for 1 ft = 12 in
1
12 foot inches or
12 inches
1 foot
There are almost an infinite number of conversion factors that include meters:
1000 m
1 km
,
1 m
100 cm
,
1 m
1000 mm
1 m
3.28
feet
,
1 m
39.37
inches
,
0.9144
yards
1 m

Now we are ready to solve problems using the factor label method. The steps involved are:
1.
2.
3.
4.
Write down the given quantity
Determine what conversion factors you will use to turn the given label into the needed label.
1.
2.
Set up the conversion factor
Given unit in the denominator
Desired unit in the numerator
Complete the math

How many kilometers are in 47.0 miles?
(note: 1 km = 0.621 miles)

Now we are ready to solve problems using the factor label method. The steps involved are:
1.
2.
3.
Complete the math with no rounding
Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end
Don ’ t forget the order of operations when you complete the math:
“ Please Excuse My Dear Aunt Sally ” !

How many kilometers are in 47.0 miles?
(note: 1 km = 0.621 miles)
# km = 47.0
x 1 km
0.621
= 75.7 km

The previous problem was not that hard
In other words, you probably could have done it faster using a different method
However, for harder problems the factor label method is easiest

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Steps
1.
2.
1.
2.
Write the given quantity
Set up units in the conversion factor
Larger unit gets a 1
Determine what goes in front of smaller unit
3.
4.
Cancel units
Complete the math

An Easier Way
G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

Converting Metric to Metric
A rattlesnake is 2.44 m long. How long is the snake in cm?

The Factor-Label Method
At the conclusion of our time together, you should be able to:
1. Recognize a problem that can be solved by moving the decimal point.
2. Use the appropriate conversion factor in the correct way so that the labels cancel and the correct conversion is found with two changes of labels or labels that are squared or cubed.

Convert 55.00 km/h to m/s
55.00 km x 1000 m x 1 h___ = h 1 km 3600 s
15.28 m/s

If your pace on a treadmill is 65 meters per minute, what is your rate in km per hour

What about Square and Cubic units?
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Use the conversion factors you already know, but when you square or cube the unit, don ’ t forget to cube the number also!
Best way: Square or cube the Entire conversion factor
Example: Convert 4.3 cm 3 to mm 3
4.3 cm 3
( )
3
=
4.3 cm
1 cm
3 10 3 mm 3
1 3 cm 3
= 4300 mm 3

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A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (DHMO).
How many cubic decimeters is that?

1000 cm 3 ( )
= 1 dm 3
So, a dm 3 is the same as a Liter !
A cm 3 is the same as a milliliter .

Learning Check
A person ’ s blood contains 185 mg of cholesterol per deciliter of blood. How many grams of cholesterol are there in 1 liter of this blood?
A. 0.0185 g
B. 0.185 g
C. 1.85 g
D. 18.5 g
E. 1850 g