Factor Label Method and Metric Conversions
I. Lecture Notes
The Factor Label Method or Dimensional Analysis is one of the most powerful skills you can learn in science. By using the factor label method, you can generate an equation and know that the answer will be correct simply by examining if the end unit that you ended up with was the unit that you desired.
One of the first ways you can use the factor label method is metric conversions. The metric system or also known as Le Système International d'Unités is a measurement based on the powers of ten. The metric system is not only consistent numerically but it is also consistent in terms of nomenclature (naming system) where each prefix translates to a certain power of 10.
In order to convert from one unit to another, you must find the relationship from one unit to another by using the metric ladder. You can use the mnemonic "KING HENRY DOESN'T USUALLY DRINK CHOCOLATE MILK," to remember the steps of the metric ladder from top to bottom.
To find the EQUIVALENT RELATIONSHIP by using the metric ladder follow these steps.
I. FINDING EQUIVALENT METRIC RELATIONSHIPS
Step 1:
Find the two units on the metric ladder
Step 2:
Assign the value of "1" to the unit on the higher step on the metric ladder.
Step 3:
For each step from the lower unit to the
to the higher unit, multiply by the magnitude
of "10" to get calculate how many of the
smaller units makes up the larger unit.
Example:
The units hectoliter (hL) and milliliter (mL)
Example:
1 hL = _________mL
Example:
It takes 5 steps to climb from milliliters (mL) to
hectoliters (hL).
5 steps= (10)(10)(10)(10)(10)
= 10,000
Therefore,
1 hL = 10,000 mL
PRACTICE PROBLEMS FOR FINDING EQUIVALENT METRIC RELATIONSHIPS
Directions: Using the metric ladder, find the equivalent metric values
1) 47 mL = _______dL 10) 55 mg = _________ g
2) 156 g = _______kg 11) 1.27 km = ________m
3) 320 mm = ______ cm 12) .475 L = _______mL
4) .805 kg = ______ dag 13) 5,000, 000 mm = ____ km
5) 1.52 m = _______cm 14) 29,000 m = _______ km
6) 1,000 mL = ______L 15) 46 mm + 27 cm = ____m
7) 3,000 mg = ______ g 16) 5.5 mg + 5 g =_______ g
8) 45, 000 mL = _______ kL 17) 6 L + 6000 mL = ______L
9) .21 L = _______ mL 18) .08 m + 3000 mm=__cm
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II. USING THE FACTOR LABEL METHOD FOR METRIC CONVERSION
Step 1:
Set up the equation for the units you were starting from and the units you want to end up with.
Step 2:
Use the metric ladder to find the equivalent
relationship between the two units. Refer
to the chart above
Step 3:
Convert the equivalent relationship to a
fraction so as to cross cancel out units
when you are multiplying. This will give you
the correct answer with the desired unit.
Example:
.001 hL = _____?_____ mL
Example:
1 hL = 10,000 mL
Example:
.001 hL X 10,000 mL = 100 mL
1 1 hL
VIDEO ON CONVERTING UNITS USING THE FACTOR LABEL METHOD
PRACTICE PROBLEMS FOR USING THE FACTOR LABEL METHOD FOR METRIC CONVERSION
Directions: Using the metric ladder, use the the factor label method to find answers. Show equations for each problem.
1) 35 mL = ___________ dL
2) 950 g = ________ kg
3) 275 mm= _______ cm
4) 1,000 L= ________ kL
5) 1,000 mL = _______ L
6) 4,500 mg = _______ g
7) 25 cm = _______ mm
8) 0.005 kg =______ dag
9) 0.075 m = ______ cm
10) 15 g = ______ mg
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