Factor Label Method and Metric Conversions

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 DRINKCHOCOLATE 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.

FINDING EQUIVALENT 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

After finding the equivalent relationship between units, you can set up a FACTOR LABEL EQUATION to solve for the problem.

SETTING UP A FACTOR LABEL PROBLEM

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

Exercise 1: Metric Conversions

1) 0.20 L = ___________mL 6) 250,000 mm = __________ km

2) 251 cm = __________ m 7) .00056 hg = __________ mg

3) 341 g = ___________ kg 8) 450 mL = _________ daL

4) 40 cg = ___________ mg 9) 589 cm = _________ m

5) 450 mm = ___________ hm 10) .000001 km = _________ cm

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