Using Conversion Factors in Unit Analysis

(Dimensional Analysis)

Problem-solving method that uses the fact that any number or expression can be

multiplied by one without changing its value 1 dozen eggs

or12 eggs

12 eggs 1 dozen eggs

Doing Problems

1. Read problem completely

2. Determine the measured qty. in the problem and the units

3. Determine units being requested

4. Determine conversion factor that will allow you to change to the new unit

We will look at converting:

1. English units 2. English units to Metric Units3. Metric units

Converting from English to English,

• 75 cookies is equivalent to how many dozen cookies?

? dozen = 75 cookies X

1 dozen= 6.25 dozen12

cookies

Series of unit factors – 2 possible formats

Converting English Units

Converting English Units to Metric Units

• How many centimeters are in 6.00 inches?

? cm = 6.00 inches X

2.54 cm= 15.24 cm1 inch

= 15.2 cm

Conversion of Metric Units

Remember the order of the units!

kilo hecto deca Base Unit deci centi milli micro

k h da gram (g) d c m μ

1000 100 10 liter (L) 0.1 0.01 0.001 0.000001

103 102 101 meter (m) 10-1 10-2 10-3

10-4 10-5

10-6

Steps:1. Given quantity w/its unit2. Set up conversion factor

a. Place given unit as the denominator of the conversion factorb. Place desired unit as the numeratorc. Place a “1” in front of the large unitd. Place a 10 in front of the smaller unite. Repeat b-d until reaching the final answer

3. Cancel Units – only the desired unit should be left4. Solve the problem

An aspirin tablet contains 325 mg of active ingredient. How much is this in cg?

325 mg 1 cg = 325 = 32.5 cg1 10 mg 10

= 32.5cg of active ingredient

• Convert 50.0 mL to liters?

50.0mL 1 cL 1 dL 1 L = 50

1 10 mL 10 cL 10 dL 1000

= 0.0500L