1. 09/24/07
DIMENSIONAL ANALYSIS

2. Objectives
To learn how dimensional analysis can be used to solve problems
To learn to convert from one metric unit to another
To learn to convert between SI units and standard US units
To practice using problem solving techniques

3. A. Tools for Problem Solving
Be systematic
Ask yourself these questions
Where do we want to go?
What do we know?
How do we get there?
Does it make sense?

4. A. Tools for Problem Solving
Converting Units of Measurement
We can convert from one system of units to another by a method called dimensional analysis using conversion factors.
Unit1  conversion factor = Unit2

5. A. Tools for Problem Solving
Converting Units of Measurement
Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems.
Conversion factors are ratios of the two parts of the equivalence statement that relate the two units.

6. A. Tools for Problem Solving
Converting Units of Measure
2.85 cm = ? in cm  conversion factor = ? in. Equivalence statement cm = 1 in. Possible conversion factors
Does this answer make sense?

7. ***THINGS TO REMEMBER when doing Conversions
Take what you are given
-i.e. What is/are my starting unit(s)?
Determine what units want to convert to
-i.e. What is/are the unit(s) I want in my final answer (what are the ending unit(s))?
Find the Equivalence Statement.
-To convert between any units you must have a conversion factor
What is/are the possible conversion factors?

8. ***THINGS TO REMEMBER when doing Conversions cont…
Choose the conversion factor that fits your problem.
Conversion factor should be a ratio.
The unit you want to get rid of should be on the bottom (i.e. in the denominator) to cancel out (or on the top depending on your conversion)
The ending unit should be on the top (i.e. in the numerator)
-The answer should make sense if you got to the right unit(s)
Check you Sig. Figs.
-Remember the EXACT NUMBERS Sig. Figs. Rule???

9. A. Tools for Problem Solving
Tools for Converting from One Unit to Another
Step 1 Find an equivalence statement that relates the units. Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units). Step 3 Multiply the original quantity by the conversion factor. Step 4 Make sure you have the correct number of significant figures.