1. DIMENSIONAL ANALYSIS
NOTES 6

2. Derived Units
Combinations of SI base units form derived units

3. Quantity sought = Quantity given x Conversion factor
Conversion Problems
Conversion Factors
A ratio derived from the equality between two different units that can be used to convert from one unit to the other
Quantity sought = Quantity given x Conversion factor
100 cm = 1 m or 1 m = 100 cm 100 cm or 1 m
1 m 100cm
1 km = 1000 m or 1000 m = km 1 km or 1000 m
1000m 1 km

4. Deriving Conversion factors
You can derive conversion factors from the known relationship between the unit you have and the unit you want
Operations with Units
Cancellation occurs with the units in the same way that it occurs with numbers common to both the numerator and denominator
a. Units are handled algebraically, just like numbers
b. Analysis of units can be a clue as to whether a problem was set up correctly
Calculations involving units must have the correct units shown throughout the working of the problem and attached to the answer

5. Solving Problems with Dimensional Analysis
Analyze
1. Identify the “given quantity”
2. Identify the “question” – what are you supposed to find?
Plan
1. Develop a plan for solving the problem, using cancellation of units as a guide
Compute
1. Plug in the numbers, perform the required calculations
Evaluate
1. Examine your answer to determine what is reasonable

6. SAMPLE PROBLEMS 1. 0.057 m to km 2. 13 cm3 to mL
hours to seconds
L to mL
5. 86 kg to g
6. 24 cm3 to L
7. 56,000 μg to kg
8. 56 km to mm
Get out your math hat!!
9. 20 km to feet