1. Chapter 3: Measurement: Dimensional Analysis

2. Objectives Construct conversion factors from equivalent measurements
Apply the techniques of dimensional analysis to a variety of conversion problems
Solve problems by breaking the solution into steps
Convert complex units, using dimensional analysis

3. Conversion factors Conversion factor used in dimensional analysis
ratio of equivalent measurements.
example: 24 hrs = 1 day
They represent the same amount of time but are expressed with different numbers and units
used in dimensional analysis
usually written as a fraction or

4. Units arithmetic Multiplication of units Division of units
add the exponents together
3 m x 2 m = 6 m2
8 cm3 x 2 cm2 x 1 cm = 16 cm6
Division of units
exponents and/or entire units cancel
Addition/subtraction of units
Units don’t change, but must be same before add/subtract
8 mi - 5 mi = 3 mi 2

5. Dimensional analysis Dimensional analysis
way to analyze and solve problems using the units, or dimensions, of the measurements.
form of problem-solving
figure out units it takes to get from start to finish
line up all our conversion factors as fractions and cancel units that appear in both the numerators and denominators.

6. Dimensional analysis practice
Question 1
How many seconds are in 3 weeks?

7. Dimensional analysis practice
Answer 1
Given
3 weeks
? seconds
What We Know
1 week = 7 days
1 day = 24 hr
1 hr = 60 min
1 min = 60 sec
Work

8. Dimensional analysis practice
Question 2
Convert gold’s density (19.3 g/cm3) to kg/m3.

9. Dimensional analysis problems
Answer 2
Given
Gold = 19.3 g/cm3
Gold = ? kg/m3
What We Know
1000 g = 1 kg
100 cm = 1 m
Work

10. Conversion memorization (for now)
US to Metric
1 in = 2.54 cm
454 g = 1 lb
Metric larger
1 megameter (Mm) = 1,000,000 m
1 kilometer (km) = 1000 m
Metric smaller
10 decimeters (dm) = 1 m
100 centimeters (cm) = 1 m
1,000 millimeters (mm) = 1 m
1,000,000 micrometers (µm) = 1 m
1,000,000,000 nanometers (nm) = 1 m