1. Dimensional Analysis
In dimensional analysis always ask three questions:
What data are we given?
What quantity do we need?
What conversion factors are available to take us from what we are given to what we need?
Chapter 1

2. Dimensional Analysis Method of calculation using a conversion factor.
* ALWAYS place the #1 in front of the largest unit.!
Chapter 1

3. Example: We want to convert the distance 8 in. to feet.
Dimensional Analysis
Example: We want to convert the distance 8 in. to feet.
(12in = 1 ft)
Chapter 1

4. Example: We want to convert the distance 8 in. to feet.
Dimensional Analysis
Example: We want to convert the distance 8 in. to feet.
(12in = 1 ft)
Chapter 1

5. Dimensional Analysis
Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
First we will need to determine the conversion factors
Centimeter (cm)  Meter (m)
Meter (m)  Nanometer (nm) Or
100 cm = 1 m
109 nm = 1 m
Chapter 1

6. Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
Dimensional Analysis
Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
100 cm =1 m
1 x 109 nm = 1 m
Now, we need to setup the equation where the cm cancels and nm is left.
Chapter 1

7. Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
Dimensional Analysis
Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
1 cm = 0.01 m
1 x 10-9 m = 1 nm
Now, fill-in the value that corresponds with the unit and solve the equation.
Chapter 1

8. Dimensional Analysis
Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)
Chapter 1

9. Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
First we will need to determine the conversion factors
Mile (mi)  Meter (m)
Meter (m)  kilometer (km) Or
1 mile = 1.6 km
1000m = 1 km
Chapter 1

10. Convert the quantity from 31,820 mi2 cm to square meters (m2)
Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
Now, we need to setup the equation where the cm cancels and nm is left.
1 mile = 1.6 km 1000m = 1 km
Chapter 1

11. Convert the quantity from 31,820 mi2 cm to square meters (m2)
Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
Now, we need to setup the equation where the cm cancels and nm is left.
1 mile = 1.6 km 1000m = 1 km
Notice, that the units do not cancel, each conversion factor must be “squared”.
Chapter 1

12. Convert the quantity from 31,820 mi2 cm to square meters (m2)
Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
Chapter 1

13. Convert the quantity from 31,820 mi2 cm to square meters (m2)
Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
Chapter 1

14. Convert the quantity from 31,820 mi2 cm to square meters (m2)
Dimensional Analysis
Convert the quantity from 31,820 mi2 cm to square meters (m2)
Chapter 1

15. Dimensional Analysis
Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
Determine the conversion factors
Meter (m)  Kilometer (km) Kilometer(km)  Mile(mi)
Seconds (s)  Minutes (min) Minutes(min)  Hours (hr) Or
1 mile = 1.6 km 1000m = 1 km
60 sec = 1 min 60 min = 1 hr
Chapter 1

16. Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
Dimensional Analysis
Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
1 mile = km 1000m = 1 km
60 sec = 1 min 60 min = 1 hr
Chapter 1

17. Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
Dimensional Analysis
Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
1 mile = 1.6 km 1000m = 1 km
60 sec = 1 min 60 min = 1 hr
Chapter 1

18. Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
Dimensional Analysis
Convert the quantity from 14 m/s cm to miles per hour (mi/hr).
1 mile = km 1000m = 1 km
60 sec = 1 min 60 min = 1 hr
Chapter 1