Chapter 1 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 AnalysisMethod of calculation using a conversion factor.

* ALWAYS place the #1 in front of the largest unit.!

inches

footor

foot

inches

footinches

12

11

1

121

112

Chapter 1 3

Dimensional AnalysisExample: We want to convert the distance 8 in.

to feet. (12in = 1 ft)

in

ftin

12

18

Chapter 1 4

Dimensional AnalysisExample: We want to convert the distance 8 in.

to feet. (12in = 1 ft)

ftin

ftin 67.0

12

18

Chapter 1 5

Dimensional AnalysisConvert 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)

Or100 cm = 1 m109 nm = 1 m

Chapter 1 6

Dimensional AnalysisConvert the quantity from 2.3 x 10-8 cm to

nanometers (nm)100 cm =1 m

1 x 109 nm = 1 mNow, we need to setup the equation where the

cm cancels and nm is left.

m

nm

cm

mcm8103.2

Chapter 1 7

Dimensional AnalysisConvert the quantity from 2.3 x 10-8 cm to

nanometers (nm)1 cm = 0.01 m

1 x 10-9 m = 1 nmNow, fill-in the value that corresponds with the

unit and solve the equation.

m

nm

cm

mcm

1

10

100

1103.2

98

Chapter 1 8

Dimensional Analysis

Convert the quantity from 2.3 x 10-8 cm to nanometers (nm)

nmm

nm

cm

mcm 23.0

1

10

10

1103.2

9

28

Chapter 1 9

Dimensional AnalysisConvert 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)

Or1 mile = 1.6 km1000m = 1 km

Chapter 1 10

Dimensional AnalysisConvert 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

km

m

mi

kmmi 2820,31

Chapter 1 11

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”.

22

2820,31km

m

mi

kmmi

Chapter 1 12

Dimensional AnalysisConvert the quantity from 31,820 mi2 cm to

square meters (m2)

22

2

1

1000

1

6093.1820,31

km

m

mi

kmmi

Chapter 1 13

Dimensional AnalysisConvert the quantity from 31,820 mi2 cm to

square meters (m2)

2

26

2

22

1

101

1

5898.2820,31

km

m

mi

kmmi

Chapter 1 14

Dimensional AnalysisConvert the quantity from 31,820 mi2 cm to

square meters (m2)

2102

26

2

22 102407.8

1

101

1

5898.2820,31 m

km

m

mi

kmmi

Chapter 1 15

Dimensional AnalysisConvert 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)

Or1 mile = 1.6 km 1000m = 1 km

60 sec = 1 min 60 min = 1 hr

Chapter 1 16

Dimensional AnalysisConvert the quantity from 14 m/s cm to miles

per hour (mi/hr).

1 mile = 1.6093 km 1000m = 1 km60 sec = 1 min 60 min = 1 hr

hr

min

min

s

km

mi

m

km/14 sm

Chapter 1 17

Dimensional AnalysisConvert the quantity from 14 m/s cm to miles

per hour (mi/hr).

1 mile = 1.6 km 1000m = 1 km60 sec = 1 min 60 min = 1 hr

hr1

min60

min1

s60

km6.1

mi1

m1000

km1/14 sm

Chapter 1 18

Dimensional Analysis

Convert the quantity from 14 m/s cm to miles per hour (mi/hr).

1 mile = 1.6093 km 1000m = 1 km60 sec = 1 min 60 min = 1 hr

hrmi

sm

/31

hr1

min60

min1

s60

km6093.1

mi1

m1000

km1/14