Dimensional Analysis
Part II.
Unit conversions
involving SI unit
prefixes
Dimensional Analysis II.
Unit Prefixes

Typical problem:
The wavelength of green light is
500nm, how many meters is this?
The wavelength of green light is
500nm, how many meters is this?

Steps to solve





1. Identify starting units
2. Identify ending units
3. Identify unit conversion factor that
connects starting and ending units (you may
need more than one)
4. Arrange conversion factor in an equation so
it cancels the starting unit and changes it to
the final unit (No numbers)
5. Put in the numbers and solve the equation
The wavelength of green light is
500nm, how many meters is this?

Step 1. Identify starting units
nm (nanometers)
The wavelength of green light is
500nm, how many meters is this?

Step 2. Identify ending units
m (meters)
The wavelength of green light is
500nm, how many meters is this?

Step3. Identify unit conversion factor that connects
starting and ending units (you may need more than one)
Start
nm (nanometers)
End
m (meters)
Look at Table 1.2 on page 9 of your text (Next slide)
The wavelength of green light is
500nm, how many meters is this?
giga
mega
kilo
centi
milli
micro
nano
G
M
k
c
m
μ
n
1,000,000,000
1,000,000
1,000
.01
.001
.000001
.000000001
109
106
103
10-2
10-3
10-6
10-9
These are the prefixes I expect you to have
memorized for my class. If you are taking a
class from another instructor, check with that
instructor for the prefixes you should memorize.
The wavelength of green light is
500nm, how many meters is this?
giga
mega
kilo
centi
milli
micro
nano
G
M
k
c
m
μ
n
1,000,000,000
1,000,000
1,000
.01
.001
.000001
.000000001
109
106
103
10-2
10-3
10-6
10-9
You can see the unit you need to use in this
Problem has to do with nano or 10-9
The wavelength of green light is
500nm, how many meters is this?
nano
n
.000000001
10-9
Problem has to do with nano or 10-9
But here is where most people mess up.
How do you use this factor?
1 nanometer = 1x10-9 meters
-or1x10-9 nanometer = 1 meter
The wavelength of green light is
500nm, how many meters is this?
1 nanometer = 1x10-9 meters
-or1x10-9 nanometer = 1 meter
The way I keep this straight is that I write
the unit with the prefix = unit with prefix, I.E.
1 nm=1 nm
Then I substitute the multiplier for one of the prefixes
1 nm=1x10-9 m
so this is step 3, our conversion factor:
1 nanometer = 1x10-9 meters
The wavelength of green light is
500nm, how many meters is this?
Step 4: Set up a conversion equation that
cancels the starting units and
leaves only the ending units
nm x m/nm = m right!
nm x nm/m = (nmxnm) /m wrong
The wavelength of green light is
500nm, how many meters is this?
Step 5: Put in actual numbers and solve the
Problem:
500 nm x (1x10-9 m/nm) = 500x10-9 m
Practice Problems
The next four pages have practice
problems. Work your way through step by
step and see if you are doing them right.
I have a 40 gigabyte hard drive on my
computer. How many bytes of data
will it hold?
Step 1: Starting Unit
Gigabyte
Step 2: Ending Unit
Byte
Step 3: Unit conversion
giga (G) = 1012
1 gigabyte = 1 gigabyte
1 gigabyte = 1x1012
byte
Step 4: Equation
Gigabyte x (byte/gigabyte) = byte
Step 5: Solve
40 Gbyte x (1x1012 byte/1 Gbyte) = 40x1012 bytes
How many liters is 16 μL?
Step 1: Starting Units
μL
Step 2: Ending Units
Liters (L)
Step 3: Conversion Factor
μ=10-6
1μL =1μL
1μL =1x10-6 L
Step 4: Equation
1μL x (L/μL) = L
Step 5: Solve
16μL x (1x10-6 L/1μL) = 16x10-6 L
I am going to hike 56,710 meters.
What is this in kilometers?
Step 1: Starting Units
Meters
Step 2: Ending Units
Kilometers
Step 3: Conversion Unit
Kilo (k) = 103
1 km = 1 km
1 km = 1x103 m
Step 4: Equation
Meters x (km/m)
Step 5: Solve
56,710 m x (1 km/103 m) = 56.71 km
A solution has a concentration of 85
mM. What is the Molar (M)
concentration of this solution?
Step 1: Starting Units
mM (micromolar)
Step 2: Ending Units
M (Molar)
Step 3: Conversion factor
m(milli) = 10-3
1 mM = 1 mM
1 mM = 1x10-3
M
Step 4: Equation
mM x (M/mM)
Step 5: Solve
85 mM x (1x10-3 M/mM) = 8.5x10-2 M