Dimensional Analysis
Part III.
Unit conversions
with two SI unit
prefixes
Dimensional Analysis III.
Unit Prefixes

Typical problem:
The wavelength of green light is
500nm,what is this in millimeters?
The wavelength of green light is
500nm,what is this in millimeters?

Steps to solve





1. Identify starting units
2. Identify ending units
3. Identify two unit conversion factors that
connects starting and ending units to the
same intermediate unit (usually the base unit)
4. Arrange conversion factors in an equation
so they cancel the starting unit and
intermediate unit, and leave only to the final
unit (No numbers)
5. Put in the numbers and solve the equation
The wavelength of green light is
500nm,what is this in millimeters?

Step 1. Identify starting units
nm (nanometers)
The wavelength of green light is
500nm,what is this in millimeters?

Step 2. Identify ending units
mm (millimeters)
The wavelength of green light is
500nm,what is this in millimeters?

3. Identify two unit conversion factors that
connects starting and ending units to the same
intermediate unit (usually the base unit)
Start
nm (nanometers)
nano
milli
n
m
End
mm (millimeters)
.000000001
.001
10-9
10-3
The wavelength of green light is
500nm,what is this in millimeters?
nano
milli
n
m
.000000001
.001
10-9
10-3
1 nm = 1 nm
1 nm = 1x10-9 m
1 mm = 1 mm
1 mm = 1x10-3 m
The wavelength of green light is
500nm,what is this in millimeters?
4.
Arrange conversion factors in an equation so
they cancel the starting unit and intermediate
unit, and leave only to the final unit (No numbers)
nm
m
nm
mm
m
mm
The wavelength of green light is
500nm, how many meters is this?
Step 5: Put in actual numbers and solve the problem
9
1x10 m
500 nm
1 nm
1 mm
3
1x10 m
500 x10 6 mm
Practice Problems
The next four pages have practice
problems. Work through the problems
and see if you are doing them right
I have a 1.44 MB (megabyte) floppy
disk drive on my computer. How
many Gigabytes of data will it hold?
Step 1: Starting Unit
Mb
(Megabyte)
Step 2: Ending Unit
Gigabyte
Step 3: Unit conversion
Mega(M) = 109
Giga (G) = 1012
1 Mbyte = 1 Mbyte; 1Mbyte=1x109 byte
1 Gbyte = 1 Gbyte; 1 Gbyte=1x1012 byte
Step 4: Equation
Mbyte x (byte/Mbyte) x (Gbyte/byte) = byte
Step 5: Solve
1.44 Mbyte x (1x109 byte/1 Mbyte) x (1Gbyte/1x1012byte)
= 1.44x10-3 Mbyte
How many milliliters (ml) is 16 μL?
Step 1: Starting Units
:l (microliters)
Step 2: Ending Units
millliLiters (mL)
Step 3: Conversion Factor
μ=10-6
m=10-3
1μL =1μL
1 mL=1 mL
1μL =1x10-6 L
1mL = 1x10-3 L
Step 4: Equation
1μL x (L/μL) x (ml/L) = mL
Step 5: Solve
16μL x (1x10-6 L/1μL) x (1ml/1x10-3 L) = 16x10-3 ml
= .016 ml
I am going to hike 56.710 kilometers.
What is this in centimeters?
Step 1: Starting Units
kilometers (km)
Step 2: Ending Units
Centimeters (cm)
Step 3: Conversion Unit
Kilo (k) = 103
1 km = 1 km
1 km = 1x103 m
Step 4: Equation
centi(c) = 10-2
1 cm = 1 cm
1 cm = 1x10-2 m
km x (m/km) x (cm/m) = cm
Step 5: Solve
56.710 km x (1x103 m/1 km) x (1 cm/1x10-2 m)=
56.710 x 10+5 cm
A solution has a concentration of 85
mM. What is the micromolar (μM)
concentration of this solution?
Step 1: Starting Units
mM (micromolar)
Step 2: Ending Units
μM (micromolar)
Step 3: Conversion factor
m(milli) = 10-3
μ(micro) = 1x10-6
1 mM = 1 mM
1μM = 1 μM
1 mM = 1x10-3 M
1μM = 1x10-6 M
Step 4:
Equation
mM x (M/mM) x (μM/M) = μM
Step 5: Solve
85 mM x (1x10-3 M/mM) x (1 μM/1x10-6 M)= 8.5x10+3 M