Converting Units
Converting Units
 Often, a measurement is more convenient in one
unit but is needed in another unit for
calculations.
 Dimensional Analysis is a method for converting
unit
You may have learned another method of converting units in
math or previous science classes…trust me…learn this one
now!
It will help you solve many other chemistry problems later in the
class!
Equivalents
Dimensional Analysis uses
equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the
other?
1 foot
12 inches
Equivalents
Dimensional Analysis uses
equivalents…what are they?
1 foot = 12 inches
What happens if you put one on top of the
other?
1 foot
=1
12 inches
When you put two things that
are equal on top & on bottom,
they cancel out and equal 1
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
1
= 27 inches
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
27 inches 
1
= 27 inches
1 foot
= 2.25 feet
12 inches
Dimensional Analysis
 Dimensional analysis is based on the idea that
you can multiply anything by 1 as many times as
you want and you won’t change the physical
meaning of the measurement!
27 inches 
27 inches 
1
= 27 inches
1 foot
= 2.25 feet
12 inches
Same physical
meaning…it’s
the same
length either
way!
Remember…this equals “1”
Canceling
 Anything that is on the top and the bottom of an
expression will cancel
 When canceling units…just cancel the units…
27 inches 
1 foot
12 inches
Unless the numbers cancel as well!
12 inches 
1 foot
12 inches
Steps for using Dimensional Analysis
1
Write down your given information
2
Write down an answer blank and the
desired unit on the right side of the problem
space
3
Use equivalents to cancel unwanted unit
and get desired unit.
4
Calculate the answer…multiply across the
top & divide across the bottom of the
expression
Common Equivalents
1 ft
1 in
1 min
1 hr
1 quart (qt)
4 pints
1 pound (lb)
=
=
=
=
=
=
=
12 in
2.54 cm
60 s
3600 s
0.946 L
1 quart
454 g
Example #1
1
Write down your given information
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb
Example #1
2
Write down an answer blank and the
desired unit on the right side of the problem
space
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb
= ________ g
Example #1
3
Use equivalents to cancel unwanted unit
and get desired unit.
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb

454 g
= ________ g
1 lb
Put the unit on
bottom that you
want to cancel
out!
The equivalent with these 2 units is: 1 lb = 454 g
A tip is to arrange the units first and then fill in numbers later!
Example #1
4
Calculate the answer…multiply across the
top & divide across the bottom of the
expression
Example:
How many
grams are
equal to
1.25
pounds?
1.25 lb

454 g
568
= ________
g
1 lb
Enter into the calculator: 1.25  454  1
Metric Prefixes
 Metric prefixes can be used to form
equivalents as well
 First, you must know the common metric
prefixes used in chemistry
kilo- (k)
deci- (d)
centi- (c)
milli- (m)
micro- (μ)
nano (n)
=
=
=
=
=
=
1000
0.1
0.01
0.001
0.000001
0.000000001
These prefixes
work with any
base unit, such
as grams (g),
liters (L), meters
(m), seconds (s),
etc.
Metric Equivalents
 Many students confuse where to put the
number shown in the previous chart…it
always goes with the base unit (the one
without a prefix)
Example:
Write a
correct
equivalent
between
“kg” and
“g”
kilo = 1000
There are two options:
1 kg = 1000 g
1000 kg = 1 g
To help you write correct equivalents, read the
number that equals the prefix as the prefix itself in
a “sentence”
Metric Equivalents
 Many students confuse where to put the
number shown in the previous chart…it
always goes with the base unit (the one
without a prefix)
Example:
Write a
correct
equivalent
between
“kg” and
“g”
kilo = 1000
There are two options:
1 kg = 1000 g “1 kg is kilo-gram”…correct
1000 kg = 1 g “kilo- kg is 1 gram”…incorrect
To help you write correct equivalents, read the
number that equals the prefix as the prefix itself in
a “sentence”
Try More Metric Equivalents
Example:
Write a
correct
equivalent
between
“mL” and
“L”
Example:
Write a
correct
equivalent
between
“cm” and
“m”
milli = 0.001
There are two options:
1 L = 0.001 mL
0.001 L = 1 mL
centi = 0.01
There are two options:
1 cm = 0.01 m
0.01 cm = 1 m
Try More Metric Equivalents
Example:
Write a
correct
equivalent
between
“mL” and
“L”
Example:
Write a
correct
equivalent
between
“cm” and
“m”
milli = 0.001
There are two options:
1 L = 0.001 mL “1 L is milli-mL”…incorrect
0.001 L = 1 mL “milli-liter is 1 mL”…correct
centi = 0.01
There are two options:
1 cm = 0.01 m “1 cm is centi-meter”…correct
0.01 cm = 1 m “centi-cm is 1 m”…incorrect
Metric Volume Units
height
 To find the volume of a cube, measure each
side and calculate: length  width  height
length
 But most chemicals aren’t nice, neat cubes!
 Therefore, they defined 1 milliliter as equal to
1 cm3 (the volume of a cube with 1 cm as
each side measurement)
1 cm3
=
1 mL
Example #2
Example:
How many
grams are
equal to
127.0 mg?
127.0 mg
= ________ g
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = 0.001 g
Example #2
Example:
How many
grams are
equal to
127.0 mg?
127.0 mg 
0.001 g
0.1270 g
= ________
1 mg
You want to convert between mg & g
“1 mg is 1 milli-g”
1 mg = 0.001 g
Enter into the calculator: 127.0  0.001  1
You may be able to do this in your head…but practice the technique
on the more simple problems so that you’ll be a dimensional
analysis pro for the more difficult problems (like stoichiometry)!
Multi-step problems
 There isn’t always an equivalent that goes
directly from where you are to where you want to
go!
 Rather than trying to determine a new
equivalent, it’s faster to use more than one step
in dimensional analysis!
 This way you have fewer equivalents to
remember and you’ll make mistakes more often
 With multi-step problems, it’s often best to plug
in units first, then go back and do numbers.
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg
= _______ kg
There is no equivalent between cg & kg
With metric units, you can always get to the base unit from any
prefix!
And you can always get to any prefix from the base unit!
You can go from “cg” to “g”
Then you can go from “g” to “kg”
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
g
cg

kg
= _______ kg
g
Go to the base unit
Go from the base unit
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
0.01 g
1 cg
1 cg = 0.01 g
1000 g = 1 kg

1 kg
= _______ kg
1000 g
Remember—the # goes with the
base unit & the “1” with the prefix!
Example #3
Example:
How many
kilograms
are equal to
345 cg?
345 cg 
0.01 g
1 cg

1 kg
0.00345 kg
= _______
1000 g
Enter into the calculator: 345  0.01  1  1  1000
Whenever dividing by more than 1 number, hit the divide key
before EACH number!
It doesn’t matter what order you type this in…you could multiply,
divide, multiply divide if you wanted to!
Let’s Practice #1
Example:
0.250 kg is
equal to
how many
grams?
Let’s Practice #1
Example:
0.250 kg is
equal to
how many
grams?
0.250 kg 
1000 g
1 kg
1 kg = 1000 g
Enter into the calculator: 0.250  1000  1
250. g
= ______
Let’s Practice #2
Example:
How many
mL is equal
to 2.78 L?
Let’s Practice #2
Example:
How many
mL is equal
to 2.78 L?
2.78 L 
1 mL
.001 L
1 mL = 0.001 L
Enter into the calculator: 2.78  1  0.001
2780 mL
= ______
Let’s Practice #3
Example:
147 cm3 is
equal to
how many
liters?
Let’s Practice #3
Remember—cm3 is a volume unit, not a length like meters!
Example:
147 cm3 is
equal to
how many
liters?
147
cm3

1 mL
1 cm3

0.001 L
1 mL
There isn’t one direct equivalent
1 cm3 = 1 mL
1 mL = 0.001 L
Enter into the calculator: 147  1  0.001  1  1
0.147 L
= _______
Let’s Practice #4
Example:
How many
milligrams
are equal to
0.275 kg?
Let’s Practice #4
Example:
How many
milligrams
are equal to
0.275 kg?
0.275 kg 
1000 g
1 kg

1 mg
275,000 mg
= _______
0.001 g
There isn’t one direct equivalent
1 kg = 1000 g
1 mg = 0.001 g
Enter into the calculator: 0.275  1000  1  1  0.001