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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 units
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 12 inches
When you put two things that are equal on top & on bottom, they cancel out and equal 1
= 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!
1 foot 12 inches
= 2.25 feet27 inches
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!
1 foot 12 inches
= 2.25 feet27 inches
Remember…this equals “1”
27 inches 1 = 27 inches Same physical meaning…it’s the same length either way!
1 foot 12 inches
12 inches
Canceling
Anything that is on the top and the bottom of an expression will cancel
When canceling units…just cancel the units…
1 foot 12 inches
27 inches
Unless the numbers cancel as well!
Steps for using Dimensional Analysis
1 Write down your given information
2Write 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.
4Calculate the answer…multiply across the top & divide across the bottom of the expression
Common Equivalents
1 ft 12 in
1 in 2.54 cm
1 min 60 s
1 hr 3600 s
1 quart (qt) 0.946 L
4 pints 1 quart
1 pound (lb) 454 g
=
=
=
=
=
=
=
Example #1
Example:How many grams are equal to
1.25 pounds?
1.25 lb
1 Write down your given information
Example #1
Example:How many grams are equal to
1.25 pounds?
1.25 lb
2Write down an answer blank and the desired unit on the right side of the problem space
= ________ g
Example #1
Example:How many grams are equal to
1.25 pounds?
1.25 lb = ________ g
3 Use equivalents to cancel unwanted unit and get desired unit.
The equivalent with these 2 units is: 1 lb = 454 gA tip is to arrange the units first and then fill in numbers later!
lb
g
Put the unit on bottom that you want to cancel out!
1
454
Example #1
Example:How many grams are equal to
1.25 pounds?
1.25 lb = ________ glb
g
1
454
4Calculate the answer…multiply across the top & divide across the bottom of the expression
Enter into the calculator: 1.25 454 1
568
Metric Prefixes
Metric prefixes can be used to form equivalents as wellFirst, you must know the common metric prefixes used in chemistry
kilo- (k) 1000
deci- (d) 0.1
centi- (c) 0.01
milli- (m) 0.001
micro- (μ) 0.000001
nano (n) 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)
kilo = 1000
There are two options:1 kg = 1000 g1000 kg = 1 g
Example:Write a correct
equivalent between
“kg” and “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)
kilo = 1000
There are two options:1 kg = 1000 g1000 kg = 1 g
Example:Write a correct
equivalent between
“kg” and “g”
“1 kg is kilo-gram”…correct“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
milli = 0.001
There are two options:1 L = 0.001 mL0.001 L = 1 mL
Example:Write a correct
equivalent between “mL” and
“L”
centi = 0.01
There are two options:1 cm = 0.01 m0.01 cm = 1 m
Example:Write a correct
equivalent between “cm” and
“m”
Try More Metric Equivalents
milli = 0.001
There are two options:1 L = 0.001 mL0.001 L = 1 mL
Example:Write a correct
equivalent between “mL” and
“L”
“1 L is milli-mL”…incorrect“milli-liter is 1 mL”…correct
centi = 0.01
There are two options:1 cm = 0.01 m0.01 cm = 1 m
Example:Write a correct
equivalent between “cm” and
“m”
“1 cm is centi-meter”…correct“centi-cm is 1 m”…incorrect
Metric Volume Units
To find the volume of a cube, measure each side and calculate: length width height
length
heig
ht
width
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 = ________ gmg
g
1
0.001
Enter into the calculator: 127.0 0.001 1
0.1270
You want to convert between mg & g“1 mg is 1 milli-g”1 mg = 0.001 g
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 less 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 & kgWith 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”
345 cg = _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
Go to the base unit
g
kg
Go from the base unit
= _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
1
0.01345 cg
g
kg
1000
1
1 cg = 0.01 g1000 g = 1 kg
Remember—the # goes with the base unit & the “1” with the prefix!
= _______ kg
Example #3
Example:How many kilograms
are equal to 345 cg?
cg
g
1
0.01
Enter into the calculator: 345 0.01 1 1 1000
0.00345345 cg g
kg
1000
1
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!
10000.250 kg
Let’s Practice #1
Example:0.250 kg is
equal to how many
grams?
= ______ gkg
g
1
1 kg = 1000 g
Enter into the calculator: 0.250 1000 1
250.
12.78 L
Let’s Practice #2
Example:How many mL is equal to 2.78 L?
= ______ mLL
mL
.001
1 mL = 0.001 L
Enter into the calculator: 2.78 1 0.001
2780
Let’s Practice #3
Example:147 cm3 is equal to
how many liters?
Remember—cm3 is a volume unit, not a length like meters!
= _______ Lcm3
mL
1
1147 cm3
mL
L
1
0.001
There isn’t one direct equivalent1 cm3 = 1 mL1 mL = 0.001 L
Enter into the calculator: 147 1 0.001 1 1
0.147