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Dimensional Analysis
Learning Goal:
To understand how to use dimensional analysis to solve problems.
Dimensional analysis is a useful tool for solving problems that involve unit conversions. By carefully
tracking units and conversion factors, you can avoid many of the errors commonly encountered in chemistry
problems. Dimensional analysis can also help you work through problems when you are not sure where to
begin.
Dimensional analysis involves multiplying a given value by a conversion factor. This results in a value in the
new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one.
For example, dimensional analysis could be used to determine the number of nickels in 3432.35
.
•
To begin, write down the starting value, 3432.35
. This can also be written as a fraction:
.
•
Next, convert dollars to cents. This conversion involves a simple conversion factor:
. Note
that the "dollar" unit should appear on the bottom of this conversion factor, since "dollars" appears
on the top of the starting value.
•
Finally, convert cents to nickels. This conversion also involves a simple conversion factor:
.
This time "cents" should be on the bottom of the conversion factor, since it was on top of the
previous conversion factor.
•
Combining these expressions gives us
•
Finally, cancel units. Since dollars are divided by dollars, and cents are divided by cents, both of
these units can be canceled. Multiplying through gives the final result:
You wash dishes for a chemistry laboratory to make extra money for laundry. You earn 6
, and
each shift lasts 75
. Your laundry requires 6
.
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View Full DocumentPart A
How
many
shifts
must you
work if
you wish
to wash
10
of
laundry?
Hint A.1
How to
approac
h the
problem
Hint not
displaye
d
Hint A.2
Find the
number
of
quarters
require
d
Hint not
displaye
d
Hint A.3
Find the
number
of
dollars
require
d
Hint not
displaye
d
Scientific Notation
Scientific notation can be used to express very large or very small numbers more easily. For example,
In MasteringChemistry, you may enter answers in scientific notation in the following format:
2.998*10^8
5.09*10^6
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View Full DocumentPart A
Convert
the
number
0.000127
to
scientific
notation,
then
enter the
answer
using the
Masterin
gChemis
try
format
.
Express
your
answer
numerica
lly.
ANSWER:
1
.
2
7
×
1
0
−
4
C
o
r
r
e
c
t
Entering scientific notation on a calculator
It is important, especially for exams, that you be able to enter scientific notation in your calculator. All
calculators are different, but look for a button such as
E
,
EE
, or
EXP
. If this button exists on your calculator,
it means "times ten to the" and so
you never actually type the number 10
. For example,
would be entered on a calculator as 2.998 E 8
For entering negative exponents, some calculators require the sign to be entered after the exponent. For
example,
might be entered on a calculator as 5.09 E 6 or as 5.09 E 6
Also note that many calculators have a "change sign" button (
+/
) that should be used for exponents instead
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 Spring '05
 CHEM

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