Transcript dimensional analysis

Dimensional Analysis
Homework
Objectives
• Be able to convert between units using
dimensional analysis
Dimensional Analysis
• A VERY helpful skill in science, and one
that will get especially helpful in chemistry
and physics… Dimensional Analysis
 It will also be another way of converting
prefixes that some of you may prefer to
hopping the decimal place
• This will take PRACTICE to master
Dimensional Analysis
• Dimensional analysis is a method of
converting a measurement from one unit to
another
• Example: How many seconds is 2 hours?
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Dimensional Analysis
• First and most important in any
dimensional analysis problem
 1. Identify the unit your measurement is
already in, and identify the unit you want your
measurement to end up in.
• Example: Measurement is already in hours. We
want it in seconds.
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Dimensional Analysis
• 2. If you don’t know how many of your starting
unit directly equals your ending unit, make a
chain.
 I don’t know off the top of my head how many seconds
are in an hour, for instance. But I know how many
seconds are in a minute, and how many minutes are
in an hour. Ex: Hours -> Minutes -> Seconds will be
my chain.
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Dimensional Analysis
3. Begin your chain with your starting
measurement Write it as a fraction with a
denominator of 1.
 Ex: 2 hrs
1
NOTE: IT IS SUPER SUPER IMPORTANT WHEN
DOING THESE PROBLEMS TO ALWAYS WRITE
YOUR UNITS.
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Dimensional Analysis
• 4. The next fraction in your chain will be an
“equivalence.” The top of the fraction equals the
bottom.
 Ex: It will be 60 min
1 hr
or
1 hr
60 min
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Dimensional Analysis
• 5. Write the fraction so that it will “criss-cross”:
the bottom will have the same unit as the
previous fraction’s top did.
 Ex: We will choose 60 min
1 hr
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Dimensional Analysis
• 6. Repeat steps 4-5 until you reach an
equivalence that includes your ending unit.
 Ex: The next and last equivalence will be 60 sec
1 min
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Dimensional Analysis
• Choose the step seven that you prefer. EITHER:
• 7. Your answer will be this division: (All the top numbers
multiplied together)/(All the bottom numbers multiplied
together) and your final unit.
 Ex: (2 x 60 x 60)/(1 x 1 x 1) sec = 7200 sec
OR
• 7. Do each division one at a time, and multiply them as
you go along.
 Ex: (2/1) x (60/1) x (60/1) sec = 2 x 60 x 60 sec = 7200 sec
Dimensional Analysis
• 8. Round your final answer to the same number
of sig figs as your starting measurement.
 Ex: 2 hours has 1 sig fig. 7200 seconds -> 7000
seconds.
Dimensional Analysis
• Another, shorter example:
• How many seconds are in five minutes?
Before we write it out:
 What are our starting and finishing unit?
 What equivalences will we need?
Dimensional Analysis
• A little harder:
• How many minutes is 47 seconds?
Dimensional Analysis
• And harder:
• How many seconds is 1.89 days?
Dimensional Analysis
• Use the equivalences given on the
handout to do this one with me:
• How many feet are in 2 meters?
Dimensional Analysis
• How many meters are in 850 inches?
Dimensional Analysis
• Whiteboard Practice
Dimensional Analysis
Homework
Objectives
• Practice Dimensional Analysis
Practice Quiz
• With your partner, write ten dimensional
analysis problems for another team.
 One partner, write the quiz paper.
 Other partner, write the answer key
INCLUDING ALL WORK.
 In order to get a problem correct, they must
show all work with units by every number, and
have their answer in the correct sig figs.