Bell Ringer 9/2/15
• On a piece of paper,
• Write your name, nickname, birthdate, and
two interesting things about you.
• Oh… add a third thing to that….. Of the three
things you would have written 1 should be
untrue…A Lie!! We will try to figure out that
lie..
• 4 minutes!!
Bell Ringer 9/3/15
• NEW SEATS!!!
Answer the question below:
Give three examples of
industries/professions that utilize
measurements, describe the type of
measurements they use.
Learning Objectives
• We will convert between measurement
units of the English and metric system
using dimensional analysis.
• I will use dimensional analysis to solve
conversion problems.
Agenda
• Bell Ringer
• Dimensional analysis Essential Questions
[ ongoing]
• Teacher Model- Steps to dimensional analysis
• Partner Practice
• Partner check
• Independent questions
Dimensional Analysis
In which you will learn about:
•Conversion factors
•Standard dimensional analysis
Essential Questions
• 1. What is dimensional analysis (DA)?
• 2. What are the steps for dimensional
analysis?
• 3. What are conversion factors?
Dimensional Analysis
• Imagine math class (don’t panic)
• Imagine multiplying two fractions
• Imagine the numerator of one fraction
matches the denominator of the second (3/7 x
2/3)
• The numerator and denominator cancel!
• In dimensional analysis, we use this idea to
cancel UNITS of measurements.
Equalities
State the same measurement in two different units
length
10.0 in.
25.4 cm
Conversion Factors
Fractions in which the numerator and denominator are
EQUAL quantities expressed in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
and 2.54 cm
2.54 cm
1 in.
Let’s come
up with
some other
conversion
factors!!
Conversion Factors
Fractions in which the numerator and denominator are
EQUAL quantities expressed in different units
Example:
1 in. = 2.54 cm
Factors: 1 in.
and 2.54 cm
2.54 cm
1 in.
Essential
Question:
What are
conversion
factors?
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min
DA
Step1:What
’s the first
thing you
start your
conversion
with?
cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min
DA Step2:
How do I
know what
conversion
factor to
use?
cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min
DA Step3:
What
happens to
my units?
cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
How many minutes are in 2.5 hours?
Conversion factor
2.5 hr x 60 min
1 hr
= 150 min
DA Step4:
How do I
solve the
problem?
cancel
By using dimensional analysis / factor-label method, the UNITS
ensure that you have the conversion right side up, and the UNITS
are calculated as well as the numbers!
Sample Problem
• You have $7.25 in your pocket in quarters.
How many quarters do you have?
7.25 dollars X 4 quarters
1 dollar
= 29 quarters
Learning Check
A rattlesnake is 2.44 m long. How long is the
snake in cm?
a) 2440 cm
b) 244 cm
c) 24.4 cm
Solution
A rattlesnake is 2.44 m long. How long is the
snake in cm?
b) 244 cm
2.44 m x 100 cm
1m
= 244 cm
Learning Check
How many seconds are in 1.4 days?
Unit plan: days
hr
min
seconds
1.4 days x 24 hr x60 min x 60 s
1 hr
1 min
1 day
= 1.2 x 105 s
Wait a minute!
What is wrong with the following setup?
1.4 day
x 1 day
24 hr
x
60 min x 60 sec
1 hr
1 min
English and Metric Conversions
• If you know ONE conversion for each type of
measurement, you can convert anything!
• I will provide these equalities, but you must
be able to use them:
– Mass: 454 grams = 1 pound
– Length: 2.54 cm = 1 inch
– Volume: 0.946 L = 1 quart
Steps to Problem Solving

Read problem
 Identify data
 Make a unit plan from the initial unit to the desired
unit (good practice at beginning, not necessary as you
get comfortable with this)
 Select conversion factors
 Change initial unit to desired unit
 Cancel units and check
 Do math on calculator
 Give an answer using significant figures
Dealing with Two Units
If your pace on a treadmill is 65 meters per minute,
how many seconds will it take for you to walk a
distance of 8450 feet?
HINT: Always start with the simplest label.
You’re looking for seconds, so you can’t start there.
65 m/min has two labels so that’s not very simple.
Best STARTING place is 8450 feet!
end
How do I round multiple step
problems with the correct sig figs?
• If the problem has only one “type” of math
(adding/subtracting OR multiplying/dividing),
round at the end of the problem
– Dimensional analysis is all M/D! Round at the end.
• If the problem has more than one type, you must
follow the order of operations, round after each
type is complete.
– A good example is percent error. Round using adding
rules after 0-E, then finish the calculation and round
again using multiplying rules.
Speaking of Sig Figs…
• Exact conversion factors, such as 100 cm in 1
m, do NOT count toward the number of sig
figs!
• Numbers that are part of a mathematical
formula, such as x100 in percent error, do NOT
count toward the number of sig figs!