€ The
Nathan's Hot Dog Eating Contest is
an annual American competitive-eating
competition that is held each July 4 at
Nathan's Famous New York restaurant.
€ In
2011 over 40,000 spectators attended
the event, and an additional 1.949 million
viewers watched it live on ESPN
television.
The contest has gained
public attention in recent
years due to the sudden
stardom of Takeru
Kobayashi, his subsequent
rivalry with American
Joey Chestnut.
€ In the 96th annual contest,
held on July 4, 2011, fourtime-defending champion
Chestnut won his fifth title
by consuming
62 hot dogs and buns
(HDBs) in ten minutes.
€
€How
many hot
dogs are eaten
in a month at a
rate of 48 hot
dogs per year?
Date
Date
II. Dimensional Analysis Notes
€Scientific
problems often require
dimensional analysis to convert
from one unit of measure to
another unit of measure.
€ Then
you write…
Date
II. Dimensional Analysis Notes
What is Dimensional
Analysis used for?
A. Helps solve problems,
used to convert from one unit to another.
€To
convert units, multiply by one
or more ratios of equal quantities
called conversion factors.
€For example, to convert inches to
feet, you would use the
1 ft.
conversion factor:
12 inches
Date
What is Dimensional
Analysis used for?
Give an example of a
Conversion
Factors.
II. Dimensional Analysis Notes
A. Helps solve problems,
used to convert from one unit to another.
B. Multiply by ratio(s) of equal quantities, like 1 ft.
12 inch
€Helpful
€ Steps:
Hints:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each
bottom number hit enter.
4. Check units & answer.
€ Then
you write…
Date
What is Dimensional
Analysis used for?
Give an example of a
Conversion
Factors.
II. Dimensional Analysis Notes
A. Helps solve problems,
used to convert from one unit to another.
B. Multiply by ratio(s) of equal quantities, like 1 ft.
(Equals 1)
C. Steps:
12 inch
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number hit enter.
4. Check units & answer.
Date
What is Dimensional
Analysis used for?
Give an example of a
Conversion
Factors.
Summarize
the steps in
dimensional
analysis.
II. Dimensional Analysis Notes
A. Helps solve problems,
used to convert from one unit to another.
B. Multiply by ratio(s) of equal quantities, like 1 ft.
(Equals 1)
C. Steps:
12 in.
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom
number hit enter.
4. Check units & answer.
Now write a 2‐3 sentence SUMMARY of your notes!
€Write
all the steps shown in
black to help you solve
dimensional analysis problems.
€Be sure to show your work when
cancelling out units.
D. Sample Problems
1.) How many inches are in 1 mile?
?
____ inches =
Start with the units you want for your answer:
“How many inches…?”
D. Sample Problems 1.) How many inches are in 1 mile?
Then use the units given in the problem
?
____ inches =
( ) 1 mile
1
Remember:
When dividing by 1, the number remains the same
€What
is a conversional factor I
know that uses miles?
€There
are 5,280 feet in 1 mile.
€So I can use the conversion
factor:
5280 ft.
1 mile
1.) How many inches are in 1 mile?
If no symbol of operation is shown between parentheses, you will multiply
?
____ inches =
( ) ( ) 1 mile
1
5280 ft.
1 mile
Remember to put “mile” in the denominator so your units will cancel out
mile
mile
=1
€What
is a conversional factor I
know that uses feet and inches?
€There
are 12 inches in 1 foot.
€So I can use the conversion
factor:
12 inches
1 ft.
1.) How many inches are in 1 mile?
?
____ inches =
( ) ( ) ( ) 1 mile
1
5280 ft.
1 mile
12 inch
1 ft.
Remember to put “ft.” in the denominator so your units will cancel out
ft.
ft.
=1
€First, cancel
out your units to
make sure your answer will be in
inches.
1.) How many inches are in 1 mile?
?
____ inches =
( ) ( ) ( ) 1 mile
1
5280 ft.
1 mile
12 inch
1 ft.
Draw a line through each unit you find in both the numerator AND the denominator. (Any unit divided by itself equals 1.)
mile
mile
=1
and
ft.
ft.
=1
1.) How many inches are in 1 mile?
?
=
____ inches ( ) ( ) ( ) 1 mile
1
5280 ft.
1 mile
12 inch
1 ft.
Since “inch” is the only unit remaining, your answer will be in inches per mile. (This should match the start of the problem!)
€Multiply
the numerators (top #s)
together.
€Multiply the denominators
together. (bottom #s)
€Then divide. (Be sure to include
the correct units in your answer!)
1.) How many inches are in 1 mile?
?
____ inches =
( ( ) ( ) ( ) 1 mile
1
5280 ft.
1 mile
) 12 inch
1 ft.
1 X 5280 X 12 inch 63,360 inch
=
=
1
1 X 1 X 1
= 63,360 inches
€The Twin
Cities
Marathon is 26.2
miles. How far is
this in yards?
Solution:
What you want
What you have
C
( V
) ( ) ( ) 26.2 mile
?
____ yards =
1
( What you know
5280 ft.
1 mile
26.2 X 5280 X 1 yard
=
1 X 1 X 3
) = 46,112 yards
1 yard
3 ft.
Problem Set Starters:
?
1.) __ miles =
hour
( ) ( ) ?
2.) __ ounces =
year
?
3.) __ miles =
hour
( ) 25 euro
?
__ $ 4.)
=
500 g
kg
Conversion Factor:
1000 g = 1 kg
Problem Set Starters:
( ) 20 nautical mile
?
5.) __ meter =
sec
1 hour
?
6.) __ mile =
hour
?
7.) __ feet =
day
Conversion Factor:
365 days = 1 year
?
8.) __ km =
hour
Conversion Factor:
1000 m = 1 km
€You
watch a
Vikings football
game for 3
hours. How
long is this in
seconds?
Solution:
What you have
C
What you want
?
____ sec. =
=
( ( V
3 hours
1
What you know
) ( ) ( ) 3 X 60 X 60 sec.
1 X 1 X 1
60 min.
1 hour
) = 10,800 seconds
60 sec.
1 min.
€How
many hot
dogs are eaten
in a month at a
rate of 48 hot
dogs per year?
Solution:
What you want
What you have
What you know
?
____ hot dogs 48 hot dogs
=
month
1 year
) ( ( =
( 48 hot dogs
12 months
) ) 1 year
12 months
4 hot dogs
=
month
€How
many miles
can you jog in
one hour at an
average rate of
7.3 feet per
second?
What you want
What you have
Solution:
What you know
( ) ( ) ( ) ( ) ( ) ?
__ miles 7.3 ft.
1 mile 60 sec. 60 min.
=
hour
1 sec. 5280 ft. 1 min. 1 hour
=
26,280 miles
4.98 miles
=
hour
5280 hours