Warm Up – Dimensional Analysis
Practice
1. Susanna is 5.50 ft tall.
What is her height in
centimeters?
(1 in = 2.54 cm)
2. If we are in class for
1.5 hours, how many
seconds are we in
class?
Warm Up – Dimensional Analysis
Practice
We are going to plan a hypothetical pizza party.
How much will it cost? (write it down with
explanation)
If you’re stuck consider these questions:
• How many students are in the class?
• How many slices of pizza do you think each
student will eat?
• How many slices of pizza are in a whole pizza
• How much does a whole pizza cost?
Let’s Throw a Pizza Party
How much will it cost for our class?
• How many students?
• Slices per student?
Slices per pizza?
Price per pizza?
students slices
pizza price price




class
student slices pizza class
How to convert units? (1)
Step 1: When to convert
So What?:
You can’t add
Numbers with units, like
16.2 meters or 32 ft/sec², are euros to
treated exactly the same as dollars
coefficients with variables, You can’t add
feet to
like 16.2x or 32y/z².
feet/sec
How to convert units? (2)
Step 2: Multiply by 1
You can multiply anything by 1 and not change its
value.
Convert 4.5 hours to minutes:
(1) 60 minutes = 1 hour
(2) 60 minutes = 1
1 hour
(3) 4.5 hr × 60 min
1 hr
(4) 4.5 hr x 60 min = 4.5x 60 min =
1 hr
Is it really multiplying by 1?
•
In which case will you overcook the Turkey?
Which is longer, cooking a Turkey for 3.25 hours
or 195 minutes?
Note: If you converted 3.5 hours and came out with
.0583 minutes, you probably messed up. Always
see if the answer makes sense
How to convert units? (3)
Step 3: How to pick a “1”
(1) Find a conversion factor between the given
units and the desired units, and write it as an
equation.
EX: to convert km to miles
1 km = 0.621 miles
(2) Convert that equation to a fraction with
the desired units on top and the given
units on the bottom
1 km  there’s your “1” conversion
0.621 miles
factor
How to convert units? (4)
Step 4: Chaining Conversions
(1) combine conversions to avoid
looking up a specific conversion
(2) Like in the pizza example
EX: how many meters are in the 440-yard
dash?
440 yd = 402 m
Converting
Inches to centimeters
10.0 in
We start by writing down the
number and the unit
Converting
Inches to centimeters
10.0 in 2.54 cm
1 in
Our conversion factor for this is 1 in = 2.54 cm.
Since we want to convert to cm, it goes on the
top.
Converting
Inches to centimeters
10.0 in 2.54 cm
1 in
Now we cancel and collect units. The inches cancel
out, leaving us with cm –
the unit we are converting to.
Converting
Inches to centimeters
10.0 in 2.54 cm = 25.4 cm
1 in
Since the unit is correct,
all that is left to
do is the arithmetic...
The
Answer
Recap of the Procedure
1. Find conversion factor as a fraction with the
given units in the opposite position from the
original measurement
1. Raise the conversion fraction to that same
power
2. Multiply the original measurement by the
conversion fraction, and simplify.