DIMENSIONAL
ANALYSIS
How to Change Units using Math
SI BASE UNITS
QUANTITY
Length
Volume
Mass
Time
Temperature
Amount
Memory
NAME
Meter
Liter
Kilogram
gram
second
Kelvin
Celsius
mole
byte
SYMBOL
m
l
Kg
g
s
K
C
mol
b
SI System Prefixes









piconanomicromillicentiKiloMegaGigaTetra-
p
n
µ
m
c
K
M
G
T
10-12
10-9
10-6
10-3
10-2
103
106
109
1012
 Know these prefixes
1/1,000,000,000,000
1/1,000,000,000
1/1,000,000
1/1000
1/100
1000
1,000,000
1,000,000,000
1,000,000,000,000
PUTTING THEM TOGETHER
• 1000 meters
• 1,000,000 bytes
• 1/1000 Liter
• 1/100 meter
• 1,000,000,000 seconds
1
1
1
1
1
Kilometer
Megabyte
milliliter
centimeter
Gigasecond
Conversion Fractions
• A Conversion Fraction is a Fraction that has the
units in it and is equal to one
• 1000m/1Km
• 100cm/1m
• 1000mm/1m
• 1000g/1Kg
• NOTE: The larger number always goes with
the smaller unit
Lets try something
How many millimeters are in 5 meters
5 m x 1000mm/1m = 5000mm
Let’s look at this:
We write our starting point first, and then
determine the fraction, there are 1000
milli’s in one whole, so the fraction is 1000
mm/1 m
Let’s try another

How many Kilometers are there in 5000
millimeters?
First, remove the starting prefix
5000mm x 1m/1000mm = 5 m
Second, place the new prefix
5 m x 1Km/1000m = 0.005 Km
Let’s Try Another
 How many milligrams are in 5000
Kilograms?
First, remove the starting prefix:
5000 Kg x 1000g/1Kg = 5000 g
Second, place the ending prefix:
5000g x 1000 mg/1g = 5,000,000
mg
LET’S LOOK AGAIN

How many meters will a car traveling 100
Km/hr travel in 1 minute?
–
This one is a little harder: You have to make two
sets of conversions

First Convert 100 Km/hr to meters per hour
–

Second you have to convert m/hr to m/min
–

100 Km/hr x 1000m/1 Km = 1000000 m/hr
1000000 m/hr x 1hr/60 min = 16667 m/min
Notice: hr goes on top in the conversion because it is
on the bottom in the initial number
Some Practice Problems

I drive 5 miles to school each morning. How
many inches is that? Express your answer in
scientific notation.
Another one

We have seven class periods here at AHS. If
you zone out 5 minutes every class period,
how many hours of education will you have
missed in the 180-day school year?
Again

If a car is traveling 60 miles per hour, how
many inches per second is it moving?
And Yet Again

Mr Simms wants to give all of his chemistry students
enough chocolate to make them goofy for the rest of
the day. It's a known fact that it takes 47 chocolate
chips to make a student goofy. The average cookie
contains 29 chocolate chips. Mr Simms has 5
classes and each class has an average of 32
students. How many toll house cookies does Mr
Simms need to make?
One Last One

If you never learn dimensional analysis, you will
have to work at a fast food restaurant for the rest of
your life wrapping hamburgers. Each hour you wrap
184 hamburgers. You work 8 hours per day and work
5 days a week. You get paid every 2 weeks with a
salary of $840.34. How many hamburgers will you
have to wrap to make your first one million dollars?
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DIMENSIONAL ANALYSIS