*
First, let’s talk about dimensions. Every physical
property has dimensions—you may call them “units”.
For example, we can measure Temperature in
Celsius
Fahrenheit
Kelvin
Another example is pressure. There’s a lot of ways
we measure the units of pressure.
psi
(pounds per square inch)
psf
(pounds per square foot)
mm HG (millimeters of Mercury)
N / m2
(Newtons per square meter)
Pascal
“Kill The Units” –
courtesy of Mr. Hagler
It is very, very useful to have the math ability to convert from one unit
to another. For instance, if you measure something in feet, it might be
useful to how far that is in miles!
Example 1:
Graham built and launched a rocket. It flew 6,500 feet.
How far is that in miles, if 1 mile = 5280 feet?
6500 feet
miles
6500 feet *
6500 feet *
6500
*
𝟏
𝒎𝒊𝒍𝒆𝒔
𝟓𝟐𝟖𝟎 𝒇𝒆𝒆𝒕
𝟏
𝒎𝒊𝒍𝒆𝒔
𝟓𝟐𝟖𝟎 𝒇𝒆𝒆𝒕
𝟏
𝟓𝟐𝟖𝟎
miles
miles
miles
1.23 miles
Example 2:
Hope went sky diving. Once she left the airplane she was
in free-fall for 53 seconds. Then the parachute was pulled
and she floated under the chute for 325 seconds.
Find the number of minutes she was in free-fall.
53 sec * 1 minute
60 sec
= .88 minutes
Find the number of minutes she floated under the chute.
324 sec * 1 minute
60 sec
= 5.4 minutes
Find the number of HOURS she was in the air total!
5.4 + .88 minutes total = 6.28 minutes
6.28 minutes * 1 hour
60 min
= .105 hour
Example 3:
Maureen and Bryan rode their bikes to the river.
Maureen rode her bike 63360 feet/hour.
Bryan rode his bike 0.2 miles/minute.
Convert Maureen’s speed to miles/hour.
63360 ft *
hour
1 mile
5280 feet
=
12 mi/hour
Convert Bryan’s speed to miles/hour.
.2 mile *
min
60 min
1 hour
Who is faster?
They’re the same! 
=
12 mi/hour
Homework Assignment
Dimensional Analysis Worksheet – only
do the odd numbered problems
tonight!
Tomorrow… we’ll correct. If you
score 85% or better, then you don’t
have to do the even problems.
Entry Task
1. Convert 60 miles/hour to feet per second.
2. The units of the chain system of measure,
used by surveyors, are as follows:
7.92 inches = 1 link
100 links = 1 chain
10 chains = 1 furlong
80 chains = 1 mile
The distance of the Kentucky Derby, a classic horse
race, is 1.25 miles. How is this distance expressed
in furlongs?
Warm Ups
Convert 20 miles per hour into feet per second.
20 Miles
hour
29.3
feet
second
There are 7 squinchies in a quirtle. There are 15 mombos in 4 droons.
Convert 83 squinchies / mombo into quirtles / droon.
83 squinchies
mombo
44.46
quirtles
droon
*
Converting square or cubic units
Sometimes, we need to convert “square” units.
For instance, if you want to spread mulch in your garden,
and measure it to be 12’ x 10’, the total area of the
garden is 12 * 10 = 120 square feet.
We write this as 120 ft2 .
You want the mulch to be 6” (1/2 foot) deep.
So, we need 60 ft3 of mulch.
But Home Depot only sells mulch in bags that are 1 yd3.
Convert 60 ft3 into yd3.
How many bags of mulch must you buy?
60 ft3
= yd3