Transcript Unit Conversion Using Dimensional Analysis Objective N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems.

Unit Conversion Using
Dimensional Analysis
Objective N-Q.1
Use units as a way to understand problems and
to guide the solution of multi-step problems
Why do you need to know how to convert units?
We use measurements every day of our lives. When
you go to the store, items are sold by weight, volume,
length, number of items, etc. It is important to know
how these units of measurement compare to each other
and how to readily convert between various units.
Let’s explore what is involved when we need to make a
conversion between different units. We need to start
with conversion factors.
What is a conversion factor?
A conversion factor is a ratio written in fraction form
that expresses the same quantity (an equality) using
two different units. Every conversion factor can be
written two ways, which are reciprocals of each other.
For example:
Same Quantity
2 Conversion Factors
1 foot = 12 inches
1 foot
12 inches
7.48 gal = 1 ft3
7.48 gal
1 ft3
or
12 inches
1 foot
or
1 ft3
7.48 gal
Write each of the given equal quantities as 2
reciprocal conversion factors.
2 conversion factors
60 seconds =1 minute
1 mile = 5280 feet
1.06 quarts = 1 liter
*All conversion factors must be labeled correctly
What is dimensional analysis?
Dimensional analysis (DA) is a systematic
mathematical method using conversion factors to move
from one unit of measurement to another.
Here is a flow chart showing DA basics.
Start with the
given quantity
Choose the
conversion
factor with the
given unit in the
denominator
Calculate
answer by
multiplying and
dividing
Example of a one-step conversion using DA
Convert 153 cm to inches (1 inch = 2.54 cm)
1. Write down the given quantity (153 cm)
2. Write the equality as two conversion factors
1 inch
2.54 cm
2.54 cm
or
1 inch
3. Choose the conversion factor that has the given
unit in the denominator and the desired unit in the
numerator.
Step 1
153 cm
Step 3
1 inch
2.54 cm
Answer
=
60.2 inches
*Notice the unit of centimeters is cancelled
Now its your turn!
Convert 13.5 feet to inches (1 foot = 12 inches)
1. Write down the given quantity
2. Write the equality as two conversion factors
3. Choose the conversion factor that has the given
unit in the denominator and the desired unit in the
numerator.
Step 1
Step 3
Answer
=
Using DA in a multi-step conversion
Follow the same steps as before, but use as many
conversion factors as necessary to obtain the desired
unit.
Example of a multi-step conversion using DA
Convert 3.5 miles to inches
Step 1
3.5 miles
Step 3
5280 feet
1 mile
Answer
12 inches
1 foot
= 221760 inches
Now it’s your turn!
On a recent trip to Canada it took 93.6 liters of
gasoline to completely fill the empty gas tank in your
truck. What is the capacity of the gas tank in gallons?
Use DA to set up the conversions and solve!
(1 gallon = 4 quarts)
(1 liter = 1.06 quarts)
One last note about DA!
All of the conversion factors we have used thus far
have been based on equalities with different units.
1 inch = 2.54 cm
1 foot = 12 inches
However, a conversion factor can be written from any
type of relation. Consider the problem below:
Suppose you can make 17 pasties in 45 minutes.
How many pasties can you make in 3.5 hours?
Notice that 1 hour = 60 min (an equality), however,
17 pasties ≠ 45 min (not an equality), but rather
17 pasties ~ 45 min. Conversion factors can still be
written from such a relation.