Bell Work 8/13
Identify what each prefix refers to: Mega: ________ Deci: ________ Kilo: _________ Micro:
__________ Hecto: _________ Deca: _________ Milli: ___________ Centi: __________
You will be quizzed on these tomorrow!
What is Dimensional Analysis?
Have you ever used a map? Since the map is a small-scale
representation of a large area, there is a scale that you can use to convert from small-scale units to large-scale units—for example, going from inches to miles or from cm to km.
What is Dimensional Analysis?
One of the most important things to do when visiting another country is to exchange currency.
For example, one United States dollar equals 1,511 Lebanese Pounds.
What is Dimensional Analysis?
Whenever you use a map or exchange currency, you are utilizing the scientific method of dimensional analysis.
What is Dimensional Analysis?
Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value.
It is used to go from one unit to another.
How Does Dimensional Analysis Work?
A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.
How Does Dimensional Analysis Work?
In our previous discussions, you could say that 3 cm equals 50 km on the map or that $1 equals 1511 Lebanese Pounds (LBP).
How Does Dimensional Analysis Work?
If we write these expressions mathematically, they would look like
3 cm = 50 km$1 = 1511 LBP
Examples of Conversions
You can write any conversion as a fraction.
Be careful how you write that fraction. For example, you can write
60 s = 1 min
as 60s or 1 min
1 min 60 s
Examples of Conversions
Again, just be careful how you write the fraction.
The fraction must be written so that like units cancel.
Given Unit
Steps
1. Start with the given value.
2. Draw fraction in parenthesis
3. Choose the appropriate conversion factor.
4. The problem is solved by multiplying the given data & their units by the appropriate unit factors so that the desired units remain.
5. Remember, cancel like units.
Let’s try some examples together…
1. Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?
Given: 7 pizzasWant: # of slices
Conversion: 12 slices = one pizza
Let’s try some examples together…
2. How old are you in days?
Given: 17 yearsWant: # of days
Conversion: 365 days = one year
Let’s try some examples together…
3. There are 2.54 cm in one inch. How many inches are in 17.3 cm?
Given: 17.3 cmWant: # of inches
Conversion: 2.54 cm = one inch
Solution
Check your work…
17.3 cm1
X1 inch
2.54 cm = 6.81 inches
Be careful!!! The fraction bar means divide.
Now, you try…
1. Determine the number of eggs in 23 dozen eggs.
2. If one package of gum has 10 pieces, how many pieces are in 0.023 packages of gum?
Multiple-Step Problems
Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions.
Example: How old are you in hours?
Given: 17 yearsWant: # of days
Conversion #1: 365 days = one yearConversion #2: 24 hours = one day
Combination Units
Dimensional Analysis can also be used for combination units.
Like converting km/h into cm/s. Write the fraction in a “clean” manner:
km/h becomes km h
Combination Units
Example: Convert 0.083 km/h into m/s.
Given: 0.083 km/hWant: # m/s
Conversion #1: 1000 m = 1 kmConversion #2: 1 hour = 60 minutes
Conversion #3: 1 minute = 60 seconds
83 m1 hour
Solution
Check your work…
0.083 km1 hour
X 1000 m1 km
X1 hour60 min
=
0.023 msec
83 m1 hour
X1 min60 sec
=
IMPERIAL TO METRIC CONVERSIONS
• The American system of measurement is known as the Imperial System. We need to be able to convert between our system and the metric system.
• Important Conversion Factors• 1mi. = 1.6km• 2.2 lb. = 1 kg• 1in. = 2.54 cm• 1 m = 3.28 ft• 1 gal. = 3.8 L
PRACTICE
Convert the following measurements
4mi. = _____km 12 gal = ____ L 22in. = _____m
220 lbs. = ____kg 18kg = _____lbs. 50 km = ____mi.
TEMPERATURES
From Fahrenheit to Celcius
°C = .556 (°F-32)
From Celcius to Fahrenheit°F = 1.8 (°C) + 32