What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going...
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Transcript of What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going...
![Page 1: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/1.jpg)
What is Dimensional Analysis?
A fancy term for converting from one unit to another
Examples …Going from dollars to centsGoing from miles to kilometersGoing from meters to cm to inchesGoing from seconds to yearsGoing from mph to m/s
![Page 2: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/2.jpg)
What is Dimensional Analysis?
I will teach you a systematic way of doing these problems
The method uses conversion factors
![Page 3: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/3.jpg)
Some Typical Conversion Factors
60 s = 1 min as 60 s or 1 min 1 min 60 s
1.6 km = 1 mile as 1.6 km or 1 mile 1 mile 1.6 km
13.38 US dollars = 0.075 Mexican pesos
as 13.38 USD or 0.075 pesos 0.075 pesos 13.38 USD
![Page 4: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/4.jpg)
How Does Dimensional Analysis Work?
A conversion factor is used, along with what you’re given, to determine what the new unit will be.
Enough talk lets do one or two on the board!!!
![Page 5: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/5.jpg)
Examples of Conversions
Again, just be careful how you write the fraction.
The fraction must be written so that like units cancel.
![Page 6: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/6.jpg)
Steps
1. Start with the given value.2. Write the multiplication symbol.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.
![Page 7: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/7.jpg)
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
![Page 8: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/8.jpg)
7 pizzas1
Solution
Check your work…
X 12 slices1 pizza = 84 slices
![Page 9: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/9.jpg)
Let’s try some examples together…
2. How old are you in days?
Given: 17 yearsWant: # of days
Conversion: 365 days = one year
![Page 10: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/10.jpg)
Solution
Check your work…
17 years1 X 365 days
1 year = 6052 days
![Page 11: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/11.jpg)
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
![Page 12: What is Dimensional Analysis? A fancy term for converting from one unit to another Examples Going from dollars to cents Going from miles to kilometers.](https://reader033.fdocuments.in/reader033/viewer/2022051202/5a4d1b777f8b9ab0599b7761/html5/thumbnails/12.jpg)
Solution
Check your work…
17 years1 X
365 days1 year X
24 hours1 day =
148,920 hours