Unit Conversion Using Dimensional Analysis Objective N-Q. 1

1. 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

2. 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.

3. 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 Quantity2 Conversion Factors 1 foot = 12 inches 7.48 gal = 1 ft3or

4. 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

5. 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

6. Example of a one-step conversion using DA Convert 153 cm to inches (1 inch = 2.54 cm) Write down the given quantity (153cm) Write the equality as two conversion factors or Choose the conversion factor that has the given unit in the denominator and the desired unit in the numerator. Step 1 Step 3 Answer *Notice the unit of centimeters is cancelled

7. Now its your turn! Convert 13.5 feet to inches(1foot = 12 inches) Write down the given quantity Write the equality as two conversion factors Choose the conversion factor that has the given unit in the denominator and the desired unit in the numerator. Step 1 Step 3 Answer

8. 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. Convert 3.5 miles to inches Example of a multi-step conversion using DA Step 1 Step 3 Answer

9. 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)

10. One last note about DA! All of the conversion factors we have used thus far have been based on equalities with different units. 1inch = 2.54cm 1foot = 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? One last note about DA! All of the conversion factors we have used thus far have been based on equalities with different units. 1inch = 2.54cm 1foot = 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