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.

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Presentation 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

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.

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. Choose the conversion factor with the given unit in the denominator Start with the given quantity Calculate answer by multiplying and dividing

Step 1 Step 3 Answer *Notice the unit of centimeters is cancelled

Step 1 Step 3 Answer

Example of a multi-step conversion using DA

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?