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Algebra 1

Learn how to convert units using dimensional analysis, a method to convert measurements. Understand the importance and principles behind dimensional analysis and practice converting units in various contexts.

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Algebra 1

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  1. (8/30/19) Algebra 1 “Education must not simply teach work – it must teach Life.“W. E. B. Du BoisPick up your notebook and go to your assigned seat BW: a) Converting feet to miles, hours to seconds, or meters to yards is called (vocabulary term): Dimensional Analysis GO TO NOTES

  2. NOTES Standard:Standard A1.N.Q.1 Identify and use units of measure within context. Convert units and rates using dimensional analysis. Today’s Objective: What is Dimensional Analysis?

  3. Unit ConversionsUsing Dimensional Analysis Units are our friends Thanks to www.jessamine.k12.ky.us  Who provided much of the material in this PowerPoint.

  4. Dimensional Analysis Is a method to convert units. Examples include: Feet Inches Kilometers  Meters Kilograms  Grams

  5. It is common to need to convert units of measure: Cooking Mechanical work Chemistry / Science Art / /Sports Metric Imperial systems Why is Dimensional Analysis Important

  6. Principle Behind Dimensional Analysis • You can multiply anything by 1 without changing the physical meaning.

  7. How Do We Multiply By 1 If the same thing is on the top and the bottom of a fraction,  8 = 1 = 1 8 Then they cancel out… and become 1

  8. All Equalities = 1 Any time you put two things that are equal to each other 1000g = 1kg On top and on bottom 1000 g --------- = 1 1 kg Then they cancel out… and become 1.

  9. All Equalities = 1 It doesn’t matter which is on top and which is on bottom. 1000 g 1 kg --------- = 1 or --------- = 1 1 kg 1000 g Both cancel out… and become 1.

  10. 1 km = 1000 m (A metric equality) Any equality can be written two ways (conversion factors) 1000 m=1 km= 1 1 km 1000 m Which one to use? Depends on which direction you are trying to go.

  11. The Rules • Write down “given” unit • Draw a horizontal & vertical line “picket fence” • Write “wanted” / “given” on the fence • Enter proper #s for “wanted units & “given” units • Cancel units & do the math

  12. For example: Convert 25 km to meters (I DO) Use the conversion factor that allows units to cancel. 1000 mor 1 km 1 km 1000 m “given” unit = “want” unit picket fence

  13. For example: Convert 25 km to meters (m) (I DO) Use the conversion factor that allows units to cancel. 1000 m 1 km 25 km 1000 m= 25000 m (or 2.5 x 104 m) 1 km Just a little Scientific notation picket fence “given” conversion ‘want’ factor

  14. Example: Convert 12.5 g to kg (I DO) (1) 12.5 g 1 kg = 0.0125 kg 1000g (4) (3) (2) (5) Don’t forget the units

  15. See what happens without UNITS?!?!?

  16. Here’s a explaining dimensional analysis from Khan Academy • Dimensional Analysis Video Demonstration

  17. Try: 18.2 km to m (WE DO)

  18. (WE DO) How many centimeters are there in 5.54 inches?Conversion rate: 1 inch = 2.54 cm

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