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Warm Up – Dimensional Analysis Practice

Warm Up – Dimensional Analysis Practice. Susanna is 5.50 ft tall. What is her height in centimeters ? (1 in = 2.54 cm). 2. If we are in class for 1.5 hours, how many seconds are we in class?. Warm Up – Dimensional Analysis Practice.

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Warm Up – Dimensional Analysis Practice

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  1. Warm Up – Dimensional Analysis Practice • Susanna is 5.50 ft tall. What is her height in centimeters? (1 in = 2.54 cm) 2. If we are in class for 1.5 hours, how many seconds are we in class?

  2. Warm Up – Dimensional Analysis Practice We are going to plan a hypothetical pizza party. How much will it cost? (write it down with explanation) If you’re stuck consider these questions: • How many students are in the class? • How many slices of pizza do you think each student will eat? • How many slices of pizza are in a whole pizza • How much does a whole pizza cost?

  3. Let’s Throw a Pizza Party How much will it cost for our class? • How many students? • Slices per student? Slices per pizza? Price per pizza?

  4. How to convert units? (1) So What?: You can’t add euros to dollars You can’t add feet to feet/sec Step 1: When to convert Numbers with units, like 16.2 meters or 32 ft/sec², are treated exactly the same as coefficients with variables, like 16.2x or 32y/z².

  5. How to convert units? (2) Step 2: Multiply by 1 You can multiply anything by 1 and not change its value. Convert 4.5 hours to minutes: (1) 60 minutes = 1 hour (2) 60 minutes = 1 1 hour (3) 4.5 hr × 60 min 1 hr (4) 4.5 hr x 60 min = 4.5x 60 min = 1 hr

  6. Is it really multiplying by 1? • In which case will you overcook the Turkey? Which is longer, cooking a Turkey for 3.25 hours or 195 minutes? Note: If you converted 3.5 hours and came out with .0583 minutes, you probably messed up. Always see if the answer makes sense

  7. How to convert units? (3) Step 3: How to pick a “1” • Find a conversion factor between the given units and the desired units, and write it as an equation. EX: to convert km to miles 1 km = 0.621 miles (2) Convert that equation to a fraction with the desired units on top and the given units on the bottom 1 km there’s your “1” conversion 0.621 miles factor

  8. How to convert units? (4) Step 4: Chaining Conversions • combine conversions to avoid looking up a specific conversion • Like in the pizza example EX: how many meters are in the 440-yard dash? 440 yd = 402 m

  9. Converting Inches to centimeters 10.0 in We start by writing down the number and the unit

  10. Converting Inches to centimeters 10.0 in 2.54 cm 1 in Our conversion factor for this is 1 in = 2.54 cm. Since we want to convert to cm, it goes on the top.

  11. Converting Inches to centimeters 10.0 in 2.54 cm 1 in Now we cancel and collect units. The inches cancel out, leaving us with cm – the unit we are converting to.

  12. Converting Inches to centimeters 10.0 in 2.54 cm 25.4 cm = 1 in Since the unit is correct, all that is left to do is the arithmetic... The Answer

  13. Recap of the Procedure • Find conversion factor as a fraction with the given units in the opposite position from the original measurement • Raise the conversion fraction to that same power • Multiply the original measurement by the conversion fraction, and simplify.

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