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Dimensional Analysis

Learn the skill of converting units using dimensional analysis. Understand conversion factors and cross-canceling units for accurate results. Practice metric to metric and metric to English conversions following a simple 6-step method.

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Dimensional Analysis

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  1. Dimensional Analysis Converting units from one unit to another

  2. Introduction • the skill of converting from one unit to another is called dimensional analysis.

  3. Introduction • involves three factors: a. the unit in the given problem b. the unit the answer should be in c. the conversion factor

  4. A conversion factor is…. 1) a fraction that always equals 1 ex. 1 kilogram equals 1000 grams 1 kg / 1000 g = 1 OR 1000 g / 1 kg = 1

  5. B. How to do a conversion – metric to metric • Read the given problem. Determine the units you are converting to (what units your answer should be in). a. Convert 2500 g to kilograms.

  6. How to do a conversion – metric to metric • Choose a conversion factor that includes both the unit given in the problem and the unit you need to convert to. You could choose: 1 kg / 1000 g = 1 OR 1000 g / 1 kg = 1

  7. How to do a conversion – metric to metric • Choose the conversion factor that will allow you to cross – cancel out the units that you DO NOT want in the answer. (hint: put the units you want for the answer in the numerator position!) 2500 grams x 1 kilogram 1000 grams

  8. How to do a conversion – metric to metric • Cancel out the like units (numerator/denominator). • Do the math. Multiply the fractions - reduce to its simplest form. • 2500 grams x 1 kilogram = 2500kilograms 1000 grams 1000

  9. How to do a conversion – metric to metric • 2500 kilograms = 2.5 kilograms 1000 Answer = 2.5 kilograms

  10. 6 Step Method 1. Read to find the given 2. Set up the problem 3. Find the conversion factor 4. Multiply and divide 5. Record answer 6. Check work

  11. . How to do a conversion – metric /english • Read the given problem. Determine the units you are converting to (what units your answer should be in). a. Convert 750 miles to kilometers.

  12. How to do a conversion – metric /english • Choose a conversion factor that includes both the unit given in the problem and the unit you need to convert to. You could choose: 1 mile / 1.602 kilometers = 1 OR 1.602 kilometers / 1 mile = 1

  13. How to do a conversion – metric /english • Choose the conversion factor that will allow you to cross – cancel out the units that you DO NOT WANT in the answer. (hint: put the units you want for the answer in the numerator position!) 750 miles x 1.602 kilometers 1 mile

  14. How to do a conversion – metric /english • Cancel out the like units (numerator/denominator). 750 miles x 1.602 kilometers 1 mile

  15. How to do a conversion – metric /english • Do the math. Multiply the fractions - reduce to its simplest form. 750 miles x 1.602 kilometers 1 mile • 1201.5 kilometers = 1201.5 kilometers 1

  16. How to do a conversion – metric /english Answer: 1200 kilometers

  17. Dimensional Analysis –Multistep Conversions • Example: If Gavin is running with a football 30ft/second, how fast is that in meters per second?

  18. Example: If Katelyn is in a Mercedes traveling 15 mph, how fast is that in ft/sec?

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