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Dimensional Analysis

Dimensional Analysis. What is Dimensional Analysis?. Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value. It is used to go from one unit to another.

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Dimensional Analysis

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  1. Dimensional Analysis

  2. What is Dimensional Analysis? • Dimensional analysisis a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value. • It is used to go from one unit to another. • A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

  3. Conversion Factors Examples • Equality- 60 seconds = 1 minute Conversion factors:60s or 1 min 1 min 60 s • Equality- 60 min = 1 hr Conversion factors: 60min or 1 hr 1 hr 60min • Any others?

  4. Dimensional Analysis • Calculate the number of minutes in 3.61 hours. • *Note: Use the number given in the question to determine the number of sig figs in your answer. 1. Write the given. 2. Draw the chart.

  5. Dimensional Analysis • Calculate the number of minutes in 3.61 hours. • *Note: Use the number given in the question to determine the number of sig figs in your answer. 3. Think of a relationship: 1 hr = 60 min 4. Cancel units diagonally.

  6. Dimensional Analysis • Calculate the number of minutes in 3.61 hours. 5. Add the rest of the relationship. • Multiply across and divide by the bottom • Count sig figs in the given. Round • the answer to that number of sig figs.

  7. Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer. Conversion Factor: 1 in= 2.54 cm

  8. Dimensional Analysis How many centimeters are in 4.2 inches? *Note: Use the number given in the question to determine the number of sig figs in your answer.

  9. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Realize that we don’t know just one step from weeks to seconds.

  10. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Start as usual.

  11. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Extend your table.

  12. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Continue adding relationships.

  13. Dimensional Analysis Multi-Step Problems Calculate the number of seconds in two weeks. Round to 1 sig fig. Add as many conversions as needed.

  14. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Notice the use of the bottom space.

  15. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Ignore the bottom unit for a moment. Concentrate on converting the top unit.

  16. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue converting the top. Stop when you get to lb…the goal.

  17. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Now, focus on the bottom units. It is OK to cancel units from a distance.

  18. Dimensional Analysis Multi-Step Problems Convert the density of 0.58 g/mL to lb/gallon. (1 L = 1.057 qt and 4 qt = 1 gal; 1kg = 2.2 lb) Continue adding until you reach the goal.

  19. iRespond Question Fill-In F If a pound of apples costs $0.79, then 5.3 lbs will cost _________. Give your answer to TWO decimal places which is customary with money. A.) 4.19;; B.) C.) D.) E.)

  20. iRespond Question Fill-In F 1849 yards = __________ miles Hint: 5280 ft = 1 mile Give your answer to 4 sig figs. A.) 1.051;; B.) C.) D.) E.)

  21. iRespond Question Fill-In F If Boston and New York City are 190 miles apart, then the distance between the two cities is _______ km. Hint: 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 310;; B.) C.) D.) E.)

  22. iRespond Question Fill-In F If a pound of apples costs $0.79, then a shopper with $2.00 will be able to purchase ________ lbs of apples. Give your answer to THREE sig figs. A.) 2.53;; B.) C.) D.) E.)

  23. iRespond Question Fill-In F If a US car advertisement brags that an SVU gets 26 miles/gallon on the highway, then the same car would be described in Europe as getting ___________ km/L. Hint: 1 L = 1.057 qt; 4 qt = 1 gal; 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 11;; B.) C.) D.) E.)

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