Dimensional Analysis

1. Dimensional Analysis • Organized method of problem-solving • Used in chemistry, physics, engineering, and medicine • Communicates the path to scientists that follow your work • Records your own path for your future use

2. 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.

3. 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. Divide the relationship in ½ at the = sign. 5. Cancel units diagonally.

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. 6. Add the rest of the relationship. Count sig figs in the given. Round the answer to that number of sig figs.

5. 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.

6. 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.

7. 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.

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

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

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

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

12. 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.

13. 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.

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) Continue converting the top. Stop when you get to lb…the goal.

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) Now, focus on the bottom units. It is OK to cancel units from a distance.

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 adding until you reach the goal.

17. 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.)

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

19. 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.)

20. iRespond Question Fill-In F 1849 yards = 1.0506 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 Boston and New York City are 190 miles apart, then the distance between the two cities is 305.96 km. Hint: 1 km = 0.621 miles Give your answer to TWO sig figs. A.) 310;; B.) C.) D.) E.)

23. 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.)

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

25. 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 you answer to TWO sig figs. A.) 11;; B.) C.) D.) E.)