Dimensional Analysis

1. Dimensional Analysis

2. Homework

3. Objectives • Be able to convert between units using dimensional analysis

4. Dimensional Analysis • A VERY helpful skill in science, and one that will get especially helpful in chemistry and physics… Dimensional Analysis • It will also be another way of converting prefixes that some of you may prefer to hopping the decimal place • This will take PRACTICE to master

5. Dimensional Analysis • Dimensional analysis is a method of converting a measurement from one unit to another • Example: How many seconds is 2 hours?

6. Dimensional Analysis • First and most important in any dimensional analysis problem • 1. Identify the unit your measurement is already in, and identify the unit you want your measurement to end up in. • Example: Measurement is already in hours. We want it in seconds.

7. Dimensional Analysis • 2. If you don’t know how many of your starting unit directly equals your ending unit, make a chain. • I don’t know off the top of my head how many seconds are in an hour, for instance. But I know how many seconds are in a minute, and how many minutes are in an hour. Ex: Hours -> Minutes -> Seconds will be my chain.

8. Dimensional Analysis 3. Begin your chain with your starting measurement Write it as a fraction with a denominator of 1. • Ex: 2 hrs 1 NOTE: IT IS SUPER SUPER IMPORTANT WHEN DOING THESE PROBLEMS TO ALWAYS WRITE YOUR UNITS.

9. Dimensional Analysis • 4. The next fraction in your chain will be an “equivalence.” The top of the fraction equals the bottom. • Ex: It will be 60 min or 1 hr 1 hr 60 min

10. Dimensional Analysis • 5. Write the fraction so that it will “criss-cross”: the bottom will have the same unit as the previous fraction’s top did. • Ex: We will choose 60 min 1 hr

11. Dimensional Analysis • 6. Repeat steps 4-5 until you reach an equivalence that includes your ending unit. • Ex: The next and last equivalence will be 60 sec 1 min

12. Dimensional Analysis • Choose the step seven that you prefer. EITHER: • 7. Your answer will be this division: (All the top numbers multiplied together)/(All the bottom numbers multiplied together) and your final unit. • Ex: (2 x 60 x 60)/(1 x 1 x 1) sec = 7200 sec OR • 7. Do each division one at a time, and multiply them as you go along. • Ex: (2/1) x (60/1) x (60/1) sec = 2 x 60 x 60 sec = 7200 sec

13. Dimensional Analysis • 8. Round your final answer to the same number of sig figs as your starting measurement. • Ex: 2 hours has 1 sig fig. 7200 seconds -> 7000 seconds.

14. Dimensional Analysis • Another, shorter example: • How many seconds are in five minutes? Before we write it out: • What are our starting and finishing unit? • What equivalences will we need?

15. Dimensional Analysis • A little harder: • How many minutes is 47 seconds?

16. Dimensional Analysis • And harder: • How many seconds is 1.89 days?

17. Dimensional Analysis • Use the equivalences given on the handout to do this one with me: • How many feet are in 2 meters?

18. Dimensional Analysis • How many meters are in 850 inches?

19. Dimensional Analysis • Whiteboard Practice

21. Dimensional Analysis

22. Homework

23. Objectives • Practice Dimensional Analysis

24. Practice Quiz • With your partner, write ten dimensional analysis problems for another team. • One partner, write the quiz paper. • Other partner, write the answer key INCLUDING ALL WORK. • In order to get a problem correct, they must show all work with units by every number, and have their answer in the correct sig figs.