1. J. Gabrielse Δ Changing Units

2. J. Gabrielse The Problem Example: You need to know an answer in μg but your scale measures in mg. Sometimes you need a different metric prefix than you have.

3. J. Gabrielse Math Fact # 1 Any quantity multiplied or divided by 1 does not change. ( )(1) =

4. J. Gabrielse Math Fact # 2 Any quantity divided by itself is equal to 1.

5. J. Gabrielse Math Fact # 2 EXAMPLE Any quantity divided by itself is equal to 1. It doesn’t matter if it is written differently! ?

6. J. Gabrielse Math Fact # 2 EXAMPLE Any quantity divided by itself is equal to 1. It doesn’t matter if it is written differently! ?

7. J. Gabrielse Math Fact # 2 Example = 1 Any quantity divided by itself equals 1. Any quantity multiplied by 1 does not change.

8. J. Gabrielse The Problem Example: You measure 1,435 mg but you need to know in μg. Sometimes you need a different metric prefix than you have.

9. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Turn your metric prefix into a power of ten.

10. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Turn your metric prefix into a power of ten.

11. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Math Fact # 1: Any quantity multiplied by 1 does not change. (1) Multiply by a fraction equal to 1.

12. J. Gabrielse STOP Complete Metric Conversion Factors Worksheet

13. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Math Fact # 2: Any quantity divided by itself is equal to 1. 1 μg = 1·10 -6 g Multiply by a fraction equal to 1.

14. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Multiply by a fraction equal to 1 Pick the fraction so: old units cancel out & new units are left

15. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Cancel Out old units cancel out & new units are left

16. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Let your calculator do the rest

17. J. Gabrielse The Solution: Use Math Facts 1 & 2 to Change Units Rewrite

18. J. Gabrielse Notes

19. J. Gabrielse Example: How many ms are in 560 ps? Write what you are given.

20. J. Gabrielse Example: How many ms are in 560 ps? Turn the SI prefix into a power of ten.

21. J. Gabrielse Example: How many ms are in 560 ps? Multiply by a fraction equal to 1

22. J. Gabrielse Example: How many ms are in 560 ps? Note: I put s (the old unit) on the bottom so it will cancel out Multiply by a fraction equal to 1

23. J. Gabrielse Example: How many ms are in 560 ps? Note: I put ms (the new unit) on the top so it will be left over Multiply by a fraction equal to 1

24. J. Gabrielse Example: How many ms are in 560 ps? Note: Use SI prefixes to pick numbers. The top of the fraction has to equal the bottom of the fraction. Multiply by a fraction equal to 1 1 ms = 1·10 -3 s

25. J. Gabrielse Example: How many ms are in 560 ps? Cancel

26. J. Gabrielse Example: How many ms are in 560 ps? Write the answer Note: your calculator can do all the hard work