1. Conversions, Rounding, Sig Figs…Oh MY!!!

2. Accuracy and Precision

3. Accuracy
How close did you get to the true or accepted value?

4. Precision
How close a series of measurements are to one another?

5. Error
Deviation from the accepted value
how much you “missed” by

6. Percent Error
The amount you “missed” by, expressed as a percentage of the accepted value
VExperimental - VAccepted
VAccepted
% Err =
x 100%

7. % Error Practice Accepted Density of sucrose is 1.59 g/cm3
Your three experimental trails were: 1.40 g/cm3, 1.68 g/cm3, and 1.45 g/cm3
Use the equation on the previous slide to calculate the percent error of your trials.
11.9% % %

8. Significant Figures
The numbers we use in science are measurements
Significant figures result from our inability to measure precisely

9. Significant Figures
All certain digits
One final uncertain digit (estimated)

10. 16.

11. 16. 7 mL

12. “Sig Figs*”
Made
Easy
*Significant Figures

13. If a decimal point is present:
Pacific
Atlantic
Pacific Atlantic
If a decimal point is present:
If a decimal point is absent:
Pacific Atlantic

14. Decimal point is present:
Pacific
Atlantic
Decimal point is present:
4.3
2 SF
3 SF
6 SF

15. Decimal point is absent:
Pacific
Atlantic
Decimal point is absent:
3 SF
153
1 000
4 SF
1 SF

16. Adding and Subtracting
30.254
30.254 –
+ 1.22
31.474
 31.47 

17. Multiplying and Dividing
Sig figs limited by the least precise measurement
Exact conversion factors do not limit sig figs
30.45 m x 1.3 m = m2  40. m2
4 SF
2 SF
2 SF

18. PRACTICE
1.35 m x m =
55.46 g g =
1 035 m2  42 m =
3.33 m2
26.6 g
25 m

19. Page 23
DIMENSIONAL ANALYSIS

20. DIMENSIONAL ANALYSIS
Treat units in calculations as if they were algebraic factors

21. DIMENSIONAL ANALYSIS
Units must always be included in the results of calculations
Units also help you to check your work as you go
= 1
weeks weeks year

22. Conversion Factor A ratio equal to one
Used to convert from one dimensional unit to another

23. Examples 1000m = 1 km 1km/1000m or 1000m/1km Denisty = 2.5g/mL
2.5g/mL 1mL/2.5g

24. “How many meters are in 3.75 km?”
THE PROBLEM
“How many meters are in 3.75 km?”

25. STEP #1: Restate the Problem
“How many meters are in 3.75 km?”
? m = 3.75 km

26. STEP #2: Begin with the Known Quantity
? m = 3.75 km
3.75 km

27. STEP #3: “ Make a Conversion Grid”
? m = 3.75 km
3.75 km 1

28. STEP #4: Find the Correct Units for the Conversion Factor
? m = 3.75 km
Units to survive on top km m
3.75 km 1
Units to cancel
on bottom*
* opposite

29. STEP #5: Attach Numbers to Units
? m = 3.75 km
1 km = m
1 000 m
3.75 km 1 km 1

30. ? m = 3.75 km m STEP #6: Do the Math! = 1 000 3.75 km 1 km 1 OR
Multiply 3.75 times (1 000  1)
Multiply (3.75 x 1 000) then  1 OR

31. ? m = 3.75 km m 3 750 m STEP #7: Tah-Dah! = 3.75 km 1 000 1 km 1
Don’t forget: Your answer must contain units!

32. How many . . .
Millimeters in meters
Kilograms in 873 grams
1,125ft/min to mi/hr

33. How many…
decaliters in 35 kL?
mg in .258 hg
km in m