1. Section 3-2 Uncertainty in Measurements

2. Ideally, measurements are both correct and reproducible.
Accuracy – measure of how close a measurement comes to the actual value
Precision – measure of how close a series of measurements are to each other.

4. Error and Percent Error
Error = accepted value – experimental value
Percent error = error x 100
accepted value

5. Significant Figures in Measurements
Significant figures – measurement includes all the digits that are known plus last digit that is estimated.

6. Rules – applies to measurements, not counting
All nonzeros are significant.
Zeros between significants are significant.
Placeholders are not significant.
Final zeros to the right of the decimal are significant.

7. Calculation with significant digits
Multiplication and Division-
-round to number that is least precise number of digits of the numbers used.
Addition and Subtraction-
-round to least precise decimal place of the numbers added.

8. How many significant figures in the following measurements?
meters
meters
meters
x 104
meters
meters
meters

9. Round the following to the # of sig figs in ( ).
meters (4)
meter (2)
64.32 x 10-1 (1)
8792 meters (2)

10. Significant Figures in Multi-step Problems
Do not round on intermediate steps but apply significant figure rules to final answer.

11. Rounding Rules Above 5 - - round up Below 5 -- round down
Exactly 5 (such as 2.45 round to 2 significant digits).
Number to the left is even-leave it
Number to the left is odd-round up
Above example = ???
2.4

12. Round the following to 3 Significant Figures
2.235 cm m
56.55 g
7.145 ml s