1. Objectives
To learn how uncertainty in a measurement arises
To learn to indicate a measurement’s uncertainty by using significant figures
To learn to determine the number of significant figures in a calculated result
To learn the difference between accuracy and precision of a measurement

2. A. Uncertainty in Measurement
A measurement always has some degree of uncertainty.
How long is this nail?

3. A. Uncertainty in Measurement
Different people estimate differently.
Record all certain numbers and one estimated number.
Whenever we measure in chemistry we always record one extra decimal place (estimated number) beyond the markings on the measurement device.

4. B. Significant Figures Numbers recorded in a measurement.
All the certain numbers plus the first estimated number
Accuracy of a measurement – how close your number comes to the actual value
similar to hitting the bull's-eye on a dart board
Precision of a measurement – how close your repeated measurements come to each other (not necessarily the actual value)
how closely grouped are your 3 darts on the board (even if they’re not close to the bull's-eye)
It is possible for measurements to be precise but not accurate, just as it is possible to be accurate but not precise

5. Accuracy and Precision

6. B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
If the number has a decimal point, attack it from the left; if the number has no decimal point, attack it from the right.
Pass through all zeros until you hit the first non-zero number
The zeros you passed through are NOT significant digits!
Every number you encounter from now on is a significant digit!
Including any zeros!

7. Rules for Counting Significant Figures (Simple Method)
B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
Pacific
if a number has a Period (decimal), come from the Pacific side
Atlantic
if a period (decimal) is Absent, come from the Atlantic side

8. B. Significant Figures
Rules for Counting Significant Figures (Simple Method)
100 attack from _____ __ sig figs
attack from _____ __ sig figs
100. attack from _____ __ sig figs
attack from _____ __ sig figs
attack from _____ __ sig figs
attack from _____ __ sig figs
attack from _____ __ sig figs
x 104 attack from _____ __ sig figs
x attack from _____ __ sig figs
x 10-6 attack from _____ __ sig figs

9. B. Significant Figures
Rules for Counting Significant Figures (Hard Method)
Nonzero integers always count as significant figures significant figures

10. B. Significant Figures
Rules for Counting Significant Figures (Hard Method)
Zeros
Leading zeros - never count significant figures
Captive zeros - always count significant figures
Trailing zeros - count only if the number is written with a decimal point significant figure significant figures significant figures

11. B. Significant Figures
Rules for Counting Significant Figures (Both Methods)
Exact numbers - unlimited significant figures
Exact counts have unlimited (infinite) sig figs; they are obtained by simple counting (no uncertainty):
3 apples, 12 eggs, 1 mole
Conversion Factors have unlimited sig figs also:
1 in. = cm
1 mole = x 1023 atoms

12. B. Significant Figures

13. B. Significant Figures
Rules for Multiplication and Division
The number of significant figures in the answer is the same as in the measurement with the smallest number of significant figures.

14. B. Significant Figures
Rules for Addition and Subtraction
The number of decimal places in the result is the same as in the measurement with the smallest number of decimal places (not sig figs!).

15. B. Significant Figures
Rules for Counting Significant Figures
VITALLY IMPORTANT:
For the rest of the year, all calculations must include the correct number of significant figures in order to be fully correct!
on all homework, labs, quizzes, and tests, etc.
even if the directions don’t specifically tell you so