1. Significant Figures

2. There are two kinds of numbers:
Exact
Example: There
are twelve eggs
in a dozen
Inexact
Example: Any
measurment

3. Which of the following would be exact numbers?
The elevation of Breckinridge, Colorado (9600 ft) OR
The announced attendance at a football game (87,451)

4. If I were to measure a piece of paper…
I might get mm
You might get mm
Somebody else may get mm
Who is right ?????

5. Precision vs. Accuracy Precision Accuracy
-Refers to how closely individual measurements agree with each other
Accuracy
-Refers to how closely a measured value agrees with the correct value

6. Describe the following in terms of precision and/or accuracy…
Scenario #1: A chemistry student uses a graduated cylinder to measure the volume of a liquid and found the measurement to be 20.1 mL. The actual measurement was 27.3 mL.
Scenario #2: A man practices his dart throws in attempt to hit the bulls-eye! Here are his results:

7. ***It also includes one estimated digit.
Remember… There is uncertainty in all measurement, but the precision is determined by the measuring device. In any measurement, the number of significant figures is the number of digits believed to be correct by the person doing the measuring
***It also includes one estimated digit.

8. A rule of thumb:
Volumes should be read to 1/10 of the smallest division.
Example: If the smallest division is 10 mL, the volume would be read as having an error of 1 mL.

9. A Beaker
The smallest division is 10 mL-so we can read the volume to 1 mL.
The volume in the beaker is 47(+ or –) 1mL. It might be 46 mL or it might be 48 mL.
So, how many sig. figs.????
(2) - The “4” we know for sure, plus the “7” that we had to estimate.

10. A Graduated Cylinder
The smallest division is 1 mL so we can read the volume to 0.1 mL.
The volume could be read as 36.5 (+ or -) 0.1 mL.
The true volume could be 36.4 mL or 36.6 mL.
How many sig. figs???
(3) - The “3” and “6” we know for sure. The “5” had to be estimated.

11. A Buret
The smallest division is 0.1 mL so we can read the volume to 0.01 mL.
A good volume reading would be (+ or -) 0.01 mL.
An equally precise answer would be mL or mL.
How many sig. figs.????
(4) - The “2”, “0”, and “3” we know for sure, the “8” we had to estimate.

12. Significant figures are directly linked with measurement.
Conclusion:
Significant figures are directly linked with measurement.

13. Determining the number of sig. figs. in a number
Picture a map of the U.S….
If a decimal point is present in a number, count from the Pacific side.
Start counting with the first nonzero digit.
All digits from here to the end, including zeros, are significant.

14. Examples: 0.00682 Answer: 3 Answer: 2 1.0 Answer: 2 60. Answer: 2

15. If the decimal point is absent, start counting from the Atlantic side.
Start with the first nonzero digit.
All digits from here to the end, including zeros, are significant.

16. Examples: 60
Answer: 1
Answer: 3
603
Answer: 3
6030

17. Significant Figures in Calculations:
Rules for Multiplication and Division
The answer contains no more significant figures than the least accurately known number.

18. Examples: The number with the least # of sig. figs. has
2 sig. figs. Therefore, the
answer must have 2.
The number with the least
# of sig. figs. has 3 sig.
figs. Therefore, the
answer must have 3.

19. Rules for Addition and Subtraction
The number of sig. figs. is determined by the location of digits in the number with the largest uncertainty, not the number of significant figures in the number.

20. Examples: The least precise # is 2.02. It has sig. figs.
out to the hundredths
place. Therefore the
answer will have sig. figs.
place.
The least precise #
has decimals carried out 4
places. Therefore the
answer will have sig. figs.
carried out 4 decimal places.