1. Scientific Notation, Significant Figures and Metric
9/10/14

2. Scientific Notation The components of scientific notation:
8.238 x 10-31
“8.238” is the coefficient
“x 10” is the base
“-31” is the exponent
Where the coefficient has to be a number:
1 ≤ coefficient < 10

3. Significant Figures
Significant Figures (sig. figs.): the number of digits that carry meaning contributing to the precision of a measurement or calculated data.

4. Precision and Accuracy
Low Accuracy High Precision
High Accuracy High Precision
High Accuracy Low Precision

5. Significant Figures
Each recorded measurement has a certain number of significant figures.
Calculations done on these measurements must follow the rules for significant figures.
Placeholders, or digits that have not been measured or estimated, are not considered significant.

6. Significant Figures
There are 5 rules to determine which zeros in a number are significant or not.

7. Rules for Significant Figures
Rule #1: All non-zero digits (1-9) are significant. For example: 453 number of sig figs______ number of sig figs______

8. Rules for Significant Figures
Rule #2: Zeroes between non-zero digits are significant. For example: number of sig figs______ number of sig figs______

9. Rules for Significant Figures
Rule #3: If a number ends in zeroes, the zeroes to the right are NOT significant IF there is NO decimal point present. For example: number of sig figs______
number of sig figs______ number of sig figs______

10. Rules for Significant Figures
Rule #4: Zeroes to the left of the first non-zero digit are NOT significant. For example: number of sig figs______ number of sig figs______ number of sig figs______ number of sig figs______

11. Rules for Significant Figures
Rule #5: If a number ends in zeroes to the right of the decimal point, those zeroes are significant. For example:
2 number of sig figs______ number of sig figs______ number of sig figs______ number of sig figs______
{This signifies greater precision.}

12. The Atlantic - Pacific Rule for Significant Figures
When determining the number of significant figures ask the question:
“Does the number have a decimal point?” (YES or NO answer)
If YES, then think of “P” for Present and the Pacific ocean
If NO, then think of “A” for Absent and the Atlantic ocean

13. The Atlantic and Pacific Rule for Significant Figures

14. The Atlantic and Pacific Rule for Significant Figures
"P" for "Present".  This means that we imagine an arrow coming in from the Pacific ocean, from the left side
"A" for "Absent".  This means that we imagine an arrow coming in from the Atlantic ocean, the right side.

15. The Atlantic and Pacific Rule for Significant Figures
Look for the first non zero number starting from that direction
That number, and all other numbers following it are considered to be significant
For “P” the numbers to the right of the first non zero number
For “A” the numbers to the left of the first non zero number

16. Examples
1) ) ) )

17. Rounding Sig. Figs.

18. Rounding Sig. Figs.
The goal is to round the number to the appropriate amount of sig. figs. without changing the value too much.

19. Rounding Calculations
For multiplication and division:
Round to the number that has the least amount of sig. figs.
Note: There are different rules for addition and subtractions

20. Rounding Sig. Figs.
Look at the left most non-zero numbers to identify the ones that you will keep
If the number to the right of the last digit is 5 or higher round up, 4 or lower round down
LEFT of Decimal: Replace non significant figures with zeroes if they are to the LEFT of the decimal point
RIGHT of Decimal: Drop non significant figures if they are to the RIGHT of the decimal point

21. Examples in Your Notes 1) 43252202 to 3 sig figs
(5 = 5 so round up and replace non sig. figs. with zeros)
2) to 4 sig figs
(4 < 5 so round down and drop non sig. figs.)

22. Examples in Your Notes 3) 47.66666667 to 5 sig figs
(6 > 5 so round up and drop non sig. figs.)
47.667
4) to 2 sig figs
(4 < 5 so round down and replace non sig. figs. with zeroes AND drop non sig. figs. to the right of the decimal)
790000

23. Rounding Calculations Examples
5.50 × 2.00
2.437 × / 4.5 × 1014

24. Rounding Calculations Examples
5.50 × 2.00
Calculator reads “11”
Answer is 11.0
2.437 × / 4.5 × 1014
Calculator reads “ E-27”
Answer is 5.4 × 10-27

25. Lab Rubric 1st column “Self Evaluation”
2nd column “Peer Evaluation” (student initials)
3rd column “Self Evaluation #2”
4th column “Teacher Evaluation”

26. Metric Units (base unit)
Quantity
Base Unit
Symbol
Length
Meter m
Mass
Gram g
Time
Second s
Volume
Liter L
Force
Newton N
Energy
Joule J

27. Metric Prefixes *Learn highlighted ones!
Prefix Symbol
Multiplier
mega- M
106 ( )
kilo- k
103 (1000)
BASE UNIT -
100 (1)
centi- c
10-2 (0.01)
milli- m
10-3 (0.001)
micro- μ
10-6 ( )

28. Extra Practice

29. Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 98070001) 2) 3) 4) 5) 6) 7) 8)

30. Sig. Figs. Practice Ex 1) 0.020110 Ex 2) 730800 1) 48001 2) 98070001) 2) 3) 4) 5) 6) 7) 8)
Ex 1) (5 sig. figs.)
Ex 2) (4 sig. figs)
1) (5 sig. figs.)
2) (4 sig. figs.)
3) (4 sig. figs.)
4) (5 sig. figs.)
5) (2 sig. figs.)
6) (5 sig. figs.)
7) (7 sig. figs.)
8) (6 sig. figs.)

31. Rounding Practice 0.0018563333 to 3 sig. figs.

32. Rounding Practice 0.0018563333 to 3 sig. figs.
4780
568.79
0.022
4.700