1. Scientific Notation

2. N x 10n Scientific Notation
A convenient way to express very large or very small numbers
N x 10n
Coefficient
Must be 1≤N<10
Exponent
(+)—large number
(-)—small number

3. Taking #’s out of Sci. Notation
For POSITIVE exponents, move the decimal to the RIGHT…positive exponents make LARGE amounts.
For NEGATIVE exponents, move the decimal to the LEFT…negative exponents make SMALL amounts.
9.998 x x x x 10-6

4. Putting #s into Sci. Notation
Move the decimal until it is positioned between the first and second NON ZERO digits. Remember that positive exponents make LARGE amounts and negative exponents make SMALL amounts.
41,000,000   50

5. Practice
1-20

6. Multiplying with Sci. Notation
Multiply the coefficients
Add the exponents
Adjust the answer so that the coefficient is 1 ≤N<10
(4.0 x 102)(2.0 x 10-12)

7. (3.0 x 106)(8.0 x 10-15)

8. Dividing with Sci. Notation
Divide the coefficients.
Subtract the exponents.
Adjust the answer so that the coefficient is
1 ≤ N<10.
5.0 x 107
2.0 x 103

9. 2.0 x 1012
4.0 x 10-3

10. Practice
21-28

11. Accuracy & Precision

12. All available digits + 1 estimated digit A. 87.5oC B. 13.0 mL
Notes sheet #1 and 2
All available digits + 1 estimated digit
A oC
B mL
C cm
The estimated digit is given in red.

13. Accuracy the agreement between experimental data and a known value.
Example: Which one is more accurate?
Before
After
Sand
20.00 g
19.59 g
Salt
3.21 g

14. Precision how well experimental values agree with each other
Example: Which data is most precise?
Before
After Group 1
After Group 2
After Group 3
Sand
20.00 g
19.59 g
15.98
9.26
Salt
10.21 g
10.23
10.19
Is it accurate?

15. Draw a target diagram that shows precision but not accuracy

16. Draw a target diagram that shows accuracy but not precision

17. Draw a target diagram that shows both accuracy and precision

18. #7
Each of five students used the same ruler to measure the length of the same pencil. These data resulted: cm, cm, cm, cm, and cm. The actual length of the pencil was cm. Describe whether accuracy and precision are each good or poor for these measurements.

19. A measurement was taken three times. The correct measurement was 68
A measurement was taken three times. The correct measurement was 68.1 mL. Circle whether the set of measurements is accurate, precise, both, or neither.
78.1 mL, 43.9 mL, 2 mL
accurate precise both neither
68.1 mL, 68.2 mL, 68.0 mL
98.0 mL, 98.2 mL, 97.9 mL
72.0 mL, 60.3 mL, 68.1 mL
accurate precise both neither

20. Significant Figures Part 1: Counting Sig figs

21. Decimal--Left 0.004703 has 4 significant digits.
 If a number has a decimal, count all digits starting with the first non-zero digit on the left.
Examples:
has 4 significant digits.
18.00 also has 4 significant digits.

22. No decimal--right
If there is no decimal , count all digits starting with the first non-zero digit on the right.
Examples:
140,000 has 2 significant digits.
20060 has 4 significant digits.

23. In both cases, start counting with the first non-zero digit.
00.015
15000

24. Complete Sig Fig Self Test
Now Try it on your paper
a) 3.57 m _________
b) g _________
c) m3 _________
d) kg _________
e) mL _________
f) 30 atoms _________
g) g/mL _________
h) s _________
i) 810 oC _________
j) mol _________
k) km _________
l) cm3 _________
Complete Sig Fig Self Test

25. Significant Figures Part 2: math with Sig figs

26. This leads to 2 rules: add/subtract & multiply/divide
Math with sig figs
Calculations shouldn't have more precision than the least precise measurement.
This leads to 2 rules: add/subtract & multiply/divide

27. Addition and Subtraction
The answer should not have more decimal places than the number with the least decimal places.
Example: = =

28. Addition Practice
A) = B) = C) = D) = E) 87.9 – 20 = F) – 119 =

29. Top half of practice sheet (Addition and Subtraction sets only)
Assignment
Top half of practice sheet (Addition and Subtraction sets only)

30. 2. For Multiplication and Division
The answer should not have more significant figures than the number with the least amount of significant figures.
Example: 502 x 3.6 =
1800

31. Multiplication Practice
A) x 402 = B) x 75.2 = C) / 45 = D) 5300 / 456 = E) 4590 / 1234 = F) 141 x =