1. SCIENTIFIC NOTATION & SIGNIFICANT FIGURES

2. Scientific Notation Multiple of Power of 10 Exponents
Decimals placed after the first digit
Can be used for any size number
zillions to picons

3. Examples of Scientific notation
1 000 g = 1.0 x 10 3 g
0.04 mL = x mL

4. Why use scientific notation?
Less chance of clerical mistake (0000?) very large & very small numbers
No zeros as placeholders

5. Why use scientific notation?
Leaves no doubt the zeros are part of an accurate measurement
Confirms the reliability of the instrument
( dm? cm ? mm? )

6. Multiplying and Dividing in Scientific Notation
Exponents represent the “powers of ten”
Same base number of “10”
WORK with exponents only

7. Multiply (x)
ADD (+) EXPONENTS

8. 1000 x =
x = =

9. When you Multiply (X) in Scientific Notation
ADD EXPONENTS =

10. Example
(3 x ) x ( 2 x 10 4) = ?

11. 1) Multiply coefficients (3 x 2) = 6 2) Add exponents 10 5 + 4 = 10 9

12. Final Answer
(3 x ) x ( 2 x 10 4) =
6 x
= 6 x

13. Sometimes the calculated answer is not in correct Scientific Notation:
Use Scientific Notation rules to fix
( 5 x 10 2 ) x ( 7 x 10 4 ) = x 10 6
35 = (3.5 x 10 1) x = 3.5 x 10 7

14. SUBTRACT (-) EXPONENTS Divisor - numerator
DIVISION
SUBTRACT (-) EXPONENTS
Divisor - numerator

15. Operate on the coefficients; Then subtract exponents
6 x = Problem: 2 x 10 5
x =
Operate on the coefficients;
Then subtract exponents

16. Subtract Exponents
6 x – =
3 x 10 2

17. Sometimes the answer is not in correct Scientific Notation
Use Scientific Notation rules to fix
4 x 10 5 = x =
8 x 10 2

18. Problem: 0.5 x 10 3 = Change to Sci Notation first, then finish
(5.0 x 10 –1) x =
5.0 x 10 – =
5.0 x 10 – = 5.0 x 10 2

19. Final Answer Correct scientific notation Measurement units
Correct number of significant figures

20. What is a significant figure (digit)?
Significant Figures
What is a significant figure (digit)?

21. Significant Figures 1. Any non-zero number
2. Zero between non-zero numbers
3. Zero after a decimal & a non-zero
4. Zero that has been physically counted

22. Significant Figures Not significant!!! 5. Zero as a place holder
1. Any non-zero number
2. Zero between non-zero numbers
3. Zero after a decimal & a non-zero
4. Zero that has been physically counted
Not significant!!!
5. Zero as a place holder
0.001 or 1 000

23. How many significant figures?
______
______
687 ______
______
______ ______ ______ ______

24. Practice rounding to the correct number!
What happens when your answer is not the right number of significant figures?
Practice rounding to the correct number!

25. Rounding to the right Sig Fig #
________________ (2)
________________ (3)
________________ (1)

26. Add or Subtract Line up vertically (up-down) Line up decimal places
Round to the lowest column that each has a measured number
NEVER fill in zeros when they were not measured
Remember units in answer

27. Find the sum to the correct sig fig
g g g g

28. Find the sum to the correct sig fig
g g g g

29. Add or Subtract 3 5. 1 1 5 g lowest common column is the tenths’ place
Round to 35.1 g

30. Practice! What is the perimeter of this figure?
1.2 cm cm cm cm

31. Practice!
What is the perimeter of this figure? cm
cm ~ cm cm cm cm

32. Remember do not add zeros in!
What is the perimeter of this figure? cm
cm ~ cm cm cm cm

33. Multiply or Divide
Count the number of Significant Figures in each measurement for the problem
Answer can only have the number of significant figures based on the
lowest # of sig figs part (measurement)

34. Multiply or Divide Example
7.6 cm x cm =
__ SF __ SF
Final answer can only have __ SF

35. Multiply or Divide Example
Final answer = cm 2
can only have __ SF so ~ 94 cm 2

36. Multiply or Divide Example
__ SF __ SF
Final answer can only have __ SF

37. Example Final Answer in Sig Fig
m x 4.2 m = m2
Round to 2 SF = 120 m2
Remember keep value of the number!
~ is about one hundred & twenty
Not 12! Think $$$$$

38. How do I know how many significant figures in my answer?
When Adding or Subtracting:
Adjust/Round to the lowest common column or lowest common decimal place
When multiplying/dividing
Adjust/round to the lowest number
(count each element) of sig figs in the problem

39. Practice

40. Practice

41. Practice