1. Significant Figures
A significant figure (sig fig) is a measured or meaningful digit
Sig figs are made of all the certain digits of a measurement plus the first uncertain digit (the extra digit you had to guess remember?)

2. Significant Figures Non-zeroes are significant
Zeroes between sig figs are significant
- e.g. 101 (3), (5)
3. Zeroes at the end of numbers without decimals are not significant
- e.g. 10 (1), 100 (1), 1100 (2), (3)

3. Significant Figures
4. Zeroes at the end of numbers with decimals are significant
- e.g (4), 1.00 (3), (5)
Zeroes in front of numbers with decimals are not significant
- e.g (1), (2), (3)

4. Practice
Hebden p.37 #55

5. Problem with Rule #3
How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant?

6. Problem with Rule #3
How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant?
The bad way: add a decimal at the end
10,000.
Do not do this in Chem 11…or ever
But you still need to recognize they mean 5 sig figs when that’s written

7. Problem with Rule #3
How can we express 10,000 as 5 sig figs if the zeroes at the end are not significant?
The good way: use scientific notation (exponents)!

8. Problem with Rule #3
How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant?
Use scientific notation (exponents)!
10,000 = ? x 10?

9. Problem with Rule #3
How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant?
Use scientific notation (exponents)!
10,000 = x 10?

10. Problem with Rule #3
How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant?
Use scientific notation (exponents)!
10,000 = x 104

11. Problem with Rule #3
How can we express 10,000 in 5 sig figs if the zeroes at the end are not significant?
Use scientific notation (exponents)!
10,000 = x 104
Rule #4: Zeroes at the end of numbers with decimals are significant

12. Scientific Notation
When you move a decimal right, you must multiply by 0.1
= x 0.1 x 0.1 x 0.1 x 0.1
= x 10-1 x 10-1 x 10-1 x 10-1
= x 10-4
When you move a decimal left, you must multiply by 10
12345 = x 101 x 101 x 101 x 101
= x 104

13. Standard Notation
These are the “regular” numbers without the exponents (the opposite if you will)
You need to know how to convert b/t the 2
Positive exponent: move decimal right
3.385x102  338.5
Negative exponent: move decimal left
3.385x10-2 

14. Practice Conversions Express the following in scientific notation
10.124
Express the following in standard notation
7.002 x 10-3
1.63 x 102
x 10-2

15. Rounding Some of us are used to always rounding 5s up
E.g  21
In Chem 11, we will round 5s to the nearest even number
E.g  20 (20 is nearer than 22)
E.g  22 (22 is nearer than 20)

17. Arrow Rule for Sig Figs
If there is decimal: arrow starts from the left
  sig figs
If no decimal: arrow starts from the right
 00 7 sig figs
Arrow moves until it hits a non-zero
Count the numbers that are left when the arrows stops and those are your sig figs
4 or 5 volunteers to help demonstrate please

18. Arrow Rule for Sig Figs Form 4 lines
Inside lines face out, outside lines face in
Each line is a team
One team makes up a number while the other team uses the arrow rule to determine the number of sig figs in that number
Switch roles after 1 person answers
Everyone must answer at least once

19. Arrow Rule for Sig Figs Use the cards I’ve given to make numbers
Move around to change the order
Can hold 0, 1 or 2 cards in your hands
Hold them up and show the other team when you’re done so they can answer
Tally up scores and the winners can go against each other

20. Arrow Rule for Sig Figs +1 point for every correct answer
-1 point for every “bad” number made up
E.g
184.
Try to let the arrow figure it out themselves
Remember: it’s not about the outcome, it’s about the process

21. Homework
Sig figs worksheet #1 and 5

22. Calculations Using Sig Figs

23. Multiplication & Division
Round the answer to the least number of sig figs contained in the question
2.391 x 4.5 = ?

24. Multiplication & Division
2.391 x 4.5 = ?

25. Multiplication & Division
2.391 x 4.5 = ?
4 sig figs x 2 sig figs = ?

26. Multiplication & Division
2.391 x 4.5 = ?
4 sig figs x 2 sig figs = ?
4 sig figs x 2 sig figs = 2 sig figs

27. Multiplication & Division
2.391 x 4.5 = ?
4 sig figs x 2 sig figs = ?
4 sig figs x 2 sig figs = 2 sig figs
2.391 x 4.5 =

28. Multiplication & Division
2.391 x 4.5 = ?
4 sig figs x 2 sig figs = ?
4 sig figs x 2 sig figs = 2 sig figs
2.391 x 4.5 =  11 (2 sig figs)

29. Multiplication & Division
Practice: Hebden p.39 #56

30. Addition & Subtraction
Round off the answer to the least precise number in the problem
Remember that least precise means fewest decimal places

31. Addition & Subtraction
= ?

32. Addition & Subtraction
= ?
3 decimals + 2 decimals = ?

33. Addition & Subtraction
= ?
3 decimals + 2 decimals = 2 decimals

34. Addition & Subtraction
= ?
3 decimals + 2 decimals = 2 decimals
=  round to 2 decimals

35. Addition & Subtraction
= ?
3 decimals + 2 decimals = 2 decimals
=  round to 2 decimals
=  2 decimals, 4 sig figs

36. Addition & Subtraction
2.45 x x 104 = ?
Must convert to the same exponent to see which is less precise
Always convert the smaller exponent into the larger one

37. Addition & Subtraction
2.45 x x 104 = ?
2.45 x x 105 = ?

38. Addition & Subtraction
2.45 x x 104 = ?
2.45 x x 105 = ?
2.45 x x 105 = 2.76 x 105

39. Practice Hebden p.28-34 #42-50, p.37 #55 (was HW)
Add/subtract: Hebden p.40 #57
All operations: Hebden p. 40 #58-59
Hand in sig figs worksheet (online).