1. Measurements and Numbers
Tools for Chemists
Measurements and Numbers

2. The King’s Foot
The story of a King, a Queen, and a carpenter who almost lost his life for the lack of a system of standard measurements.

3. Number of Pennies in a Jar
Exact or Inexact?

4. Height of Pennies in a Stack
Exact or Inexact?

5. The Great Penny Count Tom’s Team Sue’s Team Max’s Team 100 105 114 107
108
118
125
115
132
104
117
Avg =
Avg =
Avg =

6. Which team is accurate? Precise?
The Great Penny Count
Tom’s Team
Sue’s Team
Max’s Team
100
105
114
107
108
118
125
115
132
104
117
Avg =
Avg =
Avg =
Machine Count = 116.
Which team is accurate? Precise?

7. Are errors random? Systematic?
The Great Penny Count
Tom’s Team
Sue’s Team
Max’s Team
100
105
114
107
108
118
125
115
132
104
117
Avg =
Avg =
Avg =
Are errors random? Systematic?

8. Does Your Measuring Tool Matter?
Try it!
Put a line approx. .5 m long on board. Get first student to measure w meter stick with only dm marked, second to use stick with cm, third stick with mm.

9. Uncertainty
What creates it?
How do we indicate it?

10. The “Recording Uncertainty” Rule
Record all digits which you can read with certainty off the measuring device, plus one estimated digit. The resulting numbers will all be significant.

11. Try It!
Student Balance
Research Balance
22.5

12. The Horse and the Ribbon
Significant Figures
The Horse and the Ribbon
0.19 lbs
1270 lbs

13. How much do they weigh together?
1270 lbs
lbs
lbs

14. Communicating Significance
Significant Numbers and Place holders
Non-zero digits
Zeros
Leading:
Confined: 20056
Trailing: or

15. Practice
72.0
51.700
3.060
450
360,000

16. Vocabulary Summary Exact Number Inexact number Precision Accuracy
Random error
Systematic error
Uncertainty
Significant figures

17. Sig Figs and Mathematical Operations
Rounding
< 5: drop
> 5 round up
= 5: Round up if odd, drop if even
If rounding to left of decimal, replace dropped digits with placeholder zeros.
Do examples

18. Rounding Practice Round to 3 sig figs 72.311 72.382 72.353 64.453
72311
72382
72356

19. Multiplying and Dividing with Sig Figs
The number of sig figs in the answer (product or quotient) equals the number of sig figs in the multiplier or divisor with the fewest sig figs.
Huh?
Area: in x 72.6 in = in2

20. Addition and Subtraction
The precision of the number resulting from an addition or subtraction operation is the same as that of the least precise number used to carry out the operation.
Huh? Huh?

21. Small Group Practice
Carry out the following operations and write the answer with correct sig figs, rounding properly. x
3554/2.22
1.20 x ( )
0.500 x x ( )

22. Assignment
Read
Do Problems in range 2.1 – 2.77