Transcript Tools for Chemists

Tools for Chemists
Measurements and Numbers
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.
Number of Pennies in a Jar
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Exact or Inexact?
Height of Pennies in a Stack
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Exact or Inexact?
The Great Penny Count
Tom’s Team
Sue’s Team
Max’s Team
100
105
114
107
108
118
125
107
115
132
104
117
Avg = 116 + 16
Avg = 106 + 2
Avg = 116 + 2
The Great Penny Count
Tom’s Team
Sue’s Team
Max’s Team
100
105
114
107
108
118
125
107
115
132
104
117
Avg = 116 + 16
Avg = 106 + 2
Avg = 116 + 2
Machine Count = 116.
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
107
115
132
104
117
Avg = 116 + 16
Avg = 106 + 2
Avg = 116 + 2
Are errors random? Systematic?
Does Your Measuring Tool Matter?
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Try it!
Uncertainty
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
What creates it?
How do we indicate it?
The “Recording Uncertainty”
Rule
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Record all digits which you can read with
certainty off the measuring device, plus one
estimated digit. The resulting numbers will all
be significant.
Try It!
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Student Balance
22
23
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Research Balance
22.5
Significant Figures
The Horse and the Ribbon
1270 lbs
0.19 lbs
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How much do they weigh together?
1270 lbs
+
0.19 lbs
1270.19 lbs
Communicating Significance
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Significant Numbers and Place holders
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Non-zero digits
Zeros
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Leading: 0.0256
Confined: 20056
Trailing: 347000 or 347000.
Practice
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72.0
51.700
0.03400
3.060
450
360,000
Vocabulary Summary

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Exact Number
Inexact number
Precision
Accuracy
Random error
Systematic error
Uncertainty
Significant figures
Sig Figs and Mathematical
Operations
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Rounding
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< 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.
Rounding Practice
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Round to 3 sig figs
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72.311
72.382
72.353
64.453
72311
72382
72356
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: 62.059 in x 72.6 in = 4505.4834 in2
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?
Small Group Practice
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1.
2.
3.
4.
5.
6.
Carry out the following operations and write
the answer with correct sig figs, rounding
properly.
350.00 x 0.00072
3554/2.22
237 + 37 + 7
4.111 - 3.07
1.20 x (3.45 + 4.5)
0.500 x0.1723 x (0.6772 + 0.31)
Assignment

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Read 2.1-2.6
Do Problems in range 2.1 – 2.77