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Transcript of Davis. 1.Measurements 2.Understand Uncertainty in Measurement 3.Know, understand, and be able to...
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Chemistry 139
Davis
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Chapter 1 – Goals
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Chapter 2 - Goals
1. Measurements2. Understand Uncertainty in Measurement3. Know, understand, and be able to apply
significant figures to calculations.4. Know, understand, and be able to apply
scientific notation to calculations.
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Measurement…
Defined: determination of the quantities related to an object.
Dimensions Volumes TimeEtc…
Requires that someone actually
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I’m certainly uncertain…Two terms:1. Exact numbers – • Exactly • Exactly • Exactly _____ desks in this room.
2. Inexact numbers –
•Flaws in •Uncalibrated•User
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Accuracy and Precision
DefinedPrecision –
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Accuracy –
Volume measurements for a titration:
Trial 1 = 25.5 mLTrial 2 = 25.6 mLTrial 3 = 25.5 mL
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Is this accurate or precise or…?
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Sample data
Mass readings for a magnesium sample:
Trial 1 Trial 2 Trial 30.155 g 0.157 g 0.135 g
Evaluate these measurements for precision and accuracy
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From the book:
Two teams of three students count birds sitting on a power line. Team counts are:
Team A Team BMarjorie: 71 Howard: 76Marlene: 74 Alice: 76Kathleen: 71 Sharon: 67
Who was most accurate?Which team was most accurate?Which team’s count was most precise?
The actual count was 76 birds.
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Uncertainty in MeasurementWhy are digits in measurements uncertain?
1. Instruments • • Differences
2. Always involves estimation Choose the right instrument for the job
Volumetric vs ‘to hold’ glassware May be estimated for you (electronic
scales) Scale is marked but you estimate the in-
between
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Glassware/proper equipment
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Measurements
MUST
Which is correct?
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Significant Figures (Digits)…
Method to deal with All digits known
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What Sig Figs mean…
All KNOWN numbers
15023.557
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Significant DigitsThe Rules – Memorize these.All non-zeros are A zero is significant when :
It is It is
A zero is not significant when:It is It is at
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Significant Digits - PRACTICE
How many significant digits?1. 54.232. 23.000053. 0.00044. 350005. 0.0005046. 45.6232007. 5,000,0008. 4,000,000.1
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Calculations with Significant Figures
Add/subtract –
Multiply/divide –
Only round after problem is complete
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Practice Add/Subtract
122.53 + 6.448 + 145.3 274.278
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Significant Digits - Calculations
Addition and SubtractionRound answer to have final digit in the SAME PLACE as the last digit in the LEAST ACCURATE MEASUREMENT
1.21 + 5.002 + 10. = 34.5 + 12.45 + 23.0505 = 186.31 + 11.1 = 12.0231 + 3.86 = 0.100012 + 120. = 1200 + 12 + 15 + 0.5 =
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Significant Digits - Calculations
Multiplication and DivisionThe answer has as many sig figs as the number with the fewest sig figs
14.8 x 3.1 = 18.2 x 3.0 =52/1.5 =321.868783 x 1 =2400 x 2.123 =15000/12.354 =
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Practice Multiply/Divde
452.11 x 78.5 = 35490.635
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Practice
1524.57 / 32.15 = 47.4205287714
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Significant Figures and Exact Numbers
Exact numbers are never used to determine the number of significant figures to report in your answer.
6.25 ft * 1 mile 5280 ft
= 0.00118371212 mile
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Scientific Notation
Convenient way of writing very large or very small numbers and showing only significant figuresNumber between 5120 becomes Move decimal point in original number to make number 1-10Move left = Move right =
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Scientific Notation Practice
123,000 =0.000045 =23.45 =0.0000000003 =1,000,000 =
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Scientific Notation and Significant Figures
Express the number 275,364,145 with:
4 sig fig:
2 sig fig:
6 sig fig:
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Scientific Notation
Math with:Use the EE or EXP button on your calculator.For example: