Transcript Measurements and Their Uncertainty

3.1
Measurements and Their
Uncertainty
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Using and Expressing
Measurements
Using and Expressing Measurements
How do measurements relate to
science?
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Using and Expressing
Measurements
A measurement is a quantity that has both a
number and a unit.
it is important to be able to make
measurements and to decide whether
a measurement is correct.
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Scientific Notation
http://www.youtube.com/watch?v=H578q
UeoBC0
Scientific Notation Pre-Test
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Scientific Notation
210, 000,000,000,000,000,000,000
This number is written in decimal
notation. When numbers get this large,
it is easier to write it in scientific
notation
Where is the decimal in this number?
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210, 000,000,000,000,000,000,000.
Decimal needs moved to the left between
the 2 and the 1 ( numbers that are
between 1-10)
When the original number is more than 1
the exponent will be positive.
2.1 x 1023
Exponents show how many places
decimal was moved
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Express 4.58 x 106 in decimal notation
Remember the exponent tells you how many
places to move the decimal. The exponent is
positive so the decimal is moved to the right
4,580, 000
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express the number 0.000000345 in
scientific notation.
Decimal moved between first 2 non-zero
digits and will be moved 7 times
3.45 x 10 -7
The exponent is negative because the
original number is a very small number
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Express the following
in scientific notation
or standard notation
1. 74171.7
2. .07882
3. 526
4. .0000573
5. 5.8 x 10
-7
6. 5.256 x 106
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Accuracy, Precision, and Error
Accuracy, Precision, and Error
What is the difference between
accuracy and precision?
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Accuracy, Precision, and Error
Accuracy and Precision
• Accuracy is a measure of how close a
measurement comes to the actual or true
value of whatever is measured.
• Precision is a measure of how close a
series of measurements are to one another.
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Accuracy, Precision, and Error
To evaluate the accuracy of a
measurement, the measured value
must be compared to the correct
value.
To evaluate the precision of a
measurement, you must compare the
values of two or more repeated
measurements.
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Accuracy, Precision, and Error
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Accuracy, Precision, and Error
Determining Error
• The accepted (Known) value is the correct
value based on reliable references.
• The experimental value is the value
measured in the lab.
• The difference between the experimental
value and the accepted value is called the
error.
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Accuracy, Precision, and Error
The percent error is the absolute value of the
error divided by the accepted value, multiplied
by 100%.
Experimental – known
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Accuracy, Precision, and Error
Percent Error
(Error)
3.00-measurement X 100
3.00
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Accuracy, Precision, and Error
Just because a measuring device works, you
cannot assume it is accurate. The scale below
has not been properly zeroed, so the reading
obtained for the person’s weight is inaccurate.
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REVIEW
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REVIEW
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% ERROR
The density of aluminum is known to be
2.7 g/ml. In the lab you calculated the
density of aluminum to be 2.4 g/ml.
What is your percent error?
• What is 5.256X10-6 in standard format
• What is 118000 in scientific notation
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Significant Figures in Measurements
All measurement contains some degree of
uncertainty.
The significant figures in a measurement
include all of the digits that are known, plus a
last digit that is estimated.
Measurements must always be reported to the
correct number of significant figures
Using pages 66-72 – fill in your notes
regarding the rules of significant figures
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Counting Significant Figures
Number of Significant Figures
38.15 cm
5.6 ft
65.6 lb
122.55 m
4
2
___
___
Complete: All non-zero digits in a measured
number are (significant or not significant).
Timberlake lecture plus
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Leading Zeros
Number of Significant Figures
0.008 mm
1
0.0156 oz
3
0.0042 lb
____
0.000262 mL
____
Complete: Leading zeros in decimal numbers
are (significant or
not significant).
Timberlake lecture plus
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Sandwiched Zeros
Number of Significant Figures
50.8 mm
2001 min
0.702 lb
0.00405 m
3
4
____
____
Complete: Zeros between nonzero numbers
lecture
plus
23
are (significant Timberlake
or not
significant).
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Trailing Zeros
Number of Significant Figures
25,000 in.
200 yr
2
1
48,600 gal
3
25,005,000 g
____
Complete: Trailing zeros in numbers
without decimals are (significant or not
significant) if they are serving as place
Timberlake lecture plus
holders.
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Learning Check
A. Which answers contain 3 significant
figures?
1) 0.4760
2) 0.00476 3) 4760
B. All the zeros are significant in
1) 0.00307 2) 25.300
3) 2.050 x 103
C. 534,675 rounded to 3 significant figures is
1) 535
2) 535,000
3) 5.35 x 105
Timberlake lecture plus
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Significant Figures in Calculations
 A calculated answer cannot be more
precise than the measuring tool.
 A calculated answer must match the least
precise measurement.
 Significant figures are needed for final
answers from
1) adding or subtracting
Timberlake
plus
2) multiplying
or lecture
dividing
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Adding & Subtracting
The answer has the same number of
decimal places as the measurement with
the fewest decimal places.
25.2
one decimal place
+ 1.34
two decimal places
26.54
answer 26.5 one decimal place
Timberlake lecture plus
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Learning Check
In each calculation, round the answer to the
correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
1) 256.75
B.
2) 256.8
3) 257
58.925 - 18.2 =
1) 40.725
2) 40.73
3) 40.7
Timberlake lecture plus
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Solution
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B.
58.925 - 18.2 =
3) 40.7
Timberlake lecture plus
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Measurements and Their
Uncertainty
> Multiplying and Dividing
Round (or add zeros) to the calculated
answer until you have the same number
of significant figures as the measurement
with the fewest significant figures.
Timberlake lecture plus
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Multiplication + Division
Answer should have the same number of
significant figures as the measurement
with the least.
You may need to round your answer in
order to achieve this
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Learning Check
A. 2.19 X 4.2 =
1) 9
B.
2) 9.2
3) 9.198
4.311 ÷ 0.07 =
1) 61.58 2) 62
C.
3) 60
2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3 2) 11
Timberlake lecture plus
3) 0.041
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Solution
A.
2.19 X 4.2 =
2) 9.2
B.
4.311 ÷ 0.07 = 3) 60
C.
2.54 X 0.0028 =
0.0105 X 0.060
2) 11
Continuous calculator operation =
2.54 x 0.0028
 0.0105 
Timberlake lecture plus
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0.060
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Significant Figures in Calculations
Rounding
To round a number, you must first decide how
many significant figures your answer should
have.
Your answer should be rounded to the number
with the least amount of significant figures
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QUIZ
1. How many significant figures are in
the number
a.
603.040
b. 0.0828
c. 690,000
2. Perform the following operations and report
to the correct number of sig. figs
a.
4.15 cm X 1.8 cm
b.
36.47 + 2.721 + 15.1
c.
5.6 x 107 x 3.60 x 10-3
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SAMPLE PROBLEM 3.1
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SAMPLE PROBLEM 3.1
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SAMPLE PROBLEM 3.2
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SAMPLE PROBLEM 3.2
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SAMPLE PROBLEM 3.3
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SAMPLE PROBLEM 3.3
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