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© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
>
Slide 1 of 48
Using and Expressing Measurements
Using and Expressing Measurements
How do measurements relate to science?
3.1
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 2 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 3 of 48
Scientific Notation
http://www.youtube.com/watch?v=H578qUeoBC0
Scientific Notation Pre-Test
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Measurements and Their Uncertainty
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Slide 4 of 48
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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Measurements and Their Uncertainty
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Slide 5 of 48
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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 6 of 48
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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 7 of 48
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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 8 of 48
Express the Express the following in following in
scientific notation scientific notation or standard or standard
notationnotation
1. 74171.71. 74171.7 2. .078822. .07882
3. 5263. 526 4. .00005734. .0000573
5. 5.8 x 10 5. 5.8 x 10 -7-7 6. 5.256 x 106. 5.256 x 1066
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 9 of 48
Accuracy, Precision, and Error
Accuracy, Precision, and Error
What is the difference between accuracy and precision?
3.1
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Measurements and Their Uncertainty
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Slide 10 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 11 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 12 of 48
3.1 Accuracy, Precision, and Error
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Measurements and Their Uncertainty
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Slide 13 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 14 of 48
3.1 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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Measurements and Their Uncertainty
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Slide 15 of 48
Accuracy, Precision, and Error3.1
Percent Error
(Error) 3.00-measurement X 100
3.00
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Measurements and Their Uncertainty
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Slide 16 of 48
3.1 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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 19 of 48
% 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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 20 of 48
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
3.1
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Measurements and Their Uncertainty
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Slide 21 of 48
Timberlake lecture plus 21
Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
122.55 m ___
Complete: All non-zero digits in a measured number are (significant or not significant).
Counting Significant Figures
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Measurements and Their Uncertainty
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Slide 22 of 48
Timberlake lecture plus 22
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).
Leading Zeros
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 23 of 48
Timberlake lecture plus 23
Number of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb ____
0.00405 m ____
Complete: Zeros between nonzero numbers
are (significant or not significant).
Sandwiched Zeros
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 24 of 48
Timberlake lecture plus 24
Number of Significant Figures
25,000 in. 2
200 yr 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 holders.
Trailing Zeros
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Measurements and Their Uncertainty
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Slide 25 of 48
Timberlake lecture plus 25
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
Learning Check
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 26 of 48
Timberlake lecture plus 26
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
2) multiplying or dividing
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Measurements and Their Uncertainty
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Slide 27 of 48
Timberlake lecture plus 27
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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 28 of 48
Timberlake lecture plus 28
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 2) 256.8 3) 257
B. 58.925 - 18.2 =
1) 40.725 2) 40.73 3) 40.7
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Measurements and Their Uncertainty
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Slide 29 of 48
Timberlake lecture plus 29
Solution
A. 235.05 + 19.6 + 2.1 =
2) 256.8
B. 58.925 - 18.2 =
3) 40.7
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Measurements and Their Uncertainty
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Slide 30 of 48
Timberlake lecture plus 30
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.
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 31 of 48
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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 32 of 48
Timberlake lecture plus 32
Learning Check
A. 2.19 X 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =
1) 61.58 2) 62 3) 60
C. 2.54 X 0.0028 =
0.0105 X 0.060
1) 11.3 2) 11 3) 0.041
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 33 of 48
Timberlake lecture plus 33
Solution A. 2.19 X 4.2 = 2) 9.2
B. 4.311 ÷ 0.07 = 3) 60
C. 2.54 X 0.0028 = 2) 11 0.0105 X 0.060
Continuous calculator operation =
2.54 x 0.0028 0.0105 0.060
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 34 of 48
3.1 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
© Copyright Pearson Prentice Hall
Measurements and Their Uncertainty
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Slide 35 of 48
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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