2.3 4 g
DESCRIPTION
A measurement is a quantity that has both a number and a unit. Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to MAKE measurements and to decide whether a measurement is CORRECT . - PowerPoint PPT PresentationTRANSCRIPT
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Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to MAKE measurements and to decide whether a measurement is CORRECT.
-- Are you “certain” that your measurement is correct? HOW “certain” are you???
2.32.344 gg
A measurement is a quantity that has both a number and a unit.
36.36.11 mLmL 16.5 16.5 Years OldYears Old
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Accuracy, Precision, and Error
Here is an example:Here is an example:
How old is my cat?How old is my cat?
_____ Months_____ Months (everyone must guess)(everyone must guess)
How do you evaluate accuracy and precision? (Your thoughts???)
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• Accuracy is a measure of how close a measurement comes to the actual or true value of whatever is measured. (closest to TRUE Value)
• Precision is a measure of how close a series of measurements are to one another. (repeated Save Value)
Accuracy and Precision
Who was more ACCURAT and more PRECISE in your measurements of the age of my cat?
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AccuracyAccuracy – closest to TRUE Value – closest to TRUE ValuePrecisionPrecision – repeated Same Value – repeated Same Value
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Determining Error
• The experimental value (EV) is the value measured in the lab. (by the student)
• The accepted value (AV) is the correct value based on reliable references.
• The error is the difference between the experimental value and the accepted value
Error = experimental value (EV) - accepted value (AV) (measured by student) - (correct value)
What is the error in your measurement of the age of my cat?
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The percent error is an absolute valueabsolute value (there is no positive or negative value.)
Percent Error
Percent Error = x 100% EV - AVAV
What is the percent error in your measurement of the age of my cat?
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Error VS Percent ErrorWhat is Mr. Pearson’s weight? Experimental Value (EV) = 115 kgActual Value (AV) = 110 kg
= 115 kg – 110 kg x 100 % = 4.5%
Error = EV – AV
Percent Error = x 100% EV - AVAV
= 115 kg – 110 kg = 5 kg
110 kg
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Error VS Percent ErrorWhat is the weight of my car? Experimental Value (EV) = 3,585 kgActual Value (AV) = 3,580 kg
= 3,585 kg – 3,580 kg x 100 % = 0.14%
Error = EV – AV
Percent Error = x 100% EV - AVAV
= 3,585 kg – 3,580 kg = 5 kg
3,580 kg
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What is Mr. Pearson’s weight? Error VS Percent Error
What is the weight of my car? Error = 3,585 kg – 3,580 kg = 5 kg % Error = 3,585 kg – 3,580 kg x 100 % = 0.14%
3,580 kg
% Error = 115 kg – 110 kg x 100 % = 4.5% Error = 115 kg – 110 kg = 5 kg
110 kg
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The significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
Significant Figures relate to the certainty of a measurement – The PRECISION of the measurement
(If you are buying something that costs $1,000,000 per centimeter how certain (how PRECISE) do you want your measurement to be?)
Significant Figures (Sig Figs) = Known + ESTIMATE
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Precision = Same REPEATABLE Value (Certainty)More Sig Figs = more certainty = greater precision
Which measurement has the most certainty and greatest PRECISION?
_ 1 sig fig (.6 is the estimate)
_ 2 sig figs (.01 is the estimate)
_ 3 sig figs Most certainty and greatest PRECISION
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Guesses only, don’t write any of this down YET.
There are rules (hints) to help you in determining the number of significant figures there are in a measurement.
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Sig Fig Rules: Is the decimal PRESENT or ABSENT
Pacific OceanDecimal is PRESENT
Atlantic OceanDecimal is ABSENT
Find the first NON-Zero
number starting from the Left
Then count all numbers to the
Right
Find the first NON-Zero
number starting from the RightThen count all numbers to the
Left
47.3 = __ S.F. 3
0.0021 = 2 S.F
1.200 = 4 S.F
36 = 2 S.F
2400 = 2 S.F
0.0600 = 3 S.F
104,000 = 3 S.F
Do not start writing/copying until I tell you
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37 m
____S.F
Sig Fig Rules: Is the decimal PRESENT or ABSENT
PRESENT ABSENT
.037 km = = 37,000 mm2____S.F2 ____S.F2
5.60 L
____S.F
0.00560 kL = = 5600 mL3____S.F3 ____S.F3
= 5.60 x 103 mL
RULE-2: Every digit in scientific notation is Significant
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RULE-2: Every digit in scientific notation is Significant
47.3 = 3 S.F
0.0021 = 2 S.F
1.200 = 4 S.F
36 = 2 S.F
2400 = 2 S.F
0.0600 = 3 S.F
104,000 = 3 S.F
4.73 x 101
2.1 x 10-3
1.200 x 100
3.6 x 101
2.4 x 103
6.00 x 10-2
1.04 x 105
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RULE-3: Any number that is counted is an EXACT number and has UNLIMITED significant digits. There is no ESTIMATED number.
I have three cats = 3 Cats____S.FUnlimited
Sig Figs are based on the ESTIMATED Number
312 students attend GPA____S.FUnlimited
Counted = EXACT = Unlimited # of Sig FigsMeasured = ESTIMATED = Certain # of Sig Figs
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_ 1 sig fig (.6 is the estimate)
_ 2 sig figs (.01 is the estimate)
_ 3 sig figs Most certainty and greatest PRECISION
Counted = EXACT = Unlimited # of Sig FigsMeasured = ESTIMATED = Certain # of Sig Figs
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Sig Fig Rules: Is the decimal PRESENT or ABSENT
PRESENT ABSENT
RULE-2: Every digit in scientific notation is Significant
RULE-3: Any number that is counted is an EXACT number and has unlimited significant digits. There is no ESTIMATED number.
Counted = EXACT = Unlimited # of Sig FigsMeasured = ESTIMATED = Certain # of Sig Figs
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Guesses only, don’t write any of this down YET.
There are rules (hints) to help you in determining the number of significant figures there are in a measurement.
= __ S.F
= 5 S.F= 4 S.F
= 5 S.F
= Unlimited = 2 S.F
3
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Problem Solving 3.3 Solve Problem 3 with the help of an interactive guided tutorial.
for Sample Problem 3.1
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3.2
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for Sample Problem 3.2
Problem Solving 3.6 Solve Problem 6 with the help of an interactive guided tutorial.
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3.3
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for Sample Problem 3.3
Problem Solving 3.8 Solve Problem 8 with the help of an interactive guided tutorial.
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3.1 Section Quiz
1. In which of the following expressions is the number on the left NOT equal to the number on the right?
a. 0.00456 10–8 = 4.56 10–11
b. 454 10–8 = 4.54 10–6
c. 842.6 104 = 8.426 106
d. 0.00452 106 = 4.52 109
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3.1 Section Quiz
2. Which set of measurements of a 2.00-g standard is the most precise?
a. 2.00 g, 2.01 g, 1.98 g
b. 2.10 g, 2.00 g, 2.20 g
c. 2.02 g, 2.03 g, 2.04 g
d. 1.50 g, 2.00 g, 2.50 g
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3. A student reports the volume of a liquid as 0.0130 L. How many significant figures are in this measurement?
a. 2
b. 3
c. 4
d. 5
3.1 Section Quiz