precision and accuracy uncertainty in measurements
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Precision and Accuracy
Uncertainty in Measurements
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Precision and Accuracy
Uncertainty
a measurement can only be as good as the instrument or the method used to make it.
Ex. Cop’s Radar Gun vs. Car’s Speedometer.
Bank sign Thermometer vs. your skin.
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Precision and Accuracy
Accepted Value A measurement deemed by scientists to be the “true measurement.”
Accuracy The Closeness or proximity of a measurement to the accepted value.
The difference between the actual measurement and the accepted value is called the ABSOLUTE ERROR.
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Precision and Accuracy
Precision A proven agreement between the numerical values of a set of measurements done by the same instrument and/or method.
The Difference between the set of measurements is expressed as Absolute Deviation.
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Precision and Accuracy
Precision
refers to the reproducibility of a measurement.
Significant Figures are the digits used to represent the precision of a measurement.
SIG. FIGS. are equal to all known measurements plus one estimated digit.
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Rules for Significant Digits
1) ALL NON-ZERO DIGITS ARE SIGNIFICANT
2) EXACT NUMBERS have an infinite number of significant numbers.
Exact #s are #s that are defined not measured. Numbers found by counting or used for conversions such as 100 cm = 1 m.
3) Zeros can be both significant or insignficant
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Rules for Significant Digits
The Three Classes of Zeros
A. Leading Zeros Zeros that precede all of the non-zero digits are NOT significant.
Ex. 0.0025 mg
has only 2 sig. figs.( the 2 & 5)
all three zeros are not significant.
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Rules for Significant Digits
B. Captive Zeros Zeros between two or more nonzero or significant digits ARE significant.
Ex. 10.08 grams
All four #s are significant
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Rules for Significant Digits
C) Trailing Zeros Zeros located to the right of a nonzero or significant digit ARE Significant ONLY if there is a decimal in the measurement.
Ex. 20.00 lbs Has four sig. figs.
2000 lbs Has only 1 sig. figs
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Calculations with Significant Digits
Addition and Subtraction::
The answer must be Rounded so that it contains the same # of digits to the right of the decimal point as there are in the measurement with the smallest # of digits to the right of the decimal.
13.89 years + 0.00045 years = 13.89045 years
Rounds to 13.89 years 2 places to the Rt.
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Calculations with Significant Digits
Multiplication or Division
The product or quotient must be Rounded so that it contains the same # of digits as the least significant measurement in the problem.
Ex. ( 2.2880 ml )(0.305 g/ml ) = 0.69784 g
Ans. Must be rounded to 3 sig. figs.
mass = 0.698 g
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Rules for Rounding Numbers
If the digit immediately to the right of the last significant figure you want to retain is ::
Greater than 5, increase the last digit by 1
Ex) 56.87 g 56.9 g
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Rules for Rounding Numbers
If the digit immediately to the right of the last significant figure you want to retain is ::
Less than 5, do not change the last digit.
Ex) 12.02 L 12.0 L
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Rules for Rounding Numbers
If the digit immediately to the right of the last significant figure you want to retain is ::
5, followed by nonzero digit(s) increase the last digit by 1
Ex. 3.7851 seconds 3.79 seconds
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Rules for Rounding Numbers
If the digit immediately to the right of the last significant figure you want to retain is ::
5, not followed by a nonzero digit and preceded by odd digit, increase the last digit by 1.
Ex. 2.835 lbs 2.84 lbs
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Rules for Rounding Numbers
If the digit immediately to the right of the last significant figure you want to retain is ::
5, not followed by a nonzero digit and preceded by even digit, do not change the last digit.
Ex. 82.65 ml 82.6 ml