scientific measurement chapter 3. measurement & uncertainty making measurements and performing...
TRANSCRIPT
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Scientific Measurement
Chapter 3
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Measurement & Uncertainty
• Making measurements and performing calculations with measurements is very important in science and many other fields
• Any measurement has a number with a unit
• How do you know if a measurement is true?
• Are there limits to measurement?
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Scientific Notation
A convenient way of writing very large and very small numbers
A way to indicate significant figuresStandard (Decimal) notation
0.00000000000030 m (radius of H atom)Scientific notation
3.0 x 10-13 mcoefficient x 10 power
first digit must be from 1 to 91.65 x 10 4 Correct format?0.053 x 10 -2 Correct format?12.63 x 10 15 Correct format?
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Calculations with Scientific Notation
• Review scientific notation in your text– Read pages R56-57, Appendix C
• Your calculator uses a special key to enter scientific notation
• EE, E, Exp, Sci
• These keys mean “x 10exp” to your calculator
• Do not use 10^
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Calculations with Scientific Notation
• How to enter 6.022 x 1023
• 6.022
• 2nd EE
• 23
• Your calculator screen should show 6.022E23
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Calculations with Scientific Notation
• Calculate 6.52 x 1018 ÷ 4.91 x 10-5
• 6.52• 2nd EE• 18• ÷• 4.91• 2nd EE• -5• ENTER = 1.33…..E23
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Accuracy, Precision, & Error
Accuracy and precision are not the same thingAccuracy
how close a measurement is to the true value (actual or accepted value)
Precisionhow close measurements agreehow exact a measurement isExample: a centigram balance (0.01g) is more precise than a decigram balance (0.1g)
Errordifference between actual and experimental value
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Accuracy & Precision
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Accuracy & Precision
To evaluate accuracy of a measurement:
compare measurement to true value
To evaluate precision of a measurement:
compare values of two or more repeated measurements
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Uncertainty in Measurement
• All measurements are approximations• All measurements contain error, so we can
only report numbers that we know for sure (certain)
• The certainty of a measurement is determined by the precision of the measurement
• Significant figures are used to reflect certainty of measured value
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Uncertainty in Measurement
• Digital instruments (like our electronic scales) estimate the final digit
• Example: 5.67 g • In this measurement, the 7 is estimated by
the scale• The uncertainty of the scale is the smallest
division reported by the scale (0.01 g)• Recording the measurement with its
uncertainty: 5.67 ± 0.01 g
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Significant Figures
• All digits that are known, plus one last estimated digit
• Represent certainty of a measurement
• Must be handled properly in calculations to prevent overstating precision
• Review rules to determine significant figures (p. 66-67)
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Significant Figures in Measurement
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Rules for Determining Significant Figures
• All non-zeros YES
• Zeros between non-zeros YES
• Zeros at the beginning of a # NO
• Zeros at the end, to right of “.” YES
• Final zeros without “.” NO
• Final zeros with “.” YES
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Significant Figures in Calculations
• Multiplication & Division– Result must have the same # of s.f. as the
measurement with the fewest s.f.– 6.221 cm x 5.2 cm = 32.3492 cm2 → 32 cm2
• Addition & Subtraction– Result may not have more decimal places
than the number with the fewest decimal places
– 20.4 + 1.322 + 83 = 104.722 → 105
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Uncertainty in Measurement
• An error due to limitations of the instrument
• For a digital instrument– +/- the smallest digit– 62.56g +/- 0.01 g
• For an analog instrument– +/- the estimated digit– See example
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Determining ErrorError:
the difference between the accepted and experimental measurement
Example:
Water was measured to boil at 101.5ºC
The known bp of water is 100.0ºC
Calculate the error in the measurement
C 1.5 Error
C 100.0 - C 101.5 Error
valueaccepted - valuealexperiment Error
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Percent Error
Error is often better understood as a percent of the true value
Note that the numerator is absolute value!
1.5%
100x 100.0
100.0 - 101.5 error %
100x accepted
accepted - alexperiment error %
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3.2 International System of Units
• SI units (System International) used to be called the metric system
• Standard units used in science
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Metric Prefixes*
*Memorize these prefixes and their factors
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Common Units of Volume
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Mass vs. Weight
• Mass is a measure of matter
• Anything that occupies space has mass
• Weight is a force– The force of gravity acting on a mass
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Temperature Scales Used in Science
• Kelvin (Absolute Temperature)
• Absolute zero 0º K = -273.15º C
no negative temps
• Celsius0 C = +273.15 K
• A Kelvin degree and a Celsius degree have the same size
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Conversions Between the Celsius and Kelvin Scales
We will not use the Farenheit scale!
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EnergyUnits of Energy
• Energy is the capacity to do work or to produce heat.
• The joule (J) is the SI unit of energy. • One calorie (cal) is the quantity of heat that raises
the temperature of 1 g of pure water by 1°C.
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The JoulePronunciation Guide
NO
NO
YES!
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• Energy can be converted into other forms, but the units are still joules (J)
• This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.
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3.3 Conversion Problems
• Conversion Factors• Ratio of two
equivalent measurements
• 1 dozen = 12 items
dozen 1
items 12or
items 12
dozen 1
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Dimensional Analysis
• When solving problems, units must be consistent
• Unit conversion are often necessary• Use conversion factors• Problem: Determine how many centimeters
are in 1 yd.
• 1 yd x 36.0 in x 2.54 cm = 91.44 cm
1 yd 1 in
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3.4 Density
• Density is the ratio of mass to volume
• Density is an intensive property
• Density of a pure substance is constant at a given temperature V
md
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Density
• Depends on temperaturetemp density
What if temp decreased?
• Unitsg/cm3 or g/mL for solids & liquids
g/L for gases