observation, measurement and calculations
DESCRIPTION
Observation, Measurement and Calculations. Cartoon courtesy of NearingZero.net. Steps in the Scientific Method. 1.Observations - quantitative - qualitative 2.Formulating hypotheses - possible explanation for the observation 3.Performing experiments - PowerPoint PPT PresentationTRANSCRIPT
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Observation,Observation,MeasurementMeasurement
and Calculationsand Calculations
Cartoon courtesy of NearingZero.net
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Steps in the Scientific MethodSteps in the Scientific Method1.1. ObservationsObservations
-- quantitativequantitative- - qualitativequalitative
2.2. Formulating hypothesesFormulating hypotheses- - possible explanation for the possible explanation for the observationobservation
3.3. Performing experimentsPerforming experiments- - gathering new information to gathering new information to decidedecide
whether the hypothesis is validwhether the hypothesis is valid
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Outcomes Over the Long-Outcomes Over the Long-TermTerm
Theory (Model)Theory (Model)- - A set of tested hypotheses that give A set of tested hypotheses that give anan overall explanation of some natural overall explanation of some natural
phenomenon.phenomenon.Natural LawNatural Law
-- The same observation applies to The same observation applies to manymany different systemsdifferent systems-- Example - Law of Conservation of Example - Law of Conservation of MassMass
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Law vs. TheoryLaw vs. Theory
A A lawlaw summarizes what summarizes what happenshappens
A A theorytheory (model) is an attempt (model) is an attempt to explain to explain whywhy it happens. it happens.
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Nature of MeasurementNature of Measurement
Part 1 - Part 1 - numbernumberPart 2 - Part 2 - scale (unit)scale (unit)
Examples:Examples:2020 gramsgrams
6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds
Measurement - quantitative Measurement - quantitative observation observation consisting of 2 consisting of 2 partsparts
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Systems of measurementSystems of measurementMetric system vs English system
»Metric (SI) International system–Standardized -international–consistent base units–multiples of 10
»English (US) system–non-standard -only US–no consistent base units–no consistent multiples
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Using the Metric systemUsing the Metric systemPrefixes for multiples of 10
»T - G - M -k h d (base) d c m - - - - n - -p
»Tera 1012 – Giga 109 – Mega 106 – kilo 103 –
hecto 102 – deka 10 1 – base – deci 10-1 – centi 10 –2 - milli 10 –3 – micro 10 –6 –
nano 10 –9 – pico 10 -12
»move the decimal to convert
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The Fundamental SI UnitsThe Fundamental SI UnitsPhysical Quantity Name AbbreviationMass kilogram kgLength meter mTime second sTemperature Kelvin KElectric Current Ampere AAmount of Substance mole molLuminous Intensity candela cd
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SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry
Prefix Unit Abbr. ExponentKilo k 103
Deci d 10-1
Centi c 10-2
Milli m 10-3
Micro 10-6
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400 m = ? cm
Moving the decimalMoving the decimalFor measurements that are defined by a single unit such as length, mass, or liquid volume and later in the course, power, current, voltage, etc., simply move the decimal the number of places indicated by the prefix.
400 m = ? cm40,000 cm
75 mg = ? g7 5 mg = ? g0.075 g
0.025 m = ? mm0.000025 mm
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Metric Metric– multiples of 10– move decimal– *area - move twice– *volume - move three times
English Metric– conversion factors– proportion method– unit cancellation method
Converting measurementsConverting measurements
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Common ConversionsCommon Conversions
1 kilometer = .621 miles1 kilometer = .621 miles1 meter = 39.4 inches1 meter = 39.4 inches1 centimeter = .394 1 centimeter = .394
inchesinches1 kilogram = 2.2 pounds1 kilogram = 2.2 pounds
1 gram = .0353 ounce1 gram = .0353 ounce1 liter = 1.06 quarts1 liter = 1.06 quarts
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Uncertainty in MeasurementUncertainty in Measurement
A A digit that must be digit that must be estimatedestimated is called is called uncertainuncertain. A . A measurementmeasurement always has always has some degree of uncertainty.some degree of uncertainty.
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Why Is there Uncertainty?Why Is there Uncertainty? Measurements are performed with instruments No instrument can read to an infinite number of decimal places
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Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue value.value.PrecisionPrecision refers to the degree of refers to the degree of agreement among several measurements agreement among several measurements made in the same manner.made in the same manner.
Neither accurate nor
precisePrecise but not
accuratePrecise AND
accurate
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Rules for Counting Rules for Counting Significant FiguresSignificant Figures
Nonzero integersNonzero integers always count always count as significant figures.as significant figures.
34563456 hashas 44 sig figs.sig figs.
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Rules for Counting Rules for Counting Significant FiguresSignificant Figures
ZerosZeros-- Captive zeros Captive zeros always count asalways count as
significant figures.(zeros in significant figures.(zeros in between nonzeros)between nonzeros)
16.07 16.07 hashas44 sig figs. sig figs.
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Rules for Counting Rules for Counting Significant FiguresSignificant Figures
ZerosZeros-- Leading zerosLeading zeros do not count as do not count as
significant figuressignificant figures..
0.04860.0486 has has33 sig figs. sig figs.
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Rules for Counting Rules for Counting Significant FiguresSignificant Figures
ZerosZerosTrailing zerosTrailing zeros are significant are significant only if the number contains a only if the number contains a decimal point.decimal point.
9.3009.300 has has44 sig figs. sig figs.
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Rules for Counting Rules for Counting Significant FiguresSignificant Figures
Any whole number that ends in zero and does not have a decimal in unclear or unknown.
10 unknown10 unknown
20. Has 2 significant figures20. Has 2 significant figures
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Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of the following?1.0070 m
5 sig figs
17.10 kg 4 sig figs
100,890 L unclear
3.29 x 103 s 3 sig figs0.0054 cm 2 sig figs3,200,000 unclear
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Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations
Multiplication and DivisionMultiplication and Division:: # sig figs in the result # sig figs in the result equals the number with the equals the number with the least number of sig figs.least number of sig figs.
6.38 x 2.0 =6.38 x 2.0 =12.76 12.76 13 (2 sig figs)13 (2 sig figs)
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Sig Fig Practice #2Sig Fig Practice #2
3.24 m x 7.0 mCalculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m ÷ 3.0 s 236.6666667 m/s unclear1818.2 lb x 3.23 ft 5872.786 lb·ft 5.87 x 103
lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL
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Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical OperationsAddition and SubtractionAddition and Subtraction: The : The number of decimal places in number of decimal places in the result equals the number the result equals the number of decimal places in the of decimal places in the number with the least decimal number with the least decimal places.places.
6.8 + 11.934 =6.8 + 11.934 =18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))
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Sig Fig Practice #3Sig Fig Practice #3
3.24 m + 7.0 mCalculation Calculator says: Answer
10.24 m 10.2 m100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm713.1 L - 3.872 L 709.228 L 709.2 L1818.2 lb + 3.37 lb 1821.57 lb 1821.6
lb2.030 mL - 1.870 mL 0.16 mL 0.160 mL
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Significant FiguresSignificant FiguresRules for rounding off numbers (1) If the digit to be dropped is
greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13.
(2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.
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(3) If the digit to be dropped (3) If the digit to be dropped is 5, and if any digit is 5, and if any digit
following it is not zero, the following it is not zero, the last remaining digit is last remaining digit is increased by one. For increased by one. For
example, example, 12.51 is rounded to 1312.51 is rounded to 13
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Significant FiguresSignificant Figures
(4) If the digit to be dropped is 5 and is followed only by zeros, the last remaining digit is increased by one if it is odd, but left as it is if even. For example,
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11.5 is rounded to 12, 11.5 is rounded to 12, 12.5 is rounded to 12. This 12.5 is rounded to 12. This
rule means that if the digit to rule means that if the digit to be dropped is 5 followed only be dropped is 5 followed only by zeros, the result is always by zeros, the result is always
rounded to the even digit. rounded to the even digit. The rationale is to avoid bias The rationale is to avoid bias in rounding: half of the time in rounding: half of the time we round up, half the time we round up, half the time
we round down.we round down.
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In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:
1 mole = 6020000000000000000000001 mole = 602000000000000000000000
In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:
Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg
Scientific NotationScientific Notation
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Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!
0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000
???????????????????????????????????
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Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large
or very small numbers in the or very small numbers in the form:form:
M x 10nM x 10n MM is a number between is a number between 11 and and 1010 nn is an integer is an integer
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2 500 000 000
Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point
.Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point
123456789
Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn
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2.5 x 102.5 x 1099
The exponent is the number of places we moved the decimal.
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0.00005790.0000579
Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn
1 2 3 4 5
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5.79 x 105.79 x 10-5-5
The exponent is negative because the number we started with was less than 1.
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Direct ProportionsDirect Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line
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Inverse ProportionsInverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola