Chapter 3Chapter 3Scientific MeasurementScientific Measurement
Hingham High SchoolHingham High School
Mr. CluneMr. Clune
MeasurementsMeasurements
QualitativeQualitative measurements - words measurements - words QuantitativeQuantitative measurements – measurements –
involves numbers (quantities)involves numbers (quantities) Depends on reliability of instrumentDepends on reliability of instrument Depends on care with which it is Depends on care with which it is
readread Scientific NotationScientific Notation
Coefficient raised to power of 10Coefficient raised to power of 10
Scientific NotationScientific Notation MultiplicationMultiplication
Multiply the coefficients, add Multiply the coefficients, add the exponentsthe exponents
(2 X 104) X (3 X 107)
4 + 7 = 11
2 X 3 = 66 X 1011
Scientific NotationScientific Notation DivisionDivision
Divide the coefficients, subtract Divide the coefficients, subtract the denominator exponent the denominator exponent from numerator exponentfrom numerator exponent
8 X 109
4 X 10584
= 2
9 - 5 = 4
2 X 104
Scientific NotationScientific Notation
Before adding or subtracting in Before adding or subtracting in scientific notation, the scientific notation, the exponents must be the sameexponents must be the same
Calculators will take care of Calculators will take care of thisthis
Scientific NotationScientific Notation AdditionAddition
Line up decimal; add as usual the Line up decimal; add as usual the coefficients; exponent stays the samecoefficients; exponent stays the same
(25 X 104) + (3.0 X 106)
(25 X 104) + (300. X 104)
(325 X 104)
Scientific NotationScientific Notation SubtractionSubtraction
Line up decimal; subtract coefficients Line up decimal; subtract coefficients as usual; exponent remains the sameas usual; exponent remains the same
(25 X 104) - (150. X 103)(25 X 104) - (15.0 X 104)
(10 X 104)
Measurements and Measurements and Their UncertaintyTheir Uncertainty
Need to make reliable Need to make reliable measurements in the labmeasurements in the lab
AccuracyAccuracy – how close a – how close a measurement is to the true measurement is to the true valuevalue
PrecisionPrecision – how close the – how close the measurements are to each measurements are to each other (reproducibility)other (reproducibility)
Bad AccuracyAnd
Good Precision
Bad AccuracyAnd
Bad Precision
Good AccuracyAnd
Bad Precision
Good AccuracyAnd
Good Precision
Measurements and Measurements and Their UncertaintyTheir Uncertainty
Accepted valueAccepted value – correct value – correct value based on reliable referencesbased on reliable references
Experimental valueExperimental value – the value – the value measured in the labmeasured in the lab
ErrorError – the difference between – the difference between the accepted and experimental the accepted and experimental valuesvalues
Measurements and Measurements and Their UncertaintyTheir Uncertainty
ErrorError = accepted – experimental = accepted – experimental Can be positive or negativeCan be positive or negative
Percent errorPercent error = the absolute = the absolute value of the error divided by the value of the error divided by the accepted value, times 100%accepted value, times 100%
| error || error |
accepted valueaccepted value x 100%% error =
% Error Example% Error Example
Accepted Value = 100gAccepted Value = 100g
Experimental Value = 102gExperimental Value = 102g
% Error = % Error = | Acc – Exp || Acc – Exp |
AccAcc X 100% X 100%
% Error = % Error = | 100 – 102 || 100 – 102 |
100100 X 100% X 100%
% Error = 2%% Error = 2%
Significant FiguresSignificant Figures Significant figuresSignificant figures in a in a
measurement include all of measurement include all of the digits that are known, plus the digits that are known, plus a last digit that is estimated.a last digit that is estimated.
Note Fig. 3.4, page 66Note Fig. 3.4, page 66 Rules for counting sig. figs.?Rules for counting sig. figs.?
Zeroes are the problemZeroes are the problem East Coast / West Coast East Coast / West Coast methodmethod
Significant FiguresSignificant Figures
1. All nonzero digits • 457 cm (3)• 0.35 g (2)
2. Zeros between nonzero digits • 10003 mL (5)• 0.2005 ms (4)
Significant FiguresSignificant Figures
3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point.
• 0.02 g (1)• 0.0026 cm (2)
Significant FiguresSignificant Figures
4. When a number ends in zeros that are to the right of the decimal point, they are significant.
• 0.0200 g (3)• 3.0 cm (2)
Significant FiguresSignificant Figures
5. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant.
•130 cm (2) •10,300 g (3)
Counting Significant Fig.Counting Significant Fig.
Sample 3-1, page 69Sample 3-1, page 69 RoundingRounding
Decide how many sig. figs. Decide how many sig. figs. NeededNeeded
Round, counting from the leftRound, counting from the left Less than 5? Drop it.Less than 5? Drop it. 5 or greater? Increase by 15 or greater? Increase by 1
Sample 3-2, page 70Sample 3-2, page 70
Sig. fig. calculationsSig. fig. calculations
Addition and SubtractionAddition and Subtraction The answer should be rounded The answer should be rounded
to the same number of to the same number of decimaldecimal placesplaces as the least number in as the least number in the problemthe problem
Sample 3-3, page 60Sample 3-3, page 60
Sig. fig. calculationsSig. fig. calculations
26.46 + 4.123 30.583
{this has the least digits to the right of the decimal point (2)
Rounds off to 30.58
Sig. Fig. calculationsSig. Fig. calculations
Multiplication and DivisionMultiplication and Division Round the answer to the same Round the answer to the same
number of number of significant figuressignificant figures as as the least number in the the least number in the measurementmeasurement
Sample 3-4, page 61Sample 3-4, page 61
Sig. Fig. calculationsSig. Fig. calculations
2.61 x1.2 3.132
{this has the smaller number of significant figures (2)
Rounds off to 3.1
International System of UnitsInternational System of Units
The number is only part of the The number is only part of the answer; it also need answer; it also need UNITSUNITS
Depends upon units that serve Depends upon units that serve as a reference standardas a reference standard
The standards of measurement The standards of measurement used in science are those of the used in science are those of the Metric SystemMetric System
International System of UnitsInternational System of Units
Metric system is now revised Metric system is now revised as the International System of as the International System of Units (SI), as of 1960Units (SI), as of 1960
Simplicity and based on 10 or Simplicity and based on 10 or multiples of 10multiples of 10
7 base units7 base units Table 3.1, page 63Table 3.1, page 63
International System of UnitsInternational System of Units
Sometimes, non-SI units are Sometimes, non-SI units are usedused Liter, Celsius, calorieLiter, Celsius, calorie
Some are derived unitsSome are derived units Made by joining other unitsMade by joining other units Speed (miles/hour)Speed (miles/hour) Density (grams/mL)Density (grams/mL)
Common prefixesCommon prefixes
Kilo (k) = 1000 (one thousand)Kilo (k) = 1000 (one thousand) Deci (d) = 1/10 (one tenth)Deci (d) = 1/10 (one tenth) Centi (c) = 1/100 (one hundredth)Centi (c) = 1/100 (one hundredth) Milli (m) = 1/1000 (one Milli (m) = 1/1000 (one
thousandth)thousandth) Micro (Micro () = (one millionth)) = (one millionth) Nano (n) = (one billionth)Nano (n) = (one billionth)
LengthLength
In SI, the basic unit of length is In SI, the basic unit of length is the meter (m)the meter (m) Length is the distance Length is the distance
between two objects – between two objects – measured with rulermeasured with ruler
We make use of prefixes for We make use of prefixes for units larger or smallerunits larger or smaller
VolumeVolume The space occupied by any The space occupied by any
sample of mattersample of matter Calculated for a solid by Calculated for a solid by
multiplying the length x multiplying the length x width x heightwidth x height
SI unit = cubic meter (mSI unit = cubic meter (m33)) Everyday unit = Liter (L), Everyday unit = Liter (L),
which is non-SIwhich is non-SI
Volume Measuring InstrumentsVolume Measuring Instruments
Graduated cylindersGraduated cylinders PipetPipet BuretBuret Volumetric FlaskVolumetric Flask SyringeSyringe
Volume changes?Volume changes? Volume of any solid, liquid, Volume of any solid, liquid,
or gas will change with or gas will change with temperaturetemperature
Much more prominent for Much more prominent for GASESGASES
Therefore, measuring Therefore, measuring instruments are calibrated instruments are calibrated for a specific temperature, for a specific temperature, usually 20 usually 20 ooC, which is about C, which is about normal room temperaturenormal room temperature
Volume – (mVolume – (m33))
Volume (L)Volume (L)
1dm3=1L
Volume Volume
Volume (mL)Volume (mL)
1cm
1cm
1cm
1cm3=1mL
Volume – Liter (L)Volume – Liter (L)
1L=1.05qt
Units of MassUnits of Mass
Mass is a measure of the Mass is a measure of the quantity of matterquantity of matter Weight is a force that Weight is a force that measures the pull by gravity- measures the pull by gravity- it changes with locationit changes with location
Mass is constant, regardless of Mass is constant, regardless of locationlocation
Mass – KiloGram (kg)Mass – KiloGram (kg)
1kg=2.2lb
s
Working with MassWorking with Mass
The SI unit of mass is the The SI unit of mass is the kilogram (kg), even kilogram (kg), even though a more convenient though a more convenient unit is the gramunit is the gram
Measuring instrument is Measuring instrument is the balance scalethe balance scale
TemperatureTemperature
Kelvin (K)Kelvin (K)Based on Absolute ZeroBased on Absolute Zero
Celsius (Celsius (°C)°C)Water freezes at 0Water freezes at 0°C (273K)°C (273K)Water boils at 100°C (373K)Water boils at 100°C (373K)
TemperatureTemperature
Water freezes at 0Water freezes at 0°C (273K)°C (273K)
Water boils at 100°C (373K)Water boils at 100°C (373K)
Tem
pera
ture
(°C
, K)
Tem
pera
ture
(°C
, K)BP of H2O
FP of H2O
Absolute Zero
TemperatureTemperature
Convert Kelvin to CelsiusConvert Kelvin to Celsius
°C = K - 273°C = K - 273345K = ? °C
°C = 345K – 273
72°C
TemperatureTemperature
Convert Celsius to KelvinConvert Celsius to Kelvin
K = °C + 273K = °C + 27320 °C = ? K
K= 20°C – 273
293K
Time – Seconds (s)Time – Seconds (s)
EnergyEnergy
Joule (J)Joule (J) Calorie (Calorie (Cal)Cal)
Energy needed to raise Energy needed to raise 1g of 1 1g of 1 °C°C
The capacity to do work or produce heat
HomeworkHomework
Practice Problem 16Page 78
Section AssessmentQuestions: 18-27(odd)
Page 79Due: 10/7/04
Dimensional AnalysisDimensional Analysis
Converting UnitsConverting Units
Conversion ProblemsConversion Problems
50cm = ?m
100cm = 1m
100cm
1m
1m
100cm
Conversion ProblemsConversion Problems
50cm X1m
100cm=
0.50 m
Conversion ProblemsConversion Problems
0.045kg =? g
1000g = 1kg
1000g
1kg
1kg
1000g
Conversion ProblemsConversion Problems
0.045kg X1000g
1kg=
45g
Conversion ProblemsConversion Problems
2.5hr =? s
60min = 1hr
60min
1hr
1hr
60min
Conversion ProblemsConversion Problems
2.5hr =? s
60s = 1min
60s
1min
1min
60s
Conversion ProblemsConversion Problems
2.5hr X60min
1hr=
9000s
60s
minX
HomeworkHomework
Practice Problem 35-37Pages 82 - 86Due: 10/7/04
DensityDensity
Which is heavier- lead or feathers?Which is heavier- lead or feathers? It depends upon the amount of the It depends upon the amount of the
materialmaterial A truckload of feathers is heavier A truckload of feathers is heavier than a small pellet of leadthan a small pellet of lead
The relationship here is between The relationship here is between mass and volume- called mass and volume- called DensityDensity
DensityDensity The formula for density is:The formula for density is: massmass volumevolume• Common units are g/mL, or Common units are g/mL, or possibly g/cmpossibly g/cm33, (or g/L for gas), (or g/L for gas)
• Density is a physical property, Density is a physical property, and does not depend upon and does not depend upon sample sizesample size
Density =
Things related to densityThings related to density
What happens when corn What happens when corn oil and water are mixed?oil and water are mixed?
Why?Why? Will lead float?Will lead float?
Density and TemperatureDensity and Temperature
What happens to density as What happens to density as the temperature increases?the temperature increases? Mass remains the sameMass remains the same Most substances increase Most substances increase in volume as temperature in volume as temperature increasesincreases
Thus, density generally Thus, density generally decreases as the decreases as the temperature increasestemperature increases
Density and waterDensity and water
Water is an important exceptionWater is an important exception Over certain temperatures, the Over certain temperatures, the
volume of water volume of water increasesincreases as as the temperature the temperature decreasesdecreases Does ice float in liquid water?Does ice float in liquid water? Why?Why?
Sample 3-10,11, page 91-92Sample 3-10,11, page 91-92
Specific GravitySpecific Gravity
A comparison of the density of A comparison of the density of an object to a reference an object to a reference standard (which is usually standard (which is usually water) at the same temperaturewater) at the same temperature Water density at 4 Water density at 4 ooC = 1 C = 1 g/cmg/cm33
1g of H2O = 1mL = 1g of H2O = 1mL = 1 g/cm1 g/cm33
FormulaFormula
D of substance (g/cmD of substance (g/cm33))
D of water (g/cmD of water (g/cm33))• Note there are no units left, since they Note there are no units left, since they
cancel each othercancel each other• Measured with a Measured with a hydrometer hydrometer – p.72– p.72• Uses?Uses? Tests urine, antifreeze, battery Tests urine, antifreeze, battery
Specific gravity =
TemperatureTemperature
Heat moves from warmer object Heat moves from warmer object to the cooler objectto the cooler object Glass of iced tea gets colder?Glass of iced tea gets colder?
Remember that most substances Remember that most substances expand with a temp. increase?expand with a temp. increase?
Basis for thermometersBasis for thermometers
Temperature scalesTemperature scales
CelsiusCelsius scale- named after a scale- named after a Swedish astronomerSwedish astronomer Uses the freezing point(0 Uses the freezing point(0 ooC) C)
and boiling point (100 and boiling point (100 ooC) of C) of water as referenceswater as references
Divided into 100 equal Divided into 100 equal intervals, or degrees Celsiusintervals, or degrees Celsius
Temperature scalesTemperature scales
KelvinKelvin scale (or absolute scale) scale (or absolute scale) Named after Lord KelvinNamed after Lord Kelvin K = K = ooC + 273C + 273 A change of one degree Kelvin A change of one degree Kelvin
is the same as a change of one is the same as a change of one degree Celsiusdegree Celsius
No degree sign is usedNo degree sign is used
Temperature scalesTemperature scales
Water freezes at 273 KWater freezes at 273 K Water boils at 373 KWater boils at 373 K 0 K is called 0 K is called absolute zeroabsolute zero, and , and
equals –273 equals –273 ooCC Fig. 3.19, page 75Fig. 3.19, page 75 Sample 3-6, page 75Sample 3-6, page 75