chapter 3 scientific measurement hingham high school mr. clune

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


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


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)


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)


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)


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


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


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


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


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)


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


Convert Kelvin to CelsiusConvert Kelvin to Celsius

°C = K - 273°C = K - 273345K = ? °C

°C = 345K – 273

72°C


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


50cm X1m

100cm=

0.50 m


0.045kg =? g

1000g = 1kg

1000g

1kg

1kg

1000g


0.045kg X1000g

1kg=

45g


2.5hr =? s

60min = 1hr

60min

1hr

1hr

60min


2.5hr =? s

60s = 1min

60s

1min

1min

60s


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 =


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


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


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

chapter 3 scientific measurement hingham high school mr. clune

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clune slide

reproducibility slide

good precision slide

bad precision slide

value correct value

g experimental value

uncertainty error

scientific notation