Ch. 3 Scientific Ch. 3 Scientific Measurement Measurement

MeasurementMeasurement

Quantitative informationQuantitative information Need a number and a unit (most of time)Need a number and a unit (most of time) Represents a quantityRepresents a quantity For example: 2 metersFor example: 2 meters

2 is number2 is number Meters is unitMeters is unit Length is quantityLength is quantity

Units compare what is being measured to Units compare what is being measured to a defined measurement standarda defined measurement standard

SI MeasurementSI Measurement

Le Systeme International d’Unites : SILe Systeme International d’Unites : SI System of measurement agreed on all System of measurement agreed on all

over the world in 1960over the world in 1960 Contains 7 base unitsContains 7 base units

We still use some non-SI unitsWe still use some non-SI units

Important SI Base UnitsImportant SI Base Units

Quantity Symbol Unit Abbreviation

Length l meter m

Mass m kilogram kg

Time t second s

Temperature T Kelvin K

Amount n mole mol

PrefixesPrefixes Prefixes are added to the base unit names to Prefixes are added to the base unit names to

represent quantities smaller or largerrepresent quantities smaller or larger

M mega 106 1,000,000 larger

k kilo 103 1,000 larger

c centi 10-2 1/100 smaller

m milli 10-3 1/1000 smaller

μ micro 10-6 1/1,000,000 smaller

LengthLength

SI unit: m SI unit: m use use cmcm a lot too a lot too kmkm is used instead of miles for is used instead of miles for

highway distances and car speeds in highway distances and car speeds in most countriesmost countries

MassMass

Measure of the quantity of matterMeasure of the quantity of matter SI unit: kg SI unit: kg use use gg a lot too a lot too mass vs. weightmass vs. weight

weight is the measure of gravitational pull on weight is the measure of gravitational pull on mattermatter

mass does not depend on gravitymass does not depend on gravity on a new planet, mass would be same but on a new planet, mass would be same but

weight could changeweight could change

Temperature ConversionsTemperature ConversionsFahrenheit to CelsiusFahrenheit to Celsius

329

5 C F

325

9F C

Celsius to Kelvin conversionsCelsius to Kelvin conversions

+273.15+273.15

→→

CC KK←←

-273.15-273.15

Temperature ConversionsTemperature Conversions

ExampleExample

What is 32°F in Kelvin?What is 32°F in Kelvin? freezing point of water!freezing point of water!

0)3232(9

5C

15.27315.2730 K

ExampleExample

What is 298 K in Fahrenheit?What is 298 K in Fahrenheit?

CC o25273298

FF 7732)25(5

9

Derived SI UnitsDerived SI Units

come from combining base unitscome from combining base units combine using multiplication or divisioncombine using multiplication or division

Example:Example: Area: A = length x widthArea: A = length x width

= m x m = m x m

= m= m22

VolumeVolume

amount of space occupied by objectamount of space occupied by object SI: mSI: m33 = m x m x m = m x m x m use use cmcm33 in lab a lot in lab a lot non-SI: non-SI:

1 liter = 1dm1 liter = 1dm33= 1000cm= 1000cm33

1 liter = 1000 mL1 liter = 1000 mL1cm 1cm 33= 1mL= 1mL

DensityDensity

ratio of mass to volumeratio of mass to volume SI:SI:

Other units: g/ cmOther units: g/ cm3 3 or g/ mLor g/ mL

volume

massDensity

3m

kg

characteristic property of substance (doesn’t characteristic property of substance (doesn’t change with amount ) because as volume change with amount ) because as volume increases, mass also increasesincreases, mass also increases density usually decreases as T increasesdensity usually decreases as T increasesexception: ice is less dense than liquid water so exception: ice is less dense than liquid water so it floatsit floats

ExampleExample

A sample of aluminum metal has a mass of A sample of aluminum metal has a mass of 8.4 g. The volume is 3.1 cm8.4 g. The volume is 3.1 cm33. Find the . Find the density.density.

Known Unknown

m = 8.4 g D = ?

V = 3.1 cm3

337.2

1.3

4.8

cm

g

cm

g

V

mD

Conversion FactorsConversion Factors ratio that comes from a statement of ratio that comes from a statement of

equality between 2 different unitsequality between 2 different units every conversion factor is equal to 1every conversion factor is equal to 1

dollarquarters 14

Example:Example:

statement of equalitystatement of equality

conversion factorconversion factor1

4

1

quarters

dollar

Dimensional AnalysisDimensional Analysis

Conversion FactorsConversion Factors

can be multiplied by other numbers can be multiplied by other numbers without changing the value of the without changing the value of the number number

since you are just multiplying by 1since you are just multiplying by 1

quartersdollar

quartersdollars 12

1

43

Example 1Example 1

Convert 5.2 Convert 5.2 cm to mmcm to mm

5.2 5.2 cm= 5.2 x 10 cm= 5.2 x 10 11mmmm = 52 mm = 52 mm Known:Known: 100 cm = 1 m100 cm = 1 m

1000 mm = 1 m1000 mm = 1 m Must use m as an intermediateMust use m as an intermediate

mmm

mm

cm

mcm 52

1

1000

100

12.5

Example 2Example 2

Convert 0.020 Convert 0.020 kg to mgkg to mg0.020 0.020 kg = 0.020 x 10 kg = 0.020 x 10 66 mg mg= 20,000 mg= 20,000 mg

Known:Known: 1 kg = 1000 g1 kg = 1000 g1000 mg = 1 g1000 mg = 1 g

Must use g as an intermediateMust use g as an intermediate

mgg

mg

kg

gkg 000,20

1

1000

1

1000020.0

Example 3Example 3

Convert 500,000 Convert 500,000 μμg to kgg to kg

500,000 500,000 μμg = 500,000 x 10 g = 500,000 x 10 -9-9 kg kg= 0.0005 kg= 0.0005 kg Known:Known: 1,000,000 1,000,000 μμg = 1 gg = 1 g

1 kg = 1000 g1 kg = 1000 g Must use g as an intermediateMust use g as an intermediate

kgg

kg

g

gg 0005.0

1000

1

000,000,1

1000,500

Advanced ConversionsAdvanced Conversions One difficult type of conversion deals with One difficult type of conversion deals with

squared or cubed unitssquared or cubed units

ExampleExample

Convert 3 dm Convert 3 dm 33 to cm to cm33

1dm =10 cm1dm =10 cm

3 dm 3 dm 33 = 3 x 10 cm x 10 cm x 10 cm= 3000 cm = 3 x 10 cm x 10 cm x 10 cm= 3000 cm33

ExampleExample

Convert: Convert: 2000 cm2000 cm33 to m to m33

OR

Known:Known:100 cm = 1 m100 cm = 1 m cmcm33 = cm x cm x cm = cm x cm x cmmm33 = m x m x m = m x m x m

3002.0100

1

100

1

100

12000 m

cm

m

cm

m

cm

mcmcmcm

33

3 002.0100

12000 m

cm

mcm

Advanced ConversionsAdvanced Conversions

Another difficult type of conversion deals Another difficult type of conversion deals units that are fractions themselvesunits that are fractions themselves

Be sure convert one unit at a time; don’t Be sure convert one unit at a time; don’t try to do both at oncetry to do both at once

Work on the unit on top first; then work on Work on the unit on top first; then work on the unit on the bottomthe unit on the bottom

ExampleExample

Convert 350 g/ mL to kg/LConvert 350 g/ mL to kg/L Top firstTop first

350 g to kg 350 g to kg 350 g= 350 x 10 350 g= 350 x 10 -3-3 kg= .35 kg kg= .35 kg Bottom part afterBottom part after

1mL to L1mL to L1mL= 1x 10 1mL= 1x 10 -3-3 L= 0.001 L L= 0.001 L Result:Result:350 g/ mL = .35 kg/ 0.001L= 350kg/ L350 g/ mL = .35 kg/ 0.001L= 350kg/ L

Combination ExampleCombination Example

Convert 7634 mg/mConvert 7634 mg/m33 to Mg/L to Mg/L

TopTop7634 mg= 7634 x 10 7634 mg= 7634 x 10 -9-9 Mg= 0.000007634 Mg Mg= 0.000007634 Mg

BottomBottom1m= 10 dm1m= 10 dm1 m1 m33= 10 dm x 10 dm x10 dm= 1000 dm = 10 dm x 10 dm x10 dm= 1000 dm 33 = 1000 L = 1000 L

Result:Result:7634 mg/m7634 mg/m3 3 = 0.000007634 Mg/ 1000 L= 0.000000007634 Mg/L= 0.000007634 Mg/ 1000 L= 0.000000007634 Mg/L= 7.634 x 10 = 7.634 x 10 -9-9 Mg/L Mg/L

Accuracy vs. PrecisionAccuracy vs. Precision

AccuracyAccuracy- closeness of measurement to - closeness of measurement to correct or accepted valuecorrect or accepted value

PrecisionPrecision- closeness of a set of - closeness of a set of measurementsmeasurements

Accuracy vs. PrecisionAccuracy vs. Precision

Percent Error vs. Percent DifferencePercent Error vs. Percent Difference

Percent Error:Percent Error: Measures the accuracy of an Measures the accuracy of an

experimentexperiment Can have + or – valueCan have + or – value

%100accepted

lexperimetaaccepted

Percent Error vs. Percent DifferencePercent Error vs. Percent Difference

Percent Difference: Percent Difference: Used when one isn’t “right”Used when one isn’t “right” Compare two valuesCompare two values Measures precisionMeasures precision

%1002 and 1 valueof average

2 value1 value

ExampleExample

Measured density from lab experiment is Measured density from lab experiment is 1.40 g/mL. The correct density is 1.36 1.40 g/mL. The correct density is 1.36 g/mL. g/mL.

Find the percent error.Find the percent error.

%94.210036.1

1.40-1.36 error %

ExampleExample

Two students measured the density of a Two students measured the density of a substance. Sally got 1.40 g/mL and Bob got 1.36 substance. Sally got 1.40 g/mL and Bob got 1.36 g/mL.g/mL.

Find the percent difference.Find the percent difference.

%90.2100

21.361.401.36-1.40

difference %