Chapter 2Chapter 2Standards of MeasurementStandards of Measurement

Objectives:

Understand Mass and Weight (2.1)

Identify the metric units of measurement (2.6)

Explain what causes uncertainty in measurements (2.7, 2.8 – 2.12)

Learn how to use significant digits and scientific notation (2.2 – 2.5)

Dimensional Analysis (2.8)

Density (2.12)

The Metric System (2.6)The Metric System (2.6)The International System of UnitsThe International System of Units

Standards of measurementStandards of measurementBase units (7) – see Table 2.2 (pg 20)Base units (7) – see Table 2.2 (pg 20)

1.1. MASS: MASS: 2.2. LENGTH: LENGTH: 3.3. TIME: TIME: 4.4. COUNT, QUANTITY: COUNT, QUANTITY: 5.5. TEMPERATURE: TEMPERATURE: 6.6. ELECTRIC CURRENT: ELECTRIC CURRENT: 7.7. LUMINOUS INSTENSITY: LUMINOUS INSTENSITY:

The Metric SystemThe Metric SystemDerived Units:Derived Units: AREA: AREA: VOLUME: VOLUME: ENERGY: ENERGY: FORCE: FORCE: PRESSURE:PRESSURE: POWER: POWER: VOLTAGE: VOLTAGE: FREQUENCY: FREQUENCY: ELECTRIC CHARGE: ELECTRIC CHARGE:

The Metric SystemThe Metric System

Metric Prefixes – make base unit larger Metric Prefixes – make base unit larger or smalleror smaller

Table 2.1 – must know bolded prefixesTable 2.1 – must know bolded prefixes

Based on 10Based on 10

Math method vs. “Stairs”Math method vs. “Stairs”

Convert a volume of 12 microliters into Convert a volume of 12 microliters into centiliterscentiliters

Express a distance of 15 meters in Express a distance of 15 meters in kilometerskilometers

Which is the longer amount of time, 1351 Which is the longer amount of time, 1351 ps or 1.2 ns?ps or 1.2 ns?

Conversion PracticeConversion Practice

Uncertainty in MeasurementUncertainty in Measurement

Why are digits in measurements uncertain?Why are digits in measurements uncertain?

1.1. Instruments never completely free of flawsInstruments never completely free of flaws

2.2. Always involves estimationAlways involves estimation Choose the right instrument for the jobChoose the right instrument for the job May be estimated for you (electronic May be estimated for you (electronic

scales)scales) Scale is marked but you estimate the in-Scale is marked but you estimate the in-

betweenbetween

Uncertainty in MeasurementUncertainty in Measurement

Precision: Precision:

Accuracy: Accuracy:

Significant DigitsSignificant DigitsAll digits known with certainty plus one All digits known with certainty plus one final digit which is uncertain (or estimated)final digit which is uncertain (or estimated)All non-zeros are significant (143.34)All non-zeros are significant (143.34)A zero is significant when :A zero is significant when :– It is between nonzero digits (2004)It is between nonzero digits (2004)–

A zero is not significant when:A zero is not significant when:– –

Significant Digits - PRACTICESignificant Digits - PRACTICE

How many significant digits?How many significant digits?1.1. 54.2354.232.2. 23.0000523.000053.3. 0.00040.00044.4. 35000350005.5. 0.0005040.0005046.6. 45.62320045.6232007.7. 5,000,0005,000,0008.8. 4,000,000.14,000,000.1

Significant Digits - CalculationsSignificant Digits - Calculations

Addition and SubtractionAddition and Subtraction– Round answer to have final digit in the SAME Round answer to have final digit in the SAME

PLACE as the last digit in the LEAST PLACE as the last digit in the LEAST ACCURATE MEASUREMENTACCURATE MEASUREMENT

1.21 + 5.002 + 10. = 1.21 + 5.002 + 10. = 34.5 + 12.45 + 23.0505 = 34.5 + 12.45 + 23.0505 = 186.31 + 11.1 = 186.31 + 11.1 = 12.0231 + 3.86 = 12.0231 + 3.86 = 0.100012 + 120. =0.100012 + 120. = 1200 + 12 + 15 + 0.5 =1200 + 12 + 15 + 0.5 =

Significant Digits - CalculationsSignificant Digits - Calculations

Multiplication and DivisionMultiplication and Division– The answer has as many sig figs as the The answer has as many sig figs as the

number with the number with the 14.8 x 3.1 =14.8 x 3.1 =

18.2 x 3.0 =18.2 x 3.0 =

52/1.5 =52/1.5 =

321.868783 x 1 =321.868783 x 1 =

2400 x 2.123 =2400 x 2.123 =

15000/12.354 =15000/12.354 =

Scientific NotationScientific Notation

Convenient way of writing very large or Convenient way of writing very large or very small numbers and showing only very small numbers and showing only significant figuressignificant figures

Number between Number between

5120 becomes 5120 becomes

Move decimal point in original number to Move decimal point in original number to make number make number

Move left = ; move right = Move left = ; move right =

Scientific Notation PracticeScientific Notation Practice

123,000 =123,000 =

0.000045 =0.000045 =

23.45 =23.45 =

0.0000000003 =0.0000000003 =

1,000,000 =1,000,000 =

Scientific NotationScientific Notation

Adding and subtractingAdding and subtracting

– Numbers must be the SAME POWERNumbers must be the SAME POWER

– 1.4 x 101.4 x 1044 + 2.1 x 10 + 2.1 x 1055 (must change to (must change to 21.0 x 1021.0 x 1044) and then = ) and then =

– 3.2 x 103.2 x 103 3 + 1.8 x 10+ 1.8 x 1022 = =

Scientific NotationScientific Notation

MultiplyingMultiplying– – (2.0 x 10(2.0 x 1033) x (3.0 x 10) x (3.0 x 1044) = ) =

DividingDividing– – (8.2 x 10(8.2 x 1088) / (4.1 x 10) / (4.1 x 1044) = ) =

Types of MeasurementsTypes of Measurements

Mass – amount of matter in a bodyMass – amount of matter in a body–

Weight – measure of earth’s gravitational Weight – measure of earth’s gravitational attraction for that objectattraction for that object– –

Types of MeasurementsTypes of Measurements

Volume – the amount of space occupied Volume – the amount of space occupied by matterby matter– –

Temperature – measure of the intensity of Temperature – measure of the intensity of heat (figure 2.6)heat (figure 2.6)– – –

Conversion FactorsConversion Factors

Enable movement between metric system Enable movement between metric system and “English” systemand “English” system

See back cover of book and Appendix IIISee back cover of book and Appendix III

Common conversions you should Common conversions you should memorizememorize

Dimensional AnalysisDimensional Analysis(Problem Solving)(Problem Solving)

Remember:Remember:

A technique of converting between unitsA technique of converting between units

Dimensional AnalysisDimensional Analysis(Problem Solving)(Problem Solving)

Conversion Factors: ratio derived from the Conversion Factors: ratio derived from the equality between 2 different unitsequality between 2 different units

CF can be written either wayCF can be written either way

Dimensional AnalysisDimensional Analysis(Problem Solving)(Problem Solving)

The “t” methodThe “t” method

Conversion Factor

How many seconds are in 4.15 hours?

Dimensional AnalysisDimensional Analysis(Problem Solving)(Problem Solving)

Dimensional AnalysisDimensional Analysis(Problem Solving)(Problem Solving)

If a student needs 1.5 mL of water, how many cups does he need?

DensityDensityCommon ratio used in Common ratio used in chemistrychemistry

Physical property of a Physical property of a substancesubstance

Mass/volumeMass/volume

D = D = m m

vv

SI units: kg/mSI units: kg/m33

SolidSolid– g/cmg/cm33

LiquidLiquid– g/mLg/mL

GasGas– g/Lg/L

Can change due to temperature and/or pressure changes

DensityDensity

1.Find the density of a piece of metal with a volume of 2.7 cm3 and a mass of 10.8 g.

2. Determine the mass of an object with a density of 0.24 g/cm3 and a volume of 2 cm3.

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