CHAPTER 3 NOTES CHAPTER 3 NOTES

Scientific Scientific MeasurementMeasurement

MeasurementMeasurement

Qualitative measurements give Qualitative measurements give results in results in descriptivedescriptive, , nonnumericnonnumeric form. (Red balloon, tiny animal)form. (Red balloon, tiny animal)

Quantitative measurements give Quantitative measurements give results in a results in a definite definite form, usually form, usually numbers and a unitnumbers and a unit. (8 cm radius . (8 cm radius balloon, 6.8 kg animal)balloon, 6.8 kg animal)

Accuracy and PrecisionAccuracy and Precision

AccuracyAccuracy is how close a single is how close a single measurement comes to the experimental measurement comes to the experimental value (true value).value (true value).

PrecisionPrecision is how close several is how close several measurements agree with one anothermeasurements agree with one another. . It is a measure of reproducibility of It is a measure of reproducibility of measurements. Measurements may measurements. Measurements may be precise, yet not be accurate!be precise, yet not be accurate!

Accuracy and PrecisionAccuracy and Precision

Scientific NotationScientific NotationA number written as a product of two numbers, a coefficient A number written as a product of two numbers, a coefficient and a power of ten. and a power of ten.

6.3 6.3 × 10× 10-4-4 4.2 × 104.2 × 1033

The coefficient must be greater than or equal to 1 and less The coefficient must be greater than or equal to 1 and less than 10.than 10.

63.0 63.0 × 10× 10-4 -4 should be 6.3 × 10should be 6.3 × 10-3 -3

0.42 × 100.42 × 1033 should be 4.2 × 10should be 4.2 × 102 2

Multiplication: multiply the coefficients and add the Multiplication: multiply the coefficients and add the exponents.exponents.

(3.0 (3.0 × 10× 1044) ×) × (2.0 (2.0 × 10× 1055) =) = 6.0 6.0 × 10× 1099 (3.0 (3.0 × 10× 1044) ×) × (4.0 (4.0 × 10× 1055) =) = 12.0 12.0 × 10× 109 = 9 = 1.2 1.2 × 10× 101010

Scientific NotationScientific NotationDivision: Divide the coefficients and subtract the exponent in the Division: Divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator.denominator from the exponent in the numerator.

(6.0 (6.0 × 10× 1044)÷)÷ (1.0 (1.0 × 10× 1055) =) =

6.0 6.0 × 10× 10-1-1

(3.0 (3.0 × 10× 10-3-3) ÷) ÷ (4.0 (4.0 × 10× 1055) =) =

0.75 0.75 × 10× 10-8-8 = = 7.5 X 107.5 X 10-9-9

Addition – make all the exponents the same and add.Addition – make all the exponents the same and add.

(5.0 (5.0 × 10× 10-1-1) + (5.0 ) + (5.0 × 10× 1022) + (5.0 ) + (5.0 × 10× 10-4-4)) 0.500.50 0.0005 0.0005(0.005 (0.005 × 10× 1022) + (5.0 ) + (5.0 × 10× 1022) + (0.000005 ) + (0.000005 × 10× 1022)=)=500.5005500.5005

Scientific NotationScientific Notation

Subtraction – makeSubtraction – make all the exponents the all the exponents the same and subtract.same and subtract.

Significant FiguresSignificant FiguresSignificant figures in a measurement include Significant figures in a measurement include all the digits that are known precisely plus one all the digits that are known precisely plus one last digit that is estimated.last digit that is estimated.

It is important to consider significance of It is important to consider significance of measurements! Scientists cannot ethically measurements! Scientists cannot ethically report values that indicate more accuracy than report values that indicate more accuracy than possible. The accuracy of the laboratory possible. The accuracy of the laboratory measurement devices used determine how measurement devices used determine how accurately those measurements may be accurately those measurements may be reported.reported.

Always report measurements one place past Always report measurements one place past the smallest graduation (marked spot).the smallest graduation (marked spot).

Significant FiguresSignificant FiguresRules for determining significant Rules for determining significant figuresfigures

1. Every nonzero digit is significant1. Every nonzero digit is significant135 has 135 has three significant figuresthree significant figures6.237 has 6.237 has four significant figuresfour significant figures

2. Zeros between nonzero digits are 2. Zeros between nonzero digits are significantsignificant

Significant FiguresSignificant FiguresZeros appearing in front of nonzero digits Zeros appearing in front of nonzero digits are not significant. are not significant. 0.00240.00242 SF2 SF0.000070.000071 SF1 SF

3. Zeros at the end of a number and to the 3. Zeros at the end of a number and to the right of a decimal point are significantright of a decimal point are significant6.9806.9804 SF4 SF

Significant FiguresSignificant Figures

Zeros at the end of a number are not significant Zeros at the end of a number are not significant if they are just place markers.That means no if they are just place markers.That means no decimal!decimal!

100100

1 SF1 SF

720720

2 SF2 SF

4. Exact numbers (counts) and defined quantities 4. Exact numbers (counts) and defined quantities have have infinite infinite significant figures.significant figures.

Significant Figures in Significant Figures in CalculationsCalculations

Answers cannot be more precise than the Answers cannot be more precise than the least precise measurement from which it least precise measurement from which it was calculated. If you are using three was calculated. If you are using three measurements in calculations, the value measurements in calculations, the value least precisely measured is used to least precisely measured is used to determine how many significant figures determine how many significant figures can be reported.can be reported.

Addition/SubtractionAddition/Subtraction

For addition or subtraction, round the For addition or subtraction, round the answer to the same number of decimal answer to the same number of decimal places as the measurement with the least places as the measurement with the least number of decimal places.number of decimal places.61.2 m + 9.35 m + 8.6 m61.2 m + 9.35 m + 8.6 m 61.261.2

9.359.35 8.68.6 This result may beThis result may be

79.1579.15Reported to 1 decimal place 79.2 mReported to 1 decimal place 79.2 m

Multiplication/DivisionMultiplication/DivisionFor multiplication or division, round the For multiplication or division, round the answer to the same number of significant answer to the same number of significant figures as are contained in the figures as are contained in the measurement with the least number of measurement with the least number of significant figures.significant figures.8.3 m X 2.22 m = 18.426 m8.3 m X 2.22 m = 18.426 m22

This result may be reported to 2 SF This result may be reported to 2 SF because 8.3 contains 2 SF and 2.22 because 8.3 contains 2 SF and 2.22 contains 3 SF. contains 3 SF. 18 m18 m22

SI SystemSI System

Basically, this is the metric system.Basically, this is the metric system.

Know the prefixesKnow the prefixes

Table 3.2, p. 64Table 3.2, p. 64

SI SystemSI System

Length:Length: The basic unit of length in the The basic unit of length in the metric system is the metric system is the metermeter

Volume: Volume: The basic unit of volume is the meterThe basic unit of volume is the meter33

A liter is one cubic decimeter; 1000 mL, 1000 cmA liter is one cubic decimeter; 1000 mL, 1000 cm33..

Mass:Mass:The basic unit of mass is the kilogram. The basic unit of mass is the kilogram.

We usually use grams in the laboratoryWe usually use grams in the laboratory

Density:Density: Density is mass per unit volume, Density is mass per unit volume, usually g/mL for liquids; g/cmusually g/mL for liquids; g/cm3 3 for solids, and g/L for solids, and g/L for gasesfor gases

SI SystemSI System

Specific GravitySpecific Gravity A comparison of the density of a substance A comparison of the density of a substance

to the density of a reference substance, to the density of a reference substance, usually at the same temperature. usually at the same temperature.

Water is frequently used as the reference Water is frequently used as the reference substancesubstance

Specific gravity is a unitless value. (g/cm3Specific gravity is a unitless value. (g/cm3 g/cm3)g/cm3)

Specific gravity is commonly used to test Specific gravity is commonly used to test antifreeze effectiveness and to check urine antifreeze effectiveness and to check urine for diagnosing diabetes.for diagnosing diabetes.

SI SystemSI System

TemperatureTemperature Temperature is the degree of hotness or Temperature is the degree of hotness or

coldness of a substance.coldness of a substance. The Celsius scale has water’s freezing point The Celsius scale has water’s freezing point

at 0at 0°° and its boiling point at 100 and its boiling point at 100°° The Kelvin temperature scale has water’s The Kelvin temperature scale has water’s

freezing point at 273 and its boiling point at freezing point at 273 and its boiling point at 373373

Absolute zero is 0 KAbsolute zero is 0 K

SI SystemSI System

ErrorError Error is the Error is the accepted valueaccepted value minus the minus the

experimental valueexperimental value Percent error is the Percent error is the absolute valueabsolute value of the of the

error (accepted – experimental) divided by error (accepted – experimental) divided by the accepted times 100. This is the one we the accepted times 100. This is the one we use most often.use most often.

| | accepted – experimentalaccepted – experimental || ×× 100100

acceptedaccepted