Observation,Observation,MeasurementMeasurement

and Calculationsand Calculations

Cartoon courtesy of NearingZero.net

Steps in the Scientific MethodSteps in the Scientific Method

1.1. ObservationsObservations-- quantitativequantitative- - qualitativequalitative

2.2. Formulating hypothesesFormulating hypotheses- - possible explanation for the possible explanation for the

observationobservation3.3. Performing experimentsPerforming experiments

- - gathering new information to gathering new information to decidedecide

whether the hypothesis is validwhether the hypothesis is valid

Outcomes Over the Long-Outcomes Over the Long-TermTerm

Theory (Model)Theory (Model)- - A set of tested hypotheses that A set of tested hypotheses that give angive an overall explanation of some natural overall explanation of some natural

phenomenon.phenomenon.

Natural LawNatural Law-- The same observation applies to The same observation applies to manymany different systemsdifferent systems-- Example - Law of Conservation of Example - Law of Conservation of MassMass

Law vs. TheoryLaw vs. Theory

A A lawlaw summarizes what summarizes what happenshappens

A A theorytheory (model) is an attempt (model) is an attempt to explain to explain whywhy it happens. it happens.

Nature of MeasurementNature of Measurement

Part 1 - Part 1 - numbernumberPart 2 - Part 2 - scale (unit)scale (unit)

Examples:Examples:2020 gramsgrams

6.63 x 106.63 x 10-34-34 Joule secondsJoule seconds

Measurement - quantitative Measurement - quantitative observation observation consisting of 2 consisting of 2 partsparts

Systems of measurementSystems of measurementMetric system vs English system

»Metric (SI) International system–Standardized -international–consistent base units–multiples of 10

»English (US) system–non-standard -only US–no consistent base units–no consistent multiples

Using the Metric systemUsing the Metric system

Prefixes for multiples of 10»T - G - M -k h d (base) d c m - - - - n - -p

»Tera 1012 – Giga 109 – Mega 106 – kilo 103

– hecto 102 – deka 10 1 – base – deci 10-1

– centi 10 –2 - milli 10 –3 – micro 10 –6 –

nano 10 –9 – pico 10 -12

»move the decimal to convert

The Fundamental SI UnitsThe Fundamental SI UnitsPhysical Quantity Name Abbreviation

Mass kilogram kg

Length meter m

Time second s

Temperature Kelvin K

Electric Current Ampere A

Amount of Substance mole mol

Luminous Intensity candela cd

SI PrefixesSI PrefixesCommon to ChemistryCommon to Chemistry

Prefix Unit Abbr. Exponent

Kilo k 103

Deci d 10-1

Centi c 10-2

Milli m 10-3

Micro 10-6

400 m = ? cm

Moving the decimalMoving the decimal

For measurements that are defined by a single unit such as length, mass, or liquid volume and later in the course, power, current, voltage, etc., simply move the decimal the number of places indicated by the prefix.

400 m = ? cm40,000 cm

75 mg = ? g7 5 mg = ? g0.075 g

0.025 m = ? mm0.000025 mm

Metric Metric– multiples of 10– move decimal– *area - move twice– *volume - move three times

English Metric– conversion factors– proportion method– unit cancellation method

Converting measurementsConverting measurements

Common ConversionsCommon Conversions

1 kilometer = .621 miles1 kilometer = .621 miles1 meter = 39.4 inches1 meter = 39.4 inches1 centimeter = .394 1 centimeter = .394

inchesinches1 kilogram = 2.2 pounds1 kilogram = 2.2 pounds

1 gram = .0353 ounce1 gram = .0353 ounce1 liter = 1.06 quarts1 liter = 1.06 quarts

Uncertainty in MeasurementUncertainty in Measurement

A A digit that must be digit that must be estimatedestimated is is called called uncertainuncertain. A . A measurementmeasurement always has some degree of always has some degree of uncertainty.uncertainty.

Why Is there Uncertainty?Why Is there Uncertainty?

Measurements are performed with instruments No instrument can read to an infinite number of decimal places

Precision and AccuracyPrecision and AccuracyAccuracyAccuracy refers to the agreement of a refers to the agreement of a particular value with the particular value with the truetrue value.value.

PrecisionPrecision refers to the degree of refers to the degree of agreement among several measurements agreement among several measurements made in the same manner.made in the same manner.

Neither accurate nor

precisePrecise but not

accuratePrecise AND

accurate

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Nonzero integersNonzero integers always count always count as significant figures.as significant figures.

34563456 hashas

44 sig figs.sig figs.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

ZerosZeros-- Captive zeros Captive zeros always count always count

asassignificant figures.(zeros significant figures.(zeros

in in between nonzeros)between nonzeros)

16.07 16.07 hashas

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

ZerosZeros-- Leading zerosLeading zeros do not count do not count as as

significant figuressignificant figures..

0.04860.0486 has has

33 sig figs. sig figs.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

ZerosZerosTrailing zerosTrailing zeros are significant are significant only if the number contains a only if the number contains a decimal point.decimal point.

9.3009.300 has has

44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant FiguresSignificant Figures

Any whole number that ends in zero and does not have a decimal in unclear or unknown.

10 unknown10 unknown

20. Has 2 significant figures20. Has 2 significant figures

Sig Fig Practice #1Sig Fig Practice #1How many significant figures in each of the following?

1.0070 m

5 sig figs

17.10 kg 4 sig figs

100,890 L unclear

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 unclear

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Multiplication and DivisionMultiplication and Division:: # sig figs in the result # sig figs in the result equals the number with the equals the number with the least number of sig figs.least number of sig figs.

6.38 x 2.0 =6.38 x 2.0 =

12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s unclear

1818.2 lb x 3.23 ft 5872.786 lb·ft 5.87 x 103 lb·ft 1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Rules for Significant Figures Rules for Significant Figures in Mathematical Operationsin Mathematical Operations

Addition and SubtractionAddition and Subtraction: The : The number of decimal places in number of decimal places in the result equals the number the result equals the number of decimal places in the of decimal places in the number with the least decimal number with the least decimal places.places.

6.8 + 11.934 =6.8 + 11.934 =18.734 18.734 18.7 ( 18.7 (3 sig figs3 sig figs))

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Significant FiguresSignificant FiguresRules for rounding off numbers (1) If the digit to be dropped is

greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13.

(2) If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.

(3) If the digit to be dropped (3) If the digit to be dropped is 5, and if any digit is 5, and if any digit

following it is not zero, the following it is not zero, the last remaining digit is last remaining digit is increased by one. For increased by one. For

example, example, 12.51 is rounded to 1312.51 is rounded to 13

Significant FiguresSignificant Figures

(4) If the digit to be dropped is 5 and is followed only by zeros, the last remaining digit is increased by one if it is odd, but left as it is if even. For example,

11.5 is rounded to 12, 11.5 is rounded to 12, 12.5 is rounded to 12. This 12.5 is rounded to 12. This

rule means that if the digit to rule means that if the digit to be dropped is 5 followed only be dropped is 5 followed only by zeros, the result is always by zeros, the result is always

rounded to the even digit. rounded to the even digit. The rationale is to avoid bias The rationale is to avoid bias in rounding: half of the time in rounding: half of the time we round up, half the time we round up, half the time

we round down.we round down.

In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000

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Scientific Scientific Notation:Notation:A method of representing very large A method of representing very large

or very small numbers in the or very small numbers in the form:form:

M x 10nM x 10n MM is a number between is a number between 11 and and 1010 nn is an integer is an integer

2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

.

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

0.00005790.0000579

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

Direct ProportionsDirect Proportions The quotient of two variables is a constant As the value of one variable increases, the other must also increase As the value of one variable decreases, the other must also decrease The graph of a direct proportion is a straight line

Inverse ProportionsInverse Proportions The product of two variables is a constant As the value of one variable increases, the other must decrease As the value of one variable decreases, the other must increase The graph of an inverse proportion is a hyperbola