Unit 3-4:Unit 3-4:Observation,Measurement

and Calculations

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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 10M x 10nn

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.

Nature of MeasurementNature of Measurement

Part 1 - Part 1 - numbernumberPart 2 - Part 2 - label (unit)label (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 partsconsisting of 2 parts

The Fundamental SI UnitsThe Fundamental SI Units (le Système International, SI)(le Système International, SI)

Physical 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. ExponentTerra T 1012

Giga G 109

Mega M 106

kilo k 103

no prefix 100

deci d 10-1

centi c 10-2

milli m 10-3

micro 10-6

nano n 10-9

pico p 10-12

Uncertainty in Uncertainty in MeasurementMeasurement

A digit that must be A digit that must be estimatedestimated is called is called uncertainuncertain. .

A A measurementmeasurement always has always has some degree of uncertainty.some degree of 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 agreement refers to the degree of agreement among several measurements made in the among several measurements made in the same manner.same manner.

Neither accurate nor

precise

Precise but not accurate

Precise AND accurate

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - DetailsNonzero digitsNonzero digits are always are always significant.significant.

34563456 hashas 44 sig figs.sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

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 has44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Captive zeros Captive zeros always always

count ascount assignificant figures.significant figures.

16.07 16.07 hashas44 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

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

significant figuressignificant figures..

0.04860.0486 has has33 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - Details

ZerosZeros-- Trailing zerosTrailing zeros without a without a decimal pointdecimal point DO NOTDO NOT count as count as significant figuressignificant figures..

500500 has has11 sig fig. sig fig.

16 00016 000 has has22 sig figs. sig figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - DetailsExact numbersExact numbers have an unlimited have an unlimited number of significant figures.number of significant figures.

11 inch = inch = 2.542.54 cm, exactlycm, exactly

UnlimitedUnlimited Sig. Figs. Sig. Figs.

Rules for Counting Rules for Counting Significant Figures - DetailsSignificant Figures - DetailsExact numbersExact numbers have an unlimited number of have an unlimited number of significant figuressignificant figures.. Like a count of whole objects.Like a count of whole objects.

35 desks35 desks have have

Unlimited Unlimited Sig.Figs.Sig.Figs.

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 5 sig figs

3.29 x 103 s 3 sig figs

0.0054 cm 2 sig figs

3,200,000 ns 2 sig figs

1 in. = 2.54 cm Unlimited

35 students Unlimited

200 mL 1 sig fig

0.040 g 2 sig figs

1.60 m 3 sig figs1 ft. = 12 in. Unlimited

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

Multiplication and DivisionMultiplication and Division:: Round Round your result to match the your result to match the measurement with the measurement with the lowest lowest significant figuressignificant figures..

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 mCalculation 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 240 m/s1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 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 OperationsAddition and SubtractionAddition and Subtraction: The : The number of decimal places in the number of decimal places in the result equals the number of decimal result equals the number of decimal places in the places in the leastleast preciseprecise measurement.measurement.

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 mCalculation Calculator says: Answer

10.24 m 10.2 m100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm713.1 L - 3.872 L 709.228 L 709.2 L1818.2 lb + 3.37 lb 1821.57 lb 1821.6

lb2.030 mL - 1.870 mL 0.16 mL 0.160 mL