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Chemistry 103OutlinePeriodic Table - Elements to MemorizeSignificant FiguresThe Calculator ProblemSlide 6Rules for Significant FiguresRules for Sig FigsSlide 9Slide 10Slide 11Slide 12Slide 13Practice Identifying Sig FigsSignificant Figures How many assuming all numbers are measured?Slide 16Rounding off NumbersCalculator: Friend or Foe?Sig Fig Rounding Example:Sig Fig Rounding ExampleSlide 21Adding Significant ZerosPractice Rounding NumbersSignificant Figures Round each to 3 sig figsSlide 25Math Operations & Sig FigsMultiplication and DivisionAddition and SubtractionReport Answer with Correct Number of Sig FigsWhen Math Operations Are MixedSlide 31Slide 32Slide 33Slide 34Slide 35Mixed Operations and Significant FiguresScientific Notation2.2 Scientific NotationComparing Numbers in Standard and Scientific NotationSlide 40Dimensional AnalysisConversion FactorsSlide 43Slide 44Slide 45Exact vs Measured RelationshipsEnglish to Metric Conversion FactorsDimensional AnalysisPractice ProblemLearning CheckLearning CheckChemistry 103Lecture 2Outline•I. Sig Figs – Identification– Rounding– Math Operations•II. Mathematics of Chemistry–Scientific Notation–Dimensional AnalysisPeriodic Table - Elements to MemorizeCopyright © 2005 by Pearson Education, Inc.Publishing as Benjamin CummingsSignificant FiguresAre the digits in any measurement known with certainty, plus one digit that is uncertain. Measured numbers convey*Magnitude*Units*PrecisionThe Calculator Problem7.83.8The Calculator Problem7.83.8Calculator Answer: 2.05263……Rules for Significant Figures It’s ALL about the ZEROsRules for Sig Figs•All non-zero numbers in a measurement are significant.45734573 has 4 sig figsRules for Sig Figs•All zeros between sig figs are significant.2300723007 has 5 sig figsRules for Sig Figs•In a number less than 1, zeros used to fix the position of the decimal are not significant.0.000210.00021 has 2 sig figsRules for Sig Figs•When a number has a decimal point, zeros to the right of the last nonzero digit are significant0.00021000.0002100 has 4 sig figsRules for Sig Figs•When a number has a decimal point, zeros to the right of the last nonzero digit are significant3400.3400. has 4 sig figsRules for Sig Figs•When a number without a decimal point explicitly shown ends in one or more zeros, we consider these zeros not to be significant. If some of the zeros are significant, bar notation is used. _ 820000 meters 3 sig figs 820000Practice Identifying Sig FigsSignificant FiguresHow many assuming all numbers are measured?a). 75924b). 30.002c). 0.004320d). 0.000002e). 46,000Significant FiguresHow many assuming all numbers are measured?a). 75924 (5 sig figs)b). 30.002 (5 sig figs)c). 0.004320 (4 sig figs)d). 0.000002 (1 sig fig)e). 46,000 (2 sig figs)Rounding off Numbers•The number of significant figures in measurements affects any calculations done with these measurements–Your calculated answer can only be as certain as the numbers used in the calculationCalculator: Friend or Foe?•Sometimes, the calculator will show more (or fewer) significant digits than it should–If the first digit to be deleted is 4 or less, simply drop it and all the following digits–If the first digit to be deleted is 5 or greater, that digit and all that follow are dropped and the last retained digit is increased by oneSig Fig Rounding Example:•Round the following measured number to 4 sig figs:•82.56702Sig Fig Rounding Example•Round the following measured number to 4 sig figs: •82.56702Sig Fig Rounding Example•Round the following measured number to 4 sig figs: •82.56702 ANSWER: 82.57Adding Significant Zeros•Sometimes a calculated answer requires more significant digits. Then one or more zeros are added.Calculated Answer Zeros Added to Give 3 Significant Figures4 4.001.5 1.500.2 0.200 12 12.0Practice Rounding NumbersSignificant FiguresRound each to 3 sig figsa). 28.394b). 0.000230600c). 2568d). 2562e). 8Significant FiguresRound each to 3 sig figsa). 28.394 ANSWER: 28.4b). 0.000230600 ANSWER: 0.000231c). 2568 ANSWER: 2570d). 2562 ANSWER: 2560e). 8 ANSWER: 8.00Math Operations & Sig FigsWhen multiplying or dividing, use•The same number of significant figures in your final answer as the measurement with the fewest significant figures.•Rounding rules to obtain the correct number of significant figures.Example:110.5 x 0.048 = 5.304 = 5.3 (rounded) 4 SF 2 SF calculator 2 SFMultiplication and DivisionWhen adding or subtracting, use•The same number of decimal places in your final answer as the measurement with the fewest decimal places (least precise measurement).•Use rounding rules to adjust the number of digits in the answer. 25.2 one decimal place + 1.34 two decimal places 26.54 calculated answer 26.5 answer with one decimal placeAddition and SubtractionReport Answer with Correct Number of Sig FigsA). 124.54 x 2.2 =B). 3420. + 2400. + 1095 =C). 98.5564 = 45.68When Math Operations Are MixedIf you have both addition/subtraction and multiplication/division in a formula, -carry out the operations in parenthesis first, and round according to the rules for that type of operation. -complete the calculation by rounding according to the rules for the final type of operation.When Math Operations Are Mixed _____5.681g_____ =(52.15ml - 32.4ml)When Math Operations Are Mixed _____5.681g_____ =(52.15ml - 32.4ml)-carry out the operations in parenthesis first, and round according to the rules for that type of operation.When Math Operations Are Mixed _____5.681g_____ = 5.681g(52.15ml - 32.4ml) 19.8mlWhen Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs) -complete the calculation by rounding according to the rules for the final type of operation.When Math Operations Are Mixed _____5.681g_____ = 5.681g (4 sig figs)(52.15ml - 32.4ml) 19.8ml (3 sig figs)ANSWER: 0.287g/ml -complete the calculation by rounding according to the rules for the final type of operation.Mixed Operations and Significant Figures•What is the result (to the correct number of significant figures) of the following calculations? Assume all numbers are measured. (179.8) x (24.4 - 23.1)Scientific NotationScientific notation •Is used to write very large or very small numbers•For the width of a human hair of 0.000 008 m is


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UNLV CHEM 103 - Lecture 2

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