Unit 1-Math and Methods



Unit 1-Math and MethodsLesson 1 – SI Units and Dimensional AnalysisSI Units (Le Systéme Internationale)A __________________________ is a defined unit in a system of measurementThere are ______________ standard units in SI.QuantityStandard UnitDerived units of measurementA derived unit is any unit ____________________________________________________In other words:The main derived units used in this class are _________________ and _____________________.VolumeVolume = Volume can be found mathematically (Vrect. prism = )Volume can also be measured __________________________By definition 1 cm3 = _________________________ DensityDensity = D=Units for mass are usually ____________Units for volume can either be ____________________________Remember : Many known densities are listed in your reference packet, these will be useful throughout the semester.PrefixesPrefixSymbolFactorScientific Notationgiga1 000 000 000109mega1 000 000106100010310010210101BASE UNIT11001/1010-11/10010-21/1 00010-3micro1/1 000 00010-6nano1/1 000 000 00010-9pico1/1 000 000 000 00010-12Why do we use the metric system?Advantages Unit Equalities – Some Examples1 meter = 1 mole = 1 L = 1 shirt = 1 km = 1 kg = All unit equalities can be turned into conversion factors if needed.Dimensional AnalysisProcess for __________________________________The ____________________ (1 km = 1000 m) becomes the_______________________:Using Dimensional AnalysisMultiply the starting unit by _______________________________Example: Convert 4.6 m to km4.6 m x ________ = kmExamplesConvert between the following measurements using dimensional analysis (show your conversion factors):1.) 2.34 mg x _________ = g2.) .98 mol x _________= atoms 3.) 1,098 mL x _________= L4.) 5 km x ________x_______= cmMultiple Unit Dimensional Analysis Convert 455 km/hr to m/s Convert 6.67g/mL to mg/L Convert 45m/s to mm/hr(Honors) Converting Cubed UnitsExpress 4563 mm3 in m3Express 35.6 mol/m3 in atoms/cm3Lesson 2 – Sci. Notation, Accuracy, and Significant FiguresAccuracy Versus PrecisionWhat is the difference between accuracy and precision?Precision: Accuracy: . Calculating Accuracy (Percent Error)Percent error allows you to ___________________ your answer to ____________ ___________________ to see how accurate you were.The “actual answer” is referred as the ___________________________.“Your answer” is referred to as the ___________________________.% Error = ExampleThe density of water is known to be 1.00 g/mL. You measure the mass and volume of a water sample and calculate its density to be 1.18 g/mL. What is your percent error?Scale Reading and UncertaintyUncertainty: Uncertainty exists in ________________________ not in __________________________.Counted quantities are _________________________________. Uncertainty in Measurements The ________________ spot is uncertain.Measurements between usersWhat is the length of this arrow?Likely we have many different possible answers based on our own eyes.Significant FiguresSignificant Figures:Digits with meaning:How to determine which figures are significant in a given numberAll non-zero digits (1-9) _______________________________.The zeros in a number are ______________________ significant, depending on their position in the number*There are a standard set of rules for figuring out whether or not zeros are significant. Rules for zeros: These are the ones that disappear when you write the number in scientific notation. E.g. 1005 kg (4 sig. fig) and 1.03 (3 sig. fig) E.g. 0.02 (1 sig. fig) and 0.0026 (2 sig. fig) 0.0200g (3 sig. fig), 3.0 cm (2 sig. fig), 5000 (1 sig. fig)PracticeHow many significant figures are in:400.0 ________4000 _________4004 __________0.004__________Scientific notationScientific notation has two purposes:1.2. Scientific notation has three parts: a _____________________ that is 1 or greater and less than 10, a _________________ and a _____________________: Scientific Notation Practice Convert to scientific notation: 89540 = ____________________0.000345 = ____________________0.0041 = ____________________7890000 = _____________________23000 = _____________________ Convert to standard form:6.72 x 10? = _________________________2.341 x 10ˉ? = _________________________5.6 x 10? = ___________________________1.29 x 10° = ____________________________4.78 x 10ˉ? = ___________________________Significant FiguresPacific to Atlantic RulePacific = _______________________________________Start from the Pacific (left hand side), _______________________________ with the first 1-9 integer ___________________________________.Examples20.0 = _______0.00320400 = _____1000. = _______ Atlantic Rule to PacificAtlantic = __________________________________________Start from the Atlantic (right hand side), every digit beginning with the first 1-9 integer is significantExamples100020 = __________sig digits1000 = _________sig digitsReview QuestionsDetermine the number of significant figures in the following:1005000 cm1.005 g0.000125 m1000. km0.02002 s2002 mL200.200 daysMore PracticeDetermine the number of significant figures in:72.3 g60.5 cm6.20 m0.0253 kg4320 years0.00040230 s4.05 moles4500. LSignificant Figures when in Scientific Notation The number of significant figures in a measurement that is in scientific notation is simply the _______________________________________________________of the measurement. 4.5 x 10? has ______ significant figures5.234 x 10? has ______ significant figures9.65 x 10ˉ? has _______ significant figures What about when you add two measurements?When you ____________________________________________, your answer must have the same number of digits __________________________________ as the value with the ___________________digits to the right of the decimal point.Ex 456.865 g + 2 g = 458.865 g (do the calculation first)Since 2 g has no __________________________________________, neither can your answer, which would be _______________ (three sig figs)PracticeAdd the following measurements: (don’t forget conversions)2.6 g + 3.47 g + 7.678 g =30.0 mL – 2.35 mL =5.678 cm + 3.76 cm =What about when you multiply/divide two measurements?When you ____________________________________________, your answer must have the same number of significant figures as _________________________ ____________________________________________________________.*This does not apply to ____________________________________ or _________________________________, they will not impact the number of significant figures.Ex. Find the density of an object with a mass of 2.6g and a volume of 300 mL (Density = mass/volume)Practice24m x 13.6m x 3.24m =47g ÷ 32.34 mL =40m ÷ 4.3 sec =Lesson 3 – Literal Equations A ___________________________ is an equation that uses variables to represent known values.Using algebra skills, literal equations can be ______________________ to solve for any of the values that are in the equation.Examples:Solve D = m/v for the volumeSolve D = m/v for the massSolve PV = nRT for the temperatureSolve PV = nRT for the pressureApplying the Skill (Densities are in the Reference Packet)What is the mass of a piece of copper that has a volume of 8.9 cm3 ?What is the volume of a sample of sulfur dioxide that has a mass of 26.2 g ? ................
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