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CPChemistryMath Tool KitStudy and Practice Packet SI UnitsDerived UnitsMetric PrefixesScientific NotationSignificant FiguresCounting Significant FiguresCalculations with Significant FiguresDimensional AnalysisConversion FactorsCalculating Percent ErrorCPChemistry - Math Tool Kit - Study and Referemce PacketUnits of Measurement: 7 Fundamental SI UnitsPropertySI Unit and Standard of MeasurementSymbolLengthmetermMasskilogramkgTimesecondsTemperatureKelvinKAmount of SubstancemolemolCurrentampereALuminous IntensitycandelacdDerived UnitsPropertyMeaningDerived Unit SymbolAreal x wsquare meterm2m x mVolumel x w x hcubic meterm3m x m x mVolume (liquid)cubic decimeterdm3dm x dm x dmForcemass x accelerationnewtonN1N = 1kg-m/s2Pressureforce/areapascalPa1Pa = 1N/m2Energyforce x distancejouleJ1J = 1N-mFrequencycycles/secondhertzHz1Hz = 1wave cycle/secondDensitymass/volumem/s, km/hr, m/min, etc. Speeddistance/timekg/m3, g/cm3, g/mL, etcTable of Metric PrefixesPrefix:Symbol:Magnitude:Meaning (multiply by):Tera- T10121 000 000 000 000 Giga- G1091 000 000 000 Mega- M1061 000 000 kilo- k1031000 hecto- h102100 deka- da10110 - -- - deci- d10-10.1 centi- c10-20.01 milli- m10-30.001 micro- u (mu)10-60.000 001 nano- n10-90.000 000 001 pico- p10-120.000 000 000 001 femto- f10-150.000 000 000 000 001 Scientific NotationThe speed of light is approximately 300,000,000 meters per second. Working with a large number such as this can become cumbersome so we use scientific notation to represent very large and very small numbers. 300,000,000 m/s can also be written as: 3 x 100,000,000 or 3 x 108, where 8, the exponent, is the number of zeros.Positive exponentsLarge numbers can be written in scientific notation by moving the decimal point to the left. For example, Avogadro's number, 602,200,000,000,000,000,000,000, is central to chemistry. The decimal point that you don’t see is to the right of the last zero in the measurement. The decimal point is moved left until you have a number between 1 and 10. In the example above, the decimal point was moved 23 places to the left. That number is now the positive exponent of the base 10. Negative exponentsNumbers less than 1 can be expressed in scientific notation by moving the decimal to the right. In this instance, the decimal point needs to move to the right by 4 places to the first non-zero number. For every place we move the decimal to the right we decrease the power of ten by one, starting from zero. That number can be written as 7.2 x 10-4 Review: Power of 10 notationFor any positive whole number, n, 10n is 1 followed by n zeros. Remember a positive power of 10 means a large number, greater than 1.100 = 1101 = 10102 = 100103 = 1000When 10 is raised to a negative power, the exponent tells you how many places after the decimal point to place the 1. Remember, a negative power of 10 means a small number, less than 1.10-1 = 0.110-2 = 0.0110-3 = 0.00110-4 = 0.0001 YOU TRY!!! Practice Problems: Scientific NotationExpress the following in scientific notation. Remember to retain the same significant figures.Ordinary notationScientific Notation137,000,0000.0002900.000001587380.02042007.050 x 10-34.00005 x 1072.3500 x 1041.15 x 10-3Significant FiguresSome numbers are exact and some are not. For example, your family has exactly 5 people, your class has exactly 21 students, and there are exactly 100 centimeters in one meter. The last example is a conversion factor. There is no uncertainty in a conversion factor.In chemistry lab this year you will be making measurements of mass, volume and temperature. Numbers that are obtained by making measurements are not exact. There is always uncertainty as a result of the limitations of the instrument scale and the skill of the technician reading the scale. Calculations made with measured values must be rounded off properly to the appropriate number of significant figures. Careful measurements together with rounding correctly make your reported measurements reliable.The significant figures in a measurement are all of the digits known with certainty (those for which there is a marking on the scale) plus one digit which is estimated between the smallest markings. Counting Significant FiguresIn numbers written with decimal points, count significant figures from the left beginning with the first nonzero digit. In numbers written without decimal points, count from the right beginning with the first nonzero digit.Examples: MeasurementsNumber of SFs0.03703200120.220.03400,90040.009903YOU TRY!!! Practice Problems: Counting SGsmeasurementSFs0.231002310023100.7.2030.002312000Calculating With Significant Figures:? When you use your measurements in calculations, your answer may only be as exact as your least exact measurement! RULE FOR ADDITION AND SUBTRACTION: Round to fewest decimal places.ExampleUnrounded answerRounded answerExplanation4.1cm + 0.07cm4.17cm4.2cm 4.1 has one decimal so answer rounded to tenths place18.3m – 11m7.3m7m11 has no decimals so answer rounded to ones place8.120g-7.090g1.03g1.030gBoth measurements have three decimals so answer should have three decimalsRULE FOR MULTIPLICATION AND DIVISION: Round to fewest significant figures. (abbreviated SFs)ExampleUnrounded answerRounded answerExplanation4.1cm x 0.07cm0.287cm20.3 cm2 0.07 has one SF, answer rounded to one SF7.079cm0.53s13.356603774cms13cms0.53 has two SFs, answer rounded to two SFs8.120m x 7.090m57.5708m257.57 m2Both measurements have four SFs so answer should have four SFs? Notice that units of measurement are carried through the calculations and shown in all results.YOU TRY!!! Practice Problems: Calculations with SFsPractice Problems: Using Significant Figures in CalculationsExampleUnrounded answerRounded answerExplanation145.71cm x 0.20cm210.2s0.43100. mm – 1.6 mm44302g + 0.837g587.3cm – 1.655cm62.099g + 0.05681g72.4gmL x 15.82mL8105.725g39.1mLDimensional Analysis: Units in science are sometimes called dimensions. Keeping track of units in calculations is called dimensional analysis.When you multiply or divide numbers with units (measurements) you also multiply or divide the units. Examples: Area = length x width = 3cm x 2cm = 6cm2 32 s4 s=8 (The time units, seconds, have divided out.)Density = massvolume = 853.76g310.1mL = 2.7531763947 gmL = 2.753 gmL (The units haven’t changed in the calculation and so are brought out in the result. The answer is rounded to the same number of SFs as the measurement with the fewest, the volume, which has four SFs.)Convert 3.72 hours to seconds:?s = 3.72h x 60min1h x 60s1min = 13,392s = 13,400s (Hours & minutes divided out)Conversion FactorsConversion Factors can be used to convert from one unit of measurement to another. The ability to convert between units of measurement with confidence is essential in the lab, research, industry, and hospital settings. Another name for a conversion factor is Unit Equality. That’s because a conversion factor is equal to ONE; the original quantity will not be changed when you multiply it by a Unit Equality. The reciprocal of a unit equality is also equal to one! Conversion factors are written like fractions.Example:Convert the height of a student from inches to centimeters: ? cm =63in x 2.54cm1in=160cm ?cm=63in x 1cm0.3937in =160cmCalculating Percent Error (Percent Difference)Use the equation: Percent Error=measured value-accepted valueaccepted value x 100Example: Your teacher asks you to demonstrate your skill on the balance by massing an object in the lab. You measure its mass 6.878g but the teacher’s measurement was 6.085g. If the teacher’s value is the accepted value, what is the percent error in your mass measurement?Percent Error=6.878-6.0856.085 = 0.7936.085=13.0% with 3SFsIt’s important to show the intermediate step above because this step determines the number of SFs in your answer. If your answer is a negative value it simply means that your result is lower than the true value. YOU TRY!!! Practice Problems: Percent Error 1. What is the percent error of a length measurement of 0.229cm if the correct value is 0.225cm?2. A handbook gives the density of calcium as 1.54 gmL. Lab measurements resulted in a density of 1.25 gmL. What is the percent error?YOUR NAME:Practice Problems: Unit conversions using dimensional analysis Convert 0.000830m to cm.Convert 7.56kg to g.Convert 4.02 hours to seconds.Add 9.78m to 245cm. Express your answer in cm.Convert 10km to miles.Convert 36.7miles to kilometers.The distance from wing to wing is 0.75 mi. How many cm is this?A Motrin tablet is 200. mg. How many ounces is this?The price of gas in Germany is $2.118 per liter. What is the price per gallon? ................
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