2 Measurement & Uncertainty Making measurements and performing calculations with measurements is very important in science and many other fieldsAny measurement has a number with a unitHow do you know if a measurement is true?Are there limits to measurement?
3 Scientific NotationA convenient way of writing very large and very small numbersA way to indicate significant figuresStandard (Decimal) notationm (radius of H atom)Scientific notation3.0 x mcoefficient x 10 powerfirst digit must be from 1 to 91.65 x Correct format?0.053 x Correct format?12.63 x Correct format?
4 Calculations with Scientific Notation Review scientific notation in your textRead pages R56-57, Appendix CYour calculator uses a special key to enter scientific notationEE, E, Exp, SciThese keys mean “x 10exp” to your calculatorDo not use 10^
5 Calculations with Scientific Notation How to enter x 10236.0222nd EE23Your calculator screen should show 6.022E23
6 Calculations with Scientific Notation Calculate 6.52 x 1018 ÷ 4.91 x 10-56.522nd EE18÷4.91-5ENTER = 1.33…..E23
7 Accuracy, Precision, & Error Accuracy and precision are not the same thingAccuracyhow close a measurement is to the true value (actual or accepted value)Precisionhow close measurements agreehow exact a measurement isExample: a centigram balance (0.01g) is more precise than a decigram balance (0.1g)Errordifference between actual and experimental value
9 Accuracy & Precision To evaluate accuracy of a measurement: compare measurement to true valueTo evaluate precision of a measurement:compare values of two or more repeated measurements
10 Uncertainty in Measurement All measurements are approximationsAll measurements contain error, so we can only report numbers that we know for sure (certain)The certainty of a measurement is determined by the precision of the measurementSignificant figures are used to reflect certainty of measured value
11 Uncertainty in Measurement Digital instruments (like our electronic scales) estimate the final digitExample: gIn this measurement, the 7 is estimated by the scaleThe uncertainty of the scale is the smallest division reported by the scale (0.01 g)Recording the measurement with its uncertainty: ± 0.01 g
12 Significant FiguresAll digits that are known, plus one last estimated digitRepresent certainty of a measurementMust be handled properly in calculations to prevent overstating precisionReview rules to determine significant figures (p )
14 Rules for Determining Significant Figures All non-zeros YESZeros between non-zeros YESZeros at the beginning of a # NOZeros at the end, to right of “.” YESFinal zeros without “.” NOFinal zeros with “.” YES
15 Significant Figures in Calculations Multiplication & DivisionResult must have the same # of s.f. as the measurement with the fewest s.f.6.221 cm x 5.2 cm = cm2 → 32 cm2Addition & SubtractionResult may not have more decimal places than the number with the fewest decimal places= → 105
16 Uncertainty in Measurement An error due to limitations of the instrumentFor a digital instrument+/- the smallest digit62.56g +/ gFor an analog instrument+/- the estimated digitSee example
17 Determining Error Error: the difference between the accepted and experimental measurementExample:Water was measured to boil at 101.5ºCThe known bp of water is 100.0ºCCalculate the error in the measurement
18 Percent ErrorError is often better understood as a percent of the true valueNote that the numerator is absolute value!
19 3.2 International System of Units SI units (System International) used to be called the metric systemStandard units used in science
20 Metric Prefixes**Memorize these prefixes and their factors
26 EnergyUnits of EnergyEnergy is the capacity to do work or to produce heat.The joule (J) is the SI unit of energy.One calorie (cal) is the quantity of heat that raises the temperature of 1 g of pure water by 1°C.
28 Energy can be converted into other forms, but the units are still joules (J) This house is equipped with solar panels. The solar panels convert the radiant energy from the sun into electrical energy that can be used to heat water and power appliances.
29 3.3 Conversion Problems Conversion Factors Ratio of two equivalent measurements1 dozen = 12 items
30 Dimensional Analysis When solving problems, units must be consistent Unit conversion are often necessaryUse conversion factorsProblem: Determine how many centimeters are in 1 yd.1 yd x in x 2.54 cm = cm1 yd in
31 3.4 Density Density is the ratio of mass to volume Density is an intensive propertyDensity of a pure substance is constant at a given temperature
32 Density Depends on temperature Units temp density What if temp decreased?Unitsg/cm3 or g/mL for solids & liquidsg/L for gases