2Measuring & Calculating No experimentally obtained value is exactHuman errorsMethod errorsInstrument errors
3MeasurementsErrors can arise depending on the instrument that is used.It is important to use the right instrumentWould you use a balance that is calibrated to 1 g to weigh g of a substance?Which graduated cylinder would you use from Figure 2-7 to measure 8.6 mL
4Accuracy vs. Precision 2 things to consider when making a measurement What is the difference between accuracy and precision?
5Accuracy vs. Precision Accuracy: How exact it is The extent to which a measurement approaches the true value of a quantityExample:You measure 35.8 MLLab partner measures 37.2 mLTrue volume = 36.0 mLYour measurement is more accurate than your lab partner’s
6Accuracy vs. Precision Precision: How closely several measurements of the same quantity made in the same way agree with each otherMeasure the mass of a substance four times using the same balance110 g, 109 g, 111 g, and 110 g.
7Accuracy vs. PrecisionThe measurements were close to each other so they are preciseRemember that precise measurements are not always accurate measurementsEx:If the balance was not reset to zero the measurements are close to each other (precise) but not but not accurate
8Significant Figures Significant Figures: Measurement or calculation that consists of all the digits known with certainty plus one estimated or uncertain digitEx:g is accurate to 5 placesThe 6th place is the estimated digit
9Significant FiguresUsing the markings on the thermometer we can estimate the temperature to be 28.4 degree C28.4 is 3 significant figuresThe first two digits we know for certainThe third digit is an estimateThe actual temperature is between 28.2 and 28.6Report the measurements with the correct number of significant figuresExample:Measuring temperature with a thermometer marked in intervals of 1 degree C
10Significant FiguresBurets vs. Graduated Cylinders
11Significant Figures Buret vs. Graduated Cylinder 100 mL graduated cylinders are calibrated to the nearest 1 mLBurets are calibrated to the nearest 0.1 mLBest measurement with a graduated cylinder is 25.0 mL – uncertainty is in the tenths placeBest measurement with a buret is mL – uncertainty is in the hundredths place
12RuleExampleZeroes appearing between nonzero digits are significant40.7 has 3 significant figures87009 has 5 significant figuresZeroes appearing in front of nonzero digits are not significanthas 4 significant figureshas 1 significant figureZeroes at the end of a number and to the right of a decimal point are significant85.00 g has 4 significant figureshas 10 significant figuresZeros at the end of a number with no decimal point may or may not be significant. Read the rest of 4 in the book2000 may contain 1-4 significant figures2000. Has 4 significant figures
13Significant FiguresBe careful when calculating with significant figuresEx: Mass of a 32.4 mL sample = gIf we used this information to determine density D = m/v we would get g/mLThe volume has 4 significant figures while the mass has 3 and the density has 10So what do we do?
14Operation Rule Example Multiplication and DivisionThe answer can have no more significant figures than there are in the measurement with the smallest amount of significant figures12.257X________Answer = 14.24Addition and SubtractionThe answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point3.952.879Answer = 220.4
15Significant Figures Multiplication and Division The answer should have the same number of significant figures as the measurement with the least amount of significant figuresDo NOT round until the end when doing calculations
16Significant Figures Addition and Subtraction The answer can have no more digits to the right of the decimal than there are in the measurement with the smallest number of digits to the right of the decimalRemember it is only significant figures to the right of the decimal not total significant figures
17Significant Figures Exact value: Value that has no uncertainty Has an unlimited number of significant figures2 categories of exact valuesCount ValuesConversion Factors
18Significant Figures Count Values Value that is determined by counting and not by measuringExample a water molecule has 2 hydrogen atoms and 1 oxygen atomNo uncertainty in this value because we count the number of atoms NOT measure them
19Significant Figures 2. Conversion Factors 1 m = 1000 mm No uncertainty because a millimeter is determined as exactly one-thousandth of a meter1 mm = mExact values ALWAYS have more significant figures than any other value in the calculationNever use counted or conversion factors to determine the number of significant figures in your calculated results
20Scientific NotationVery large and very small numbers are written in scientific notation2 parts to each value written in scientific notation1. Number between 1 and 102. A power of 10
21Scientific Notation 1st part: 2nd part: Move the decimal to the right or left so only 1 nonzero digit is to the left of it2nd part:ExponentDetermined by counting the number of decimal places the decimal point must be moved.
22Scientific NotationIf the decimal point is moved to the left the exponent is positiveIf the decimal point is moved to the right the exponent is negativeEliminates the need to count zeroes
23Examples are in the Book page 63 Table 2-6Examples are in the Book page 63RuleAddition & Subtraction: All values must have the same exponent before they can be added or subtracted. The result is the sum or difference of the first factors all multiplied by the same exponent of 10.Multiplication: The first factors of the numbers are multiplied and the exponents of 10 are addedDivision: The first factors of the number are divided, and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator
24Scientific Notation Table 2-7 on page 64 Questions to Check for LearningPage 64 Problems 5-10 and 12
25Additional Problems1. Determine the # of significant figures in each of the following quantities218 kPa0.025 L200. m21.05 g
26Additional Problems2. Round the following quantities to the # of significant figures indicated in parentheseskm (3)155.8 g (3)cm (2)12000 kPa (3)