2 Accuracy and Precision Accuracy is the closeness of measurements tothe correct or accepted value of the quantitymeasured.Precision is the closeness of a set ofmeasurements of the same quantity made in thesame way (close to one another, but notnecessarily close to accepted value.
4 How is accuracy and precision measured? Percent error is calculated by subtracting theaccepted value from the experimental value,dividing the difference by the accepted value,and then multiplying by 100.
5 A student measures the mass and volume of Sample Problem:A student measures the mass and volume ofa substance and calculates its density as1.40 g/mL. The correct, or accepted, value ofthe density is 1.30 g/mL. What is the percentageerror of the student’s measurement?1.40 g/mL-1.30 g/mLx 100= 7.7%% Error =1.30 g/mLNotice that the student’s percentage error is a positive number.
6 What does a positive or negative percentage error mean? (-) Percent Error – accepted value is greaterthan experimental value(+) Percent Error – accepted value is less thanexperimental valueIn the sample problem the student’s experimentalvalue was 1.40 g/mL and the accepted valuewas 1.30 g/mL. His percentage error waspositive.
7 Why do (should) we care about percentage error? Error or uncertainty always exists in anymeasurement. The skill of the measurer orinstrument may affect the outcome.
8 Significant Figures Significant Figures in a measurement consist of all the digits known with certainty plus onefinal digit, which is somewhat uncertain or isestimated.The term “significant” does not mean certain.
9 Yes!!!!! What value should be recorded for the length of this nail? 6. What digit should berecorded first?Second?Third?Yes!!!!!6.35cmDo we need to add a unit?
10 Rules for Determining Significant Zeros Zeros appearing between nonzero digits are significant.Example: has 4 significant figures.Zeros appearing in front of all nonzero digits are not significant.Example: has 1 significant figure.Zeros at the end of a number and to the right of the decimal point are significant.Example: has 4 significant figures.
11 Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just the placeholder, it is not significant. A decimal point placed after zeros indicated that they are significant.Example: 500 has 1 significant figure500. has 3 significant figures500.0 has 4 significant figures
12 Addition or Subtraction with Significant Figures When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.2 decimalplacesExample: cmcm3 decimalplaces3.709 cmanswer canonly have 2decimal places3.71 cm
13 Multiplication and Division with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.Example: cm x cm = cm29.74 cm23 significantfigures5 significantfiguresRound to 3significant figures