Accuracy and Precision•Accuracy is the closeness of measurements to the correct or accepted value of the quantity measured.

•Precision is the closeness of a set of measurements of the same quantity made in thesame way (close to one another, but notnecessarily close to accepted value.

•Percent error is calculated by subtracting theaccepted value from the experimental value,dividing the difference by the accepted value,and then multiplying by 100.

100 x valueAccepted

valueAccepted - valuealExperiment

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?

100 x valueAccepted

valueAccepted - valuealExperiment

% Error = 1.40 g/mL - 1.30 g/mL1.30 g/mL

x 100 = 7.7%

Notice that the student’s percentage error is a positive number.

•(-) Percent Error – accepted value is greaterthan experimental value•(+) Percent Error – accepted value is less thanexperimental value

In the sample problem the student’s experimentalvalue was 1.40 g/mL and the accepted value was 1.30 g/mL. His percentage error was positive.

•Error or uncertainty always exists in anymeasurement. The skill of the measurer orinstrument may affect the outcome.

Significant Figures

•Significant Figures in a measurement consistof all the digits known with certainty plus onefinal digit, which is somewhat uncertain or isestimated.•The term “significant” does not mean certain.

What value shouldbe recorded for thelength of this nail?

What digit should berecorded first?

Second?

Third?

6. 3 5Do we need to add a unit?

cm

Rules for Determining Significant Zeros1.Zeros appearing between nonzero digits

are significant.Example: 1001 has 4 significant figures.

2.Zeros appearing in front of all nonzero digits are not significant.

Example: 0.004 has 1 significant figure.

3.Zeros at the end of a number and to the right of the decimal point are significant.

Example: 0.004500 has 4 significant figures.

4.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 figure 500. has 3 significant figures 500.0 has 4 significant figures

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.Example: 2.35 cm + 1.359 cm

3.709 cm3 decimal places

2 decimalplaces

3.71 cmanswer can only have 2 decimal places

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: 2.35 cm x 4.1456 cm = 9.74216 cm2

3 significantfigures

5 significantfigures

9.74 cm2

Round to 3 significant figures