Chapter 2

Section 3

Objectives• Be able to define: accuracy, precision, percent error, significant

figures, scientific notation, conversion factor, hyperbola.

• Be able to distinguish between accuracy and precision.

• Be able to determine the number of significant figures in a measurement.

• Be able to perform mathematical operations and express the result in the proper number of significant figures.

• Be able to convert measurements into scientific notation.

• Be able to distinguish between inversely and directly proportional.

• Be able to perform calculations involving measurements (addition, subtraction, multiplication, division) and express the result in the proper number of significant figures and the proper units.

Accuracy

When you measure something several times, you see that measurements can vary. For a reported measurement to be useful, there must be some indication of its reliability or uncertainty. Scientists like to deal with accurate and precise measurements.

Measurements

• Scientists like to deal with precise and accurate measurements.

Accuracy

• Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured (Does it hit the bull’s eye?).

Precision

• Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

ProblemDescribe what you see in terms of accuracy and precision.

ProblemDescribe what you see in terms of accuracy and precision.

High Accuracy

High Precision

ProblemDescribe what you see in terms of accuracy and precision.

ProblemDescribe what you see in terms of accuracy and precision.

Low Accuracy

High Precision

ProblemDescribe what you see in terms of accuracy and precision.

ProblemDescribe what you see in terms of accuracy and precision.

Low Accuracy

Low Precision

ProblemDescribe what you see in terms of accuracy and precision.

ProblemDescribe what you see in terms of accuracy and precision.

High Accuracy

(on average)

Low Precision

Error

• Scientists use a number of statistical tests to see how well their data compare to their expected results.

• The accuracy of results can be compared to the correct or accepted value.

Percent Error

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

Percent Error = x 100Valueexperimental – Valueaccepted

Valueaccepted

Percent Error

• Percent error may be a positive or a negative number based on the difference between the experimental and accepted values.

• Percent error has a negative value if the accepted value is MORE than the experimental value.

• Percent error has a positive value if the accepted value is LESS than the experimental value.

Sample Problem C, Pg. 45

Measurements

• Some error or uncertainty ALWAYS exists in any measurements.

• The measuring instruments themselves place limitations on precision.

• Every measuring device has values marked on it or provides you with a readout.

• The only values you know for certainty are those marked on the device or presented in the readout.

(Next Slide)

Measurements

• In science, measured values are reported in terms of significant figures.

• Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or estimated.

• The term significant does not mean certain.

This is Imperative

• You MUST use and recognize significant figures when you work with measured quantities and report your results, and when you evaluate measurements reported by others. So, LEARN THE RULES FOR DETERMINING SIGNIFICANT FIGURES.

Rules

1. All nonzero digits are significant.

2. All zeros between two nonzero digits are significant (87 009 Km, 40.7 L).

3. Zeros at the end of a number and to the right of a decimal point are significant. (85.00 g, 9.000 000 000 mm).

Rules cont’d

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 a placeholder, it is not significant. A decimal point placed after zeros indicates that they are significant. (2000 or 2000.)

5. Conversion factors have an unlimited number of significant figures (1 Km = 1000 m).

How many significant figures?

Problem D, pg. 47

a) 28.6 g

b) 3440. cm

c) 910 m

d) 0.046 04 L

e) 0.006 700 0 Kg

How many significant figures?

Practice Prob. 1, pg. 48

a) 804.05 g

b) 0.014 403 0 Km

c) 1002 m

d) 400 mL

e) 30 000 cm

f) 0.000 625 000 Kg

Problem

Practice Prob. 2, pg. 48

Suppose the value “seven thousand centimeters” is reported to you. How should the number be expressed if it is intended to contain the following:

a) 1 sig. fig.b) 4 sig. figs.c) 6 sig. figs.

(7000 cm)(7000. cm)

(7000.00 cm)