1. Chapter 2
Section 3-A

2. 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.

3. 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.

4. Measurements
Scientists like to deal with precise and accurate measurements.

5. 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?).

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

7. Problem
Describe what you see in terms of accuracy and precision.

8. Problem Describe what you see in terms of accuracy and precision.
High Accuracy
High Precision

9. Problem
Describe what you see in terms of accuracy and precision.

10. Problem Describe what you see in terms of accuracy and precision.
Low Accuracy
High Precision

11. Problem
Describe what you see in terms of accuracy and precision.

12. Problem Describe what you see in terms of accuracy and precision.
Low Accuracy
Low Precision

13. Problem
Describe what you see in terms of accuracy and precision.

14. High Accuracy (on average)
Problem
Describe what you see in terms of accuracy and precision.
High Accuracy (on average)
Low Precision

15. 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.

16. Percent Error
Percent error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
Percent Error =
x 100
Valueexperimental – Valueaccepted
Valueaccepted

17. 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

18. 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)

20. Chapter 2
Section 3-B

21. 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.

22. 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.

23. Rules All nonzero digits are significant.
All zeros between two nonzero digits are significant ( Km, 40.7 L).
Zeros at the end of a number and to the right of a decimal point are significant. (85.00 g, mm).

24. 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).

25. How many significant figures?
Problem D, pg. 47
28.6 g
3440. cm
910 m L Kg

26. How many significant figures?
Practice Prob. 1, pg. 48 g Km
1002 m
400 mL cm Kg

27. 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:
1 sig. fig.
4 sig. figs.
6 sig. figs.
(7000 cm)
(7000. cm)
( cm)

28. B. Rounding Significant Figures:
The answers given on a calculator can be derived results with more digits than are justified.
Supposed you use a calculator to divide 154g by 327g.
Each of these numbers has three significant figures but the calculator will show an answer of –
Such an answer has to be rounded off.

29. Rounding Rules

30. Rounding Significant Figures
When performing calculations involving measurements certain rules apply whether you are adding, subtracting, multiplying, or dividing. FOLLOW THOSE RULES.

31. Addition and Subtraction with Significant Figures:
When adding or subtracting decimals, the answer must have the same number of the 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.

32. Addition and Subtraction
Steps when adding or subtracting:
Place all measurements in a column.
Find the rightmost place where there is a digit for each number.
Round all measurements to that place, then add or subtract.

33. Addition and Subtractioncm cm cm cm + cm

34. Addition and Subtractioncm
2.03 cm + cm

35. Addition and Subtraction
When working with WHOLE numbers, the answer should be rounded so that the FINAL sig fig digit is in the SAME PLACE as the leftmost uncertain digit.
= 5800

36. Multiplication and Division
For multiplication and division, the answer can have NO MORE significant figures than are in the measurement with the FEWEST number of significant figures

37. Multiplication and Division
Count the number of significant figures in each measurement.
Round your answer to the number of significant figures in the measurement with the LEAST number of significant figures.
3.05 g
8.47 mL
D =
= g/mL = g/mL