1. Chemistry: Matter and Change
Chapter 2
Analyzing Data

2. Chemistry: Matter and Change
Section 2.3
Uncertainty in Data

3. Chemistry: Matter and Change
Objectives
Define and compare accuracy and precision.
Describe the accuracy of experimental data using error and percent error.
Apply rules for significant figures to express uncertainty in measured and calculated values.

4. Chemistry: Matter and Change
Review Vocabulary
experiment: a set of controlled observations that test a hypothesis
New Vocabulary
accuracy percent error
precision significant figures
error

5. Chemistry: Matter and Change
Measurements contain uncertainties that affect how a result is presented.

6. Chemistry: Matter and Change
Accuracy and Precision
Accuracy refers to how close a measured value is to an accepted value.
Precision refers to how close a series of measurements are to one another.

7. Chemistry: Matter and Change
Accuracy and Precision
Error is defined as the difference between an experimental value and an accepted value.
Table 2.3
Student Density and Error Data (Unknown was sucrose; density = 1.59 g/cm3)
Student A
Student B
Student C
Density (g/cm3)
Error (g/cm3)
Trial 1
1.54
-0.05
1.40
-0.19
1.70
+0.11
Trial 2
1.60
+0.01
1.68
+0.09
1.69
+0.10
Trial 3
1.57
-0.02
1.45
-0.14
1.71
+0.12
Average
1.51

8. Chemistry: Matter and Change
Accuracy and Precision
The error equation is error = experimental value – accepted value ( = 1.54 g/cm3 – 1.59 g/cm3 = g/cm3)
Table 2.3
Student Density and Error Data (Unknown was sucrose; density = 1.59 g/cm3)
Student A
Student B
Student C
Density (g/cm3)
Error (g/cm3)
Trial 1
1.54
-0.05
1.40
-0.19
1.70
+0.11
Trial 2
1.60
+0.01
1.68
+0.09
1.69
+0.10
Trial 3
1.57
-0.02
1.45
-0.14
1.71
+0.12
Average
1.51

9. Chemistry: Matter and Change
Accuracy and Precision
The error equation is error = experimental value – accepted value ( = 1.54 g/cm3 – 1.59 g/cm3 = g/cm3)
Percent error expresses error as a percentage of the accepted value:
|error|
accepted value
x 100%
Percent error =
= 0.05 g/cm3 ÷ 1.59 g/cm3 x 100%
= 3.14 %

10. Chemistry: Matter and Change
Significant Figures
Often, precision is limited by the tools available.
Significant figures include all known digits plus one estimated (uncertain) digit.
0.05 cm is an estimated digit
0.6 cm is a known digit
11 cm is a known digit

11. Chemistry: Matter and Change
Significant Figures
Rules for significant figures:
Rule 1: Nonzero numbers are always significant.
Rule 2: Zeros between nonzero numbers are always significant.
Rule 3: All final zeros to the right of the decimal are significant.
Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation.
Rule 5: Counting numbers and defined constants have an infinite number of significant figures.

12. Chemistry: Matter and Change
Rounding Numbers
Calculators are not aware of significant figures.
Answers should not have more significant figures than the original data with the fewest figures, and should be rounded.

13. Chemistry: Matter and Change
Rounding Numbers
Rules for rounding:
Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure.
Rule 2: If the digit to the right of the last significant figure is 5 or greater, round up the last significant figure.

14. Chemistry: Matter and Change
Rounding Numbers
Addition and subtraction
Round numbers so all numbers have the same number of digits to the right of the decimal. = = =
33.44

15. Chemistry: Matter and Change
Rounding Numbers
Multiplication and division
Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.
3.62 * =

16. Chemistry: Matter and Change
Assessment
Determine the number of significant figures in the following:
8 200, 723.0, and 0.01
4, 4, and 3
4, 3, and 3
2, 3, and 1
2, 4, and 1

17. Chemistry: Matter and Change
Assessment
Determine the number of significant figures in the following:
8 200, 723.0, and 0.01
4, 4, and 3
4, 3, and 3
2, 3, and 1
2, 4, and 1

18. Chemistry: Matter and Change
Assessment
A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is your percent error?
0.20 g/L
-0.20 g/L
0.10 g/L
0.90 g/L

19. Chemistry: Matter and Change
Assessment
A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is your percent error?
0.20 g/L
-0.20 g/L
0.10 g/L
0.90 g/L

20. Chemistry: Matter and Change