1. Section 2.3 Uncertainty in Data
Pages 47-49

2. Types of Observations and Measurements
We make QUALITATIVE observations of reactions — changes in color and physical state.
We also make QUANTITATIVE MEASUREMENTS, which involve numbers. 2

3. Nature of Measurement
Measurement – quantitative observation consisting of two parts:
Number
Scale (unit)
Examples:
20 grams
6.63 × joule·seconds 3

4. Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT
Accuracy - how close a measurement is to the accepted value
Precision - how close a series of measurements are to each other
ACCURATE = CORRECT
PRECISE = CONSISTENT

5. Accuracy vs. Precision

6. Precision and Accuracy in Measurements
In the real world, we never know whether the measurement we make is accurate
We make repeated measurements, and strive for precision
We hope (not always correctly) that good precision implies good accuracy 6

7. Percent Error your value given value
Indicates accuracy of a measurement
your value
given value

8. Percent Error
A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.
(correct sig figs)

9. Section 2.3 Significant Figures or Digits
Pages 50-54

10. Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

11. Why Is there Uncertainty?
Measurements are performed with instruments
No instrument can read to an infinite number of decimal places

12. Significant Figures 2.31 cm Indicate precision of a measurement.
Recording Sig Figs
Sig figs in a measurement include the known digits plus a final estimated digit
2.31 cm

13. Significant Figures
What is the length of the cylinder? 13

14. Significant figures 14 The cylinder is 6.3 cm…plus a little more
The next digit is uncertain; 6.36? 6.37?
We use three significant figures to express the length of the cylinder. 14

15. When you are given a measurement to work with in a chemistry problem you may not know the type of instrument that was used to make the measurement so you must apply a set of rules in order to determine the number of significant digits that are in the measurement.

16. Rules for Counting Significant Figures
Nonzero integers always count as significant figures.
3456 has
4 significant figures

17. Rules for Counting Significant Figures
Zeros
- Leading zeros do not count as
significant figures.
has
3 significant figures

18. Rules for Counting Significant Figures
Zeros
- Captive zeros always count as
significant figures.
16.07 has
4 significant figures

19. Rules for Counting Significant Figures
Zeros
Trailing zeros are significant only if the number contains a decimal point.
9.300 has
4 significant figures
9,300 has
2 significant figures

20. Rules for Counting Significant Figures
Exact Numbers do not limit the # of sig figs in the answer. They have an infinite number of sig figs.
Counting numbers: 12 students
Exact conversions: 1 m = 100 cm
“1” in any conversion: 1 in = 2.54 cm

21. Sig Fig Practice #1 1.0070 m  5 sig figs 17.10 kg  4 sig figs
How many significant figures in each of the following?
m 
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 
2 sig figs

22. Significant Numbers in Calculations
A calculated answer cannot be more precise than the measuring tool.
A calculated answer must match the least precise measurement.
Significant figures are needed for final answers from
1) multiplying or dividing
2) adding or subtracting

23. Rules for Significant Figures in Mathematical Operations
Multiplication and Division
Use the same number of significant figures in the result as the data with the fewest significant figures.
1.827 m x m = m2 (calculator)
= 1.39 m2 (three sig. fig.)
453.6 g / 21 people = 21.6 g/person (calculator)
= g/person (four sig. fig.)
(Question: why didn’t we round to 22 g/person?)

24. Rounding Numbers in Chemistry
If the digit to the right of the last sig fig is less than 5, do not change the last sig fig.
 2.53
If the digit to the right of the last sig fig is greater than 5, round up the last sig fig.
 2.54
If the digit to the right of the last sig fig is a 5 followed by a nonzero digit, round up the last sig fig 
If the digit to the right of the last sig fig is a 5 followed by zero or no other number, look at the last sig fig. If it is odd round it up; if it is even do not round up  2.54
 2.52

25. Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3
g/cm3
4.22 g/cm3
0.02 cm x cm
cm2
0.05 cm2
710 m ÷ 3.0 s
m/s
240 m/s
lb x 3.23 ft
lb·ft
5870 lb·ft
1.030 g ÷ 2.87 mL
g/mL
2.96 g/mL

26. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement. Use the same number of decimal places in the result as the data with the fewest decimal places.
m m – m = ?
= m (calculator)
= m (2 decimal places)

27. Adding and Subtracting with Trailing Zeros
The answer has the same number of trailing zeros as the measurement with the greatest number of trailing zeros.
110 one trailing zero
two trailing zeros
2840.3
answer 2800 two trailing zeros

28. Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m
100.0 g g
76.27 g
76.3 g
0.02 cm cm
2.391 cm
2.39 cm
713.1 L L L
709.2 L
g g g g
2.030 mL mL
0.16 mL
0.160 mL