1. Chapter 3 “Scientific Measurement”
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2. Section 3.1 Measurements and Their Uncertainty
OBJECTIVES:
Convert measurements to scientific notation.

3. Section 3.1 Measurements and Their Uncertainty
OBJECTIVES:
Determine the number of significant figures in a measurement and in a calculated answer.

4. Measurements
We make measurements every day: buying products, sports activities, and cooking
Qualitative measurements are words, such as heavy or hot
Quantitative measurements involve numbers (quantities), and depend on:
The reliability of the measuring instrument
the care with which it is read – this is determined by YOU!
Scientific Notation
Coefficient raised to power of 10 (ex. 1.3 x 107)
Review: Textbook pages R56 & R57

5. Scientific Notation
Uses exponents to show very large or very small numbers.
To convert a large number- move the decimal to the left until you reach the first digit. Count how many times you have moved the decimal
Get rid of any number that isn’t significant.
Example: km- 4.5x109

6. Scientific Notation
To convert a small number- move the decimal to the right until you reach the first non zero digit. Go one past it.
Example: > 1.0 x 10-8
We keep the zero after the 1 as it was included in the original number and therefore is likely significant.

7. Examples to Try

8. Accuracy, Precision, and Error
It is necessary to make good, reliable measurements in the lab
Accuracy – how close a measurement is to the true value
Precision – how close the measurements are to each other (reproducibility)

9. Precision and Accuracy
Precise, but not accurate
accurate but not precise
Precise AND accurate

10. Accuracy, Precision, and Error
Accepted value = the correct value based on reliable references (Density Table page 90)
Experimental value = the value measured in the lab

11. Accuracy, Precision, and Error
Error = accepted value – exp. value
Can be positive or negative
Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100%
| error |
accepted value
x 100%
% error =

12. Why Is there Uncertainty?
Measurements are performed with instruments, and no instrument can read to an infinite number of decimal places
Which of the balances below has the greatest uncertainty in measurement?

13. Significant Figures in Measurements
Significant figures in a measurement include all of the digits that are known, plus one more digit that is estimated.
Measurements must be reported to the correct number of significant figures.

14. Figure 3.5 Significant Figures - Page 67
Which measurement is the best?
What is the measured value?
What is the measured value?
What is the measured value?

15. Rules for Counting Significant Figures
Non-zeros always count as significant figures:
3456 has
4 significant figures

16. Rules for Counting Significant Figures
Zeros
Leading zeroes do not count as significant figures:
has
3 significant figures

17. Rules for Counting Significant Figures
Zeros
Captive zeroes always count as significant figures:
16.07 has
4 significant figures

18. Rules for Counting Significant Figures
Zeros
Trailing zeros are significant only if the number contains a written decimal point:
9.300 has
4 significant figures

19. Rules for Counting Significant Figures
Two special situations have an unlimited number of significant figures:
Counted items
23 people, or 425 thumbtacks
Exactly defined quantities
60 minutes = 1 hour

20. Sig Fig Practice #1 How many significant figures in the following?
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
These all come from some measurements
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 mL 
2 sig figs
This is a counted value
5 dogs 
unlimited

21. Significant Figures in Calculations
In general a calculated answer cannot be more precise than the least precise measurement from which it was calculated.
Ever heard that a chain is only as strong as the weakest link?
Sometimes, calculated values need to be rounded off.

22. Rounding Calculated Answers
Decide how many significant figures are needed (more on this very soon)
Round to that many digits, counting from the left
Is the next digit less than 5? Drop it.
Next digit 5 or greater? Increase by 1

23. - Page 69
Be sure to answer the question completely!

24. Rounding Calculated Answers
Addition and Subtraction
The answer should be rounded to the same number of decimal places as the least number of decimal places in the problem.

25. - Page 70

26. Rounding Calculated Answers
Multiplication and Division
Round the answer to the same number of significant figures as the least number of significant figures in the problem.

27. - Page 71

28. Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation.
6.38 x 2.0 =
12.76  13 (2 sig figs)

29. 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 x 2.87 mL
g/mL
2.96 g/mL

30. 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. =
 (3 sig figs)

31. 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
lb lb lb lb
2.030 mL mL
0.16 mL
0.160 mL
*Note the zero that has been added.

32. Conversion Factors
Conversion factors are used in solving problems in which a given measurement must be expressed in some other unit of measure.
When a measurement is multiplied by a conversion factor, the numerical value is generally changed but the actual size of the quantity measured stays the same.

33. Conversion Factors
In a conversion factor, the numerator and denominator are equal.
Example: 1m
100cm

34. Factor Label Method
We can convert between units by using conversion factors as equivalences.
Example:
Convert 0.044km to meters
0.044km = 1000m
1km
When doing conversions write the conversion factors so that the unit of measurement cancels, leaving the correct unit for your answer.

35. Try:
4.6 mg to grams
0.107g to centigrams
7.38g to kg
3.4 m/s to km/hr