1. Chapter 3 “Scientific Measurement”
Olympic High School
Chemistry - Mr Daniel
Credits: Stephen L. Cotton
Charles Page High School
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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:
Distinguish among accuracy, precision, and error of a measurement.

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

5. Measurements
Qualitative measurements are descriptive words, such as “heavy” or “warm”
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!

6. 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 multiple measurements are to each other (reproducibility)

7. Precision and Accuracy
Precise, but not accurate
Neither accurate nor precise
Precise AND accurate

8. Accuracy, Precision, and Error
Error = accepted value – experimental value
Can be positive or negative
Accepted value = the correct value based on reliable references
Experimental value = the value measured in the lab

9. Accuracy, Precision, and Error
Percent error = the absolute value of the error divided by the accepted value, then multiplied by 100.
| error |
accepted value
accepted (true) value
% error =
x 100

10. Chemistry “Scientific Notation Review”
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Olympic High School
Mr. Daniel

11. …Is also called Exponential Notation
1. Scientific Notation
…Is also called Exponential Notation
Scientists often use very large or very small numbers
Called Avogadro’s Number m
The radius of a bromine atom

12. 1. Scientific Notation
Large numbers are very inconvenient, even difficult
Thus, very large or small numbers should be written in Scientific Notation
In Scientific Notation, the number is the product of two different components:
A coefficient
Exponent: A power of 10

13. 1. Scientific Notation 2300 is: 2.3 x 103
A coefficient is a number greater than or equal to one, and less than ten
The coefficient here is 2.3
The exponent is how many times the coefficient is multiplied by ten…
The product of 2.3 x 10 x 10 x 10 equals 2300 (2.3 x 103)

14. 1. Scientific Notation
The value of the exponent changes to indicate the number of places the decimal has moved left or right. = = = = =
1.2 x 107
3.56 x 10-3
8.513 x 104
5 x 10-5
3.42 x 10-2

15. 1. Scientific Notation Multiplication and Division
Use of a calculator is permitted
use it correctly
No calculator? Multiply the coefficients, and add the exponents:
(3 x 104) x (2 x 102) =
(3.5 x 106) x (4.0 x 1012) =
6 x 106
1.4 x 1019

16. 1. Scientific Notation Multiplication and Division
In division, divide the coefficients, and subtract the exponent in the denominator from the numerator
3.0 x 105
5 x 102 =
6.0 x 102

17. 1. Scientific Notation Addition and Subtraction
Before numbers can be added or subtracted, the exponents must be the same
Calculators will take care of this
Doing it manually, you will have to make the exponents the same - it does not matter which one you change.

18. Addition and Subtraction (6.6 x 10-8) + (4.0 x 10-9) =
1. Scientific Notation
Addition and Subtraction
(6.6 x 10-8) + (4.0 x 10-9) =
(3.42 x 10-5) – (2.5 x 10-6) =
7.0 x 10-8
3.2 x 10-5
(Note that these answers have been expressed in standard form)

19. 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 shown has the greatest uncertainty in measurement?

20. Significant Figures!!

21. 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.

22. 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?

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

24. Rules for Counting Significant Figures
Zeros
Captive zeros always count as significant figures:
16.07 cm has
4 significant figures

25. Rules for Counting Significant Figures
Zeros
Leading zeros never count as significant figures:
mL has
3 significant figures

26. Rules for Counting Significant Figures
Zeros
Trailing zeros are significant only if the number contains a written decimal point:
9.300 g has
9300 g has
9300. g has
4 significant figures
2 significant figures
4 significant figures

27. 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

28. 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 come from measurements
3.20 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 g 
2 sig figs
This is a counted value
5 dogs 
unlimited

29. Significant Figures in Calculations
A calculated answer is only as accurate as the least accurate measurement from which it is calculated.
Just like a chain which is only as strong as the weakest link…
…sometimes, calculated values need to be rounded off.

30. Rounding Calculated Answers
A quick reminder about Rounding
Determine how many significant figures are needed
Locate that final digit by counting from the left
Is the next digit to the right less than 5?
No change to the final digit
Is the next digit to the right 5 or greater?
Increase the final digit by 1

31. 314.721 meters (four) 0.001775 meter (two) c) 8792 meters (two)
- Page 59
Round off each measurement to the number of significant figures shown in parentheses:
meters (four)
meter (two)
c) meters (two)
314.7 meters
meter
8800 meters

32. Rules for Significant Figures in Mathematical Operations
Multiplication and Division: The number of significant figures in an answer equals the number in the least accurate measurement used in the calculation.
6.38 cm x 2.0 cm = cm2
sigfig answer :
13 cm2 (2 sig figs)

33. Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m
100.0 g ÷ 23.7 cm3
g/cm3
4.21 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

34. Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement.
6.8 cm cm = cm
sigfig answer 
18.7 cm (3 sig figs)

35. 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.

36. Section 3.3 The International System of Units
OBJECTIVES:
List SI units of measurement and common SI prefixes.
Distinguish between the mass and weight of an object.
Convert between the Celsius and Kelvin temperature scales.

37. International System of Units
Measurements depend upon units that serve as reference standards
The Metric system was first introduced by the French following the French Revolution
It was revised and renamed the International System of Units (SI), as of 1960.
The standards of measurement used in science are those of the SI.

38. International System of Units
SI has several advantages:
-Used world-wide
-Simple
-Based on powers of 10
There are eight base units which are commonly used in chemistry: meter, cubic meter, kilogram, kelvin, second, joule, pascal and mole.

39. The Fundamental SI Units (Le Système International, SI)
(Liter)
(gram)
(ºCelsius)
(calorie)

40. Nature of Measurements
Measurement - quantitative observation
consisting of 2 parts:
1 ) number
2 ) unit
Examples: 20 grams x joules-seconds

41. International System of Units
Derived units: These are not measured directly, but are calculated, showing the relationship between two other measurements:
Speed = miles/hour (distance/time)
Density = grams/mL (mass/volume)

42. We make use of prefixes for units larger or smaller…
Length
In SI, the basic unit of length is the meter (m)
The meter is one ten millionth ( ) the distance from the equator to the North Pole.
Or more accurately for the 21st century:
1 meter equals 1,650, wavelengths of light given off from an isotope of Krypton…
We make use of prefixes for units larger or smaller…

43. SI Prefixes Common to Chemistry
Unit Abbreviation
Meaning
Exponent
Kilo- k
thousand
103
Deci- d
tenth
10-1
Centi- c
hundredth
10-2
Milli- m
thousandth
10-3
Micro- 
millionth
10-6
Nano- n
billionth
10-9
Pico- P
Trillionth
10-12
Learn These!!!

44. Converting Measurements in the SI e.g. 1.2 mm= µm
1) Mark the value of prefixes of both units
1.2 mm= µm
2) Determine the difference in the number of place values of the two prefixes by subtracting. This is how many places the decimal is to be moved.
-3-(-6) =
10-3
10-6 +3

45. Converting Measurements in the SI (continued)
3) If the difference is a positive number, move the decimal place to the right to make the numerical value larger
If the difference is a negative number, move the decimal place to the left to make the numerical value smaller
The difference is positive (+3) therefore 1.2 becomes 1200
The final answer is µm

46. Volume The space occupied by any sample of matter.
Calculated for a solid by multiplying the length x width x height; thus derived from units of length.
SI unit = cubic meter (m3)
Everyday unit = Liter (L), which is non-SI.
Note: 1000mL = 1 L
1mL = 1cm3

47. Devices for Measuring Liquid Volume
Graduated cylinders
Pipets
Burets
Volumetric Flasks
Syringes

48. The Volume Changes!
Volumes of a solid, liquid, or gas will generally increase with temperature
Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about room temperature

49. Units of Mass Mass is a measure of the quantity of matter present
Mass is constant, regardless of location
Weight is a force that measures the pull by gravity- it changes with location

50. Working with Mass
The SI unit of mass is the kilogram (kg), even though a more convenient everyday unit is the gram
It’s measuring instrument is the balance

51. Units of Temperature
Temperature is a measure of how hot or cold an object is based upon the kinetic energy (movement) of the atoms.
Heat is a form of energy which moves from objects at higher temperatures to objects at lower temperatures.
(Measured with a thermometer.)

52. Temperature Units We use two units of temperature:
Celsius – named after Anders Celsius
Kelvin – named after Lord Kelvin

53. Units of Temperature
Celsius scale is defined by two readily determined temperatures:
Freezing point of water = 0 oC
Boiling point of water = 100 oC
Kelvin scale is based on the concept of Absolute Zero: the point at which there is no atom movement
absolute zero = 0 K (thus no negative values)

55. Temperature Continued…
Kelvin does not use the degree sign, but is just represented by K
The formulas to convert between Kelvin and Celsius:
K = oC + 273
oC = K - 273

56. Units of Energy Energy is the capacity to do work, or to produce heat.
Energy can also be measured, and two common units are:
Joule (J) = the SI unit of energy, named after James Prescott Joule
calorie (cal) = the heat needed to raise 1 gram of water by 1 oC

57. Units of Energy
Conversions between joules and calories can be carried out by using the following relationship:
1 cal = J

58. Density
Which is heavier- a kilogram of lead or a kilogram of feathers?
Many people will answer lead, but the weight is exactly the same
They are normally thinking about equal volumes of the two
The relationship here between mass and volume is called density

59. Section 3.4 Density OBJECTIVES:
Calculate the density of a material from experimental data.
Describe how density varies with temperature.

60. Density The formula for density is: Mass Density =
units used: g/mL (g/cm3) g/L for gases
Density is a physical property which does not depend upon sample size (intensive property)
Mass
Density =
Volume

61. Note temperature and density units
- Page 90

62. Density and Temperature
What happens to the density as the temperature of an object increases?
Mass remains the same
Most substances increase in volume as temperature increases
Thus, density generally decreases as the temperature increases

63. Density and Water
Water is an important exception to the previous statement.
Over certain temperatures, the volume of water increases as the temperature decreases (Do you want your water pipes to freeze in the winter?)
Does ice float in liquid water?
Why?

64. - Page 91

65. - Page 92

66. Scientific Measurement
End of Chapter 3
Scientific Measurement