1. Scientific Measurement
Chapter 3
Scientific Measurement

2. Section 3.1 Measurements and Their Uncertainty
Objectives
Convert measurements to scientific notation
Distinguish among accuracy, precision, and error of a measurement
Determine the number of significant figures in a measurement and in a calculated answer

3. Using and Expressing Measurements
Measurements are fundamental to the experimental sciences
Qualitative measurements are words such as heavy or hot
Quantitative measurements involve numbers (quantities)
Quantitative measurements 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 the power of 10
Reviewed early this year

4. Accuracy, Precision, and Error
It is necessary to make good, reliable measurements in the lab that are both correct and reproducible
Accuracy
How close a measurement is to the true value (correct)
Precision
How close the measurements are to each other (reproducibility)

5. Accuracy, Precision, and Error
To evaluate the accuracy of a measurement, the measured value must be compared to the correct value
To evaluate the precision of a measurement, you must compare the value of 2 or more repeated measurements

6. Accuracy, Precision, and Error
Precision and Accuracy
Neither accurate nor precise
Precise but not accurate
Precise and accurate

7. Accuracy, Precision, and Error
Accepted Value
The correct value based on reliable references
Experimental Value
The value measures in the lab
Error
Accepted value – experimental value
Can be positive or negative

8. Accuracy, Precision, and Error
Percent Error
The absolute value of the error divided by the accepted value, then multiplied by 100%
accepted value – experimental value
accepted value
% error =
X 100

9. Why is there uncertainty?
Measurements are performed with instruments, and no instrument can be read to an infinite number of decimal places

10. Significant Figures in Measurements
In a measurement significant figures 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

11. How many significant figures are reported in each measurement?

12. Rules for Counting Significant Figures
1st question you must ask yourself…
Is there a decimal point present?
Answer?
Absent or present
Think of our country…
We have 2 oceans on our coasts … the pacific and the atlantic
Atlantic
Pacific

13. Rules for Counting Significant Figures
If the decimal point is absent you start counting significant figures from the atlantic side (right – left)
If the decimal point is present you start counting significant figures from the pacific side (left – right)

14. Rules for Counting Significant Figures
2nd question to ask yourself …
Which numbers are significant?
THE RULES!
All non-zero numbers are significant
Example – 4,398 has 4 significant figures
Zeros appearing between non-zero digits are significant
Example – 709 has 3 significant figures

15. Rules for Counting Significant Figures
THE RULES
When a decimal point is present – begin counting from the left to the right (pacific side) with the first non-zero number. All numbers after the first non-zero number are significant, including zeros at the end of the number
Examples:
0.76 has 2 significant figures
has 4 significant figures
has 5 significant figures
5.308 has 4 significant figures

16. Rules for Counting Significant Figures
THE RULES
When a decimal point is absent – begin counting from the right to the left (atlantic side) with the first non-zero number
Examples:
189 has 3 significant figures
9,008 has 4 significant figures
23,000 has 2 significant figures
6,090 has 3 significant figures

17. Rules for Counting Significant Figures
2 special situations
Counted numbers
23 people, 5 dogs
2. Exactly defined quantities
60 minutes = 1 hour
100 cm = 1 m
Have an unlimited number of significant figures

18. Significant Figures Practice #1
How many significant figures in the following examples?
m 
17.10 kg 
100,890 L 
3.29 x 103 s 
cm 
3,200,000 
8 cats 

19. Significant Figures in Calculations
In general – a calculated answer cannot be more precise than the least precise measurement from which it was calculated
Sometimes calculated values need to be rounded off
Example
If you are asked to find the area of a floor and your 2 measurements are 7.7 m and 5.4 m (2 sig fig’s each) your answer (4 sig fig’s) must be rounded to have only 2 significant figures – 42 m

20. Rounding Calculated Answers
Decide how many significant figures are needed
Depends on the given measurements and the mathematical process
Round to that many digits, counting from the left
Is the next digit less than 5?
Drop it if so
Is the next digit 5 or greater
Increase by 1

21. Rounding Calculated Answers
Practice problem
Round each measurement to the number of significant figures shown in parentheses. Write the answer in scientific notation
meters (four)
meters (two)
8792 meters (two)

22. 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
Practice Problem
Calculate the sum of the three measurements. Give the answer to the correct number of significant figures.
m m m =
the answer can only have one decimal place
must be rounded to

23. 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
Position of decimal place has nothing to do with the rounding process
Practice Problem
perform the following operations. Give the answer to the correct number of significant figures.
2. 10 m x m =
the answer (1.47) can only have 2 significant figures
correct answer is 1.5 m2

24. Significant Figures Practice #2
Calculation
3.24 m x 7.0 m
100.0 g / 23.7 cm3
0.02 cm x cm
710 m / 3.0 s
lb x 3.23 ft
1.030 g x 2.87 mL
Calculator Says
22.68 m2
g/cm3
cm2
m/s
lb/ft
g/ml
Answer
23 m2
4.22 g/cm3
0.05 cm2
240 m/s
5870 lb/ft
2.96 g/mL

25. Significant Figures Practice #3
Calculation
3.24 m m
100.0 g g
0.02 cm cm
713.1 L L
lb lb
2.030 mL mL
Calculator Says
10.24 m
76.27 g
2.391 cm L lb
0.16 mL
Answer
10.2 m
76.3 g
2.39 cm
709.2 L lb
0.160 mL

26. Section 3.2 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

27. International System of Units
Measurements depend upon units that serve as reference standards
The standards of measurement used in science are those of the metric system

28. International System of Units
The metric system is now revised and renamed as the International System of Units (SI) as of 1960
It is based on 10 or multiples of 10
There are 7 base units
Only five commonly used in chemistry: meter, kilogram, kelvin, second, and mole

29. International System of Units

30. International System of Units
We use prefixes for units larger or smaller than the base unit
SI prefixes common to chemistry
Prefix
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

31. Nature of Measurements
Quantitative observation consisting of 2 parts:
Number
Unit
Example:
20 grams
6.63 x Joule seconds

32. International System of Units
Sometimes
Non – SI units are used
Liters, Celsius, calorie
Some are derived units
They are made of joining other units
Speed = miles/hour
Density = grams/mL

33. Length Length In SI units, the basic unit of length is the meter (m)
The distance between 2 objects
Measured with a ruler
In SI units, the basic unit of length is the meter (m)

34. Volume Volume The space occupied by any sample of matter
Calculated for a solid by multiplying the length x width x height
SI unit = cubic meter (m3)
Everyday unit = liter
1 mL = 1 cm3

35. Devices for Measuring Liquid Volume
Graduated Cylinder
Volumetric Flask
Buret
Pipets

36. The Volume Changes!
Volumes of solid, liquid, or gas will generally increase with temperature
Much more prominent with gases
Therefore, measuring instruments are calibrated for specific temperatures, usually 20 degrees Celsius, which is about room temperature

37. Mass Mass Measure of the quantity of matter present
Weight is a force that measures the pull by gravity
It changes with location
Mass is constant regardless of location
SI unit = kilogram
Measuring instrument is the balance scale

38. Temperature Temperature Measure of how hot or cold an object is
When 2 objects are in contact - heat moves from the object at the higher temperature to the object at the lower temperature
We use 2 units of temperature
Celsius
Kelvin

39. Units of Temperature Celsius scale Kelvin Scale
Defined by the freezing point of water (0 0C) and the boiling point of water (100 0C)
Kelvin Scale
Does not use the degree sign, it is just represented as K
Absolute zero = 0 K
Formula to convert: K = 0C + 273

40. Energy Energy The ability to do work, or to produce heat
Energy can also be measured
2 common units
SI unit of energy = Joule (J)
Calorie (cal) = heat needed to raise 1 gram of water by 1 0C
Conversion between joules and calories:
1 calorie = J

41. Section 3.3 Conversion Problems
Objectives
Construct conversion factors from equivalent measurements
Apply the technique of dimensional analysis to a variety of conversion problems
Convert complex units, using dimensional analysis

42. Conversion Factors Conversion Factors
A ratio of equivalent measurements
Why do we use conversion factors?
Quantities can be expressed in several ways
1 dollar = 4 quarters = 10 dimes = 100 pennies
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
These are all expressions or measurements representing the same amount of money and length

43. Conversion Factors Conversion Factors
Start with two things that are the same
One meter is one hundred centimeters
Write it as an equation
1m = 100 centimeters
Whenever 2 measurements are equivalent, a ration of the two measurements will equal 1

44. Conversion Factors 1 m = 100 cm
We can divide on each side of the equation to come up with two ways of writing the number “1”
1m = 100 cm
1m m
1m = 100 cm
The measurement in the numerator is equivalent to the measurement in the denominator
= 1
= 1
100 cm
100 cm

45. Conversion Factors A unique way of writing the number 1
In the same system they are defined quantities so they have an unlimited number of significant figures
Equivalence statements always have this relationship
Big #/Small unit = Small #/Big unit
1000 mm = 1 m
When a measurement is multiplied by a conversion factor, the numerical value is generally changed, but the actual size of the quantity measured remains the same

46. Conversion Factors
Practice by writing the two possible conversion factors for the following
Between kilograms and grams
Between feet and inches
Using qt. = 1.00 L

47. Conversion Factors What are conversion factors good for?
We can multiply by the number “one” creatively to change the units
Question: 13 inches is how many yards?
We know that 36 inches = 1 yard
1 yard
36 inches
13 inches X 1 yard
= 1

48. Conversion Factors
We can multiply by a conversion factor to change the units
Question: 13 inches is how many yards?
Known: 36 inches = 1 yard
1 yard
36 inches
13 inches X 1 yard
= 1
= yards

49. Conversion Factors
Called conversion factors because they allow us to convert units
Really just multiplying by one, in a creative way

50. Dimensional Analysis Dimensional Analysis
A way to analyze and solve problems by using units (or dimensions) of the measurement
Dimension = a unit (g, L, mL)
Analyze = to solve
Using the units to solve the problem
If you the unit of your answer are right, chances are you did the math right

51. Dimensional Analysis
Dimensional analysis provides an alternative approach to problem solving, instead of with an equation or algebra
A ruler is 12.0 inches long. How long is it in cm?
You must know the conversion factor to answer the question ( 1 inch = 2.54 cm)
12.0 inches x 2.54 cm
1 inch
= cm

52. Dimensional Analysis
A race is 10.0 km long. How far is this in miles if:
1 mile = 1,760 yards
1 meter = yards

53. Dimensional Analysis Converting Between Units
Problems in which measurements with one unit are converted to an equivalent measurement with another unit are easily solved using dimensional analysis
Question: convert 750 dg to grams

54. Dimensional Analysis Converting between units
Many complex problems are best solved by breaking the problem into manageable parts
Break the solution down into steps, and use more than one conversion factor if necessary

55. Dimensional Analysis Converting Complex Units
Complex units are those that are expressed as a ration of two units
Speed = meters/hour
Convert 15 meters/hour to cm/sec

56. Section 3.4 Density Objectives
Calculate the density of a material from the experimental data
Describe how density varies with temperature

57. Density Which is heavier – a pound of lead or a pound of feathers?
Most 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

58. Density The formula for density is: Mass Volume
Common units are: g/mL or g/cm3 (g/L for gas)
Density is a physical property, and does not depend upon sample size
Density =

59. 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

60. Density and Temperature
Water is an important exception
Over certain temperatures, the volume of water increases as the temperature decreases
Does ice float in liquid water
Why?