This document provides an overview of key concepts from a chemistry textbook chapter on representing and analyzing data, including:
1) It discusses the SI system of measurement units and defines base units for time, length, mass, and temperature. Derived units like liters and the concept of density are also introduced.
2) Scientific notation and the technique of dimensional analysis for unit conversions are explained. Dimensional analysis uses conversion factors to change between units.
3) The concepts of accuracy, precision, error, and significant figures are defined as ways to quantify uncertainty in measurements and calculations. Graphs are described as a method to visually depict data trends.
I split the presentation for the unit into two, as I added so many slides to help with student questions and misconceptions. This one focuses on mathematical aspects of the unit.
Basic Understanding of measurement errors, its definitions, types and few examples are discussed with pictures, block diagrams etc. Totally suitable for the learners of engineering and science fields.
This is a lecture note on Error and its propagation. This slide can be very much useful for As level physics students. It is totally different from the presentation. I would like to name it as slides of lecture notes on Error(uncertainty), difference on precision and accuracy, difference on two types of error (systematic and random errors). Believe me it will help you to enhance your knowledge on Uncertainty and its propagarion.
I split the presentation for the unit into two, as I added so many slides to help with student questions and misconceptions. This one focuses on mathematical aspects of the unit.
Basic Understanding of measurement errors, its definitions, types and few examples are discussed with pictures, block diagrams etc. Totally suitable for the learners of engineering and science fields.
This is a lecture note on Error and its propagation. This slide can be very much useful for As level physics students. It is totally different from the presentation. I would like to name it as slides of lecture notes on Error(uncertainty), difference on precision and accuracy, difference on two types of error (systematic and random errors). Believe me it will help you to enhance your knowledge on Uncertainty and its propagarion.
Need of measurement and unit in engineering and
science, definition of unit , requirements of standard
unit, systems of units-CGS,MKS and SI,
fundamental and derived quantities and their units
Definition of dimensions with examples, principle of
homogeneity of dimensions, limitations of dimensions.
Definition of accuracy, precision and error,
estimation of errors – absolute error, relative error
and percentage error, rules and identification of
significant figures.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2. Analyzing Data
Section 2.1 Units and
Measurements
Section 2.2 Scientific Notation and
Dimensional Analysis
Section 2.3 Uncertainty in Data
Section 2.4 Representing Data
Exit
Click a hyperlink or folder tab to view
the corresponding slides.
3. Section 2.1 Units and Measurements
• Define SI base units for time, length, mass, and
temperature.
mass: a measurement that reflects the amount of
matter an object contains
• Explain how adding a prefix changes a unit.
• Compare the derived units for volume and density.
4. Section 2.1 Units and Measurements (cont.)
base unit
second
meter
kilogram
Chemists use an internationally
recognized system of units to
communicate their findings.
kelvin
derived unit
liter
density
5. Units
• Système Internationale d'Unités (SI) is an
internationally agreed upon system of
measurements.
• A base unit is a defined unit in a system of
measurement that is based on an object or
event in the physical world, and is
independent of other units.
8. Units (cont.)
• The SI base unit of time is the second (s),
based on the frequency of radiation given
off by a cesium-133 atom.
• The SI base unit for length is the meter (m),
the distance light travels in a vacuum in
1/299,792,458th of a second.
• The SI base unit of mass is the kilogram
(kg), about 2.2 pounds
9. Units (cont.)
• The SI base unit of temperature
is the kelvin (K).
• Zero kelvin is the point where
there is virtually no particle
motion or kinetic energy, also
known as absolute zero.
• Two other temperature scales
are Celsius and Fahrenheit.
10. Derived Units
• Not all quantities can be measured with SI
base units.
• A unit that is defined by a combination of
base units is called a derived unit.
11. Derived Units (cont.)
• Volume is measured in cubic meters (m3
), but
this is very large. A more convenient measure
is the liter, or one cubic decimeter (dm3
).
12. Derived Units (cont.)
• Density is a derived unit, g/cm3
, the
amount of mass per unit volume.
• The density equation is
density = mass/volume.
13. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Section 2.1 Assessment
Which of the following is a derived unit?
A. yard
B. second
C. liter
D. kilogram
14. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Section 2.1 Assessment
What is the relationship between mass
and volume called?
A. density
B. space
C. matter
D. weight
15.
16. Section 2.2 Scientific Notation and
Dimensional Analysis
• Express numbers in scientific notation.
quantitative data: numerical information
describing how much, how little, how big, how
tall, how fast, and so on
• Convert between units using dimensional analysis.
17. Section 2.2 Scientific Notation and
Dimensional Analysis (cont.)
scientific notation
dimensional analysis
conversion factor
Scientists often express numbers in
scientific notation and solve problems
using dimensional analysis.
18. Scientific Notation
• Scientific notation can be used to express
any number as a number between 1 and
10 (the coefficient) multiplied by 10 raised
to a power (the exponent).
• Count the number of places the decimal point
must be moved to give a coefficient between
1 and 10.
19. Scientific Notation (cont.)
800 = 8.0 × 102
0.0000343 = 3.43 × 10–5
• The number of places moved equals the
value of the exponent.
• The exponent is positive when the decimal
moves to the left and negative when the
decimal moves to the right.
20. Scientific Notation (cont.)
• Addition and subtraction
– Exponents must be the same.
– Rewrite values with the same exponent.
– Add or subtract coefficients.
21. Scientific Notation (cont.)
• Multiplication and division
– To multiply, multiply the coefficients, then
add the exponents.
– To divide, divide the coefficients, then
subtract the exponent of the divisor from the
exponent of the dividend.
22. Dimensional Analysis
• Dimensional analysis is a systematic
approach to problem solving that uses
conversion factors to move, or convert,
from one unit to another.
• A conversion factor is a ratio of equivalent
values having different units.
23. Dimensional Analysis (cont.)
• Writing conversion factors
– Conversion factors are derived from equality
relationships, such as 1 dozen eggs = 12
eggs.
– Percentages can also be used as conversion
factors. They relate the number of parts of
one component to 100 total parts.
24. Dimensional Analysis (cont.)
• Using conversion factors
– A conversion factor must cancel one unit
and introduce a new one.
25. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Section 2.2 Assessment
What is a systematic approach to problem
solving that converts from one unit to
another?
A. conversion ratio
B. conversion factor
C. scientific notation
D. dimensional analysis
26. A. A
B. B
C. C
D. D
Section 2.2 Assessment
A
B
C
D
0% 0%0%0%
Which of the following expresses
9,640,000 in the correct scientific
notation?
A. 9.64 × 104
B. 9.64 × 105
C. 9.64 × 106
D. 9.64 × 610
27.
28. Section 2.3 Uncertainty in Data
• Define and compare accuracy and precision.
experiment: a set of controlled observations that
test a hypothesis
• Describe the accuracy of experimental data using
error and percent error.
• Apply rules for significant figures to express
uncertainty in measured and calculated values.
29. Section 2.3 Uncertainty in Data (cont.)
accuracy
precision
error
Measurements contain uncertainties
that affect how a result is presented.
percent error
significant figures
30. 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.
31. Accuracy and Precision (cont.)
• Error is defined as the difference between
and experimental value and an accepted
value.
32. Accuracy and Precision (cont.)
• The error equation is
error = experimental value – accepted value.
• Percent error expresses error as a
percentage of the accepted value.
33. Significant Figures
• Often, precision is limited by the tools
available.
• Significant figures include all known digits
plus one estimated digit.
34. Significant Figures (cont.)
• 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.
35. 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.
36. Rounding Numbers (cont.)
• 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 greater than 5, round up to the last
significant figure.
– Rule 3: If the digits to the right of the last significant
figure are a 5 followed by a nonzero digit, round up
to the last significant figure.
37. Rounding Numbers (cont.)
• Rules for rounding (cont.)
– Rule 4: If the digits to the right of the last significant
figure are a 5 followed by a 0 or no other number at
all, look at the last significant figure. If it is odd,
round it up; if it is even, do not round up.
38. Rounding Numbers (cont.)
• Addition and subtraction
– Round numbers so all numbers have the same
number of digits to the right of the decimal.
• Multiplication and division
– Round the answer to the same number of significant
figures as the original measurement with the fewest
significant figures.
39. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Section 2.3 Assessment
Determine the number of significant
figures in the following:
8,200, 723.0, and 0.01.
A. 4, 4, and 3
B. 4, 3, and 3
C. 2, 3, and 1
D. 2, 4, and 1
40. A. A
B. B
C. C
D. D
Section 2.3 Assessment
A
B
C
D
0% 0%0%0%
A substance has an accepted density of
2.00 g/L. You measured the density as
1.80 g/L. What is the percent error?
A. 20%
B. –20%
C. 10%
D. 90%
41.
42. Section 2.4 Representing Data
• Create graphics to
reveal patterns in data.
independent variable:
the variable that is
changed during an
experiment
graph
• Interpret graphs.
Graphs visually depict data, making it
easier to see patterns and trends.
43. Graphing
• A graph is a visual display of data that
makes trends easier to see than in a table.
44. Graphing (cont.)
• A circle graph, or pie chart, has wedges
that visually represent percentages of a
fixed whole.
45. Graphing (cont.)
• Bar graphs are often used to show how a
quantity varies across categories.
46. Graphing (cont.)
• On line graphs, independent variables are
plotted on the x-axis and dependent
variables are plotted on the y-axis.
47. Graphing (cont.)
• If a line through the points is straight, the
relationship is linear and can be analyzed
further by examining the slope.
48. Interpreting Graphs
• Interpolation is reading and estimating
values falling between points on the graph.
• Extrapolation is estimating values outside the
points by extending the line.
49. Interpreting Graphs (cont.)
• This graph shows important ozone
measurements and helps the viewer visualize
a trend from two different time periods.
50. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Section 2.4 Assessment
____ variables are plotted on the
____-axis in a line graph.
A. independent, x
B. independent, y
C. dependent, x
D. dependent, z
51. A. A
B. B
C. C
D. D
Section 2.4 Assessment
A
B
C
D
0% 0%0%0%
What kind of graph shows how quantities
vary across categories?
A. pie charts
B. line graphs
C. Venn diagrams
D. bar graphs
54. Section 2.1 Units and Measurements
Key Concepts
• SI measurement units allow scientists to report data
to other scientists.
• Adding prefixes to SI units extends the range of
possible measurements.
• To convert to Kelvin temperature, add 273 to the
Celsius temperature. K = °C + 273
• Volume and density have derived units. Density, which
is a ratio of mass to volume, can be used to identify an
unknown sample of matter.
55. Section 2.2 Scientific Notation and
Dimensional Analysis
Key Concepts
• A number expressed in scientific notation is written as a
coefficient between 1 and 10 multiplied by 10 raised to a
power.
• To add or subtract numbers in scientific notation, the
numbers must have the same exponent.
• To multiply or divide numbers in scientific notation,
multiply or divide the coefficients and then add or
subtract the exponents, respectively.
• Dimensional analysis uses conversion factors to solve
problems.
56. Section 2.3 Uncertainty in Data
Key Concepts
• An accurate measurement is close to the accepted
value. A set of precise measurements shows little
variation.
• The measurement device determines the degree of
precision possible.
• Error is the difference between the measured value and
the accepted value. Percent error gives the percent
deviation from the accepted value.
error = experimental value – accepted value
57. Section 2.3 Uncertainty in Data (cont.)
Key Concepts
• The number of significant figures reflects the
precision of reported data.
• Calculations should be rounded to the correct number
of significant figures.
58. Section 2.4 Representing Data
Key Concepts
• Circle graphs show parts of a whole. Bar graphs
show how a factor varies with time, location, or
temperature.
• Independent (x-axis) variables and dependent (y-axis)
variables can be related in a linear or a nonlinear
manner. The slope of a straight line is defined as
rise/run, or ∆y/∆x.
• Because line graph data are considered continuous,
you can interpolate between data points or
extrapolate beyond them.
59. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Which of the following is the SI derived
unit of volume?
A. gallon
B. quart
C. m3
D. kilogram
60. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Which prefix means 1/10th
?
A. deci-
B. hemi-
C. kilo-
D. centi-
61. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Divide 6.0 × 109
by 1.5 × 103
.
A. 4.0 × 106
B. 4.5 × 103
C. 4.0 × 103
D. 4.5 × 106
62. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Round the following to 3 significant
figures 2.3450.
A. 2.35
B. 2.345
C. 2.34
D. 2.40
63. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
The rise divided by the run on a line graph
is the ____.
A. x-axis
B. slope
C. y-axis
D. y-intercept
64. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Which is NOT an SI base unit?
A. meter
B. second
C. liter
D. kelvin
65. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Which value is NOT equivalent to the
others?
A. 800 m
B. 0.8 km
C. 80 dm
D. 8.0 x 105
cm
66. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Find the solution with the correct number
of significant figures:
25 × 0.25
A. 6.25
B. 6.2
C. 6.3
D. 6.250
67. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
How many significant figures are there in
0.0000245010 meters?
A. 4
B. 5
C. 6
D. 11
68. A. A
B. B
C. C
D. D
A
B
C
D
0% 0%0%0%
Which is NOT a quantitative measurement
of a liquid?
A. color
B. volume
C. mass
D. density
83. Click any of the background top tabs
to display the respective folder.
Within the Chapter Outline, clicking a section
tab on the right side of the screen will bring you
to the first slide in each respective section.
Simple navigation buttons will allow you to
progress to the next slide or the previous slide.
The “Return” button will allow you to return to the
slide that you were viewing when you clicked either
the Resources or Help tab.
The Chapter Resources Menu will allow you to
access chapter specific resources from the Chapter
Menu or any Chapter Outline slide. From within any
feature, click the Resources tab to return to this
slide.
To exit the presentation, click the Exit button on the Chapter Menu slide or
hit Escape [Esc] on your keyboards while viewing any Chapter Outline slide.