1. HigH ScHool Science Today
FourTH year
Textbook

2. HigH ScHool Science Today
Fourth Year
Textbook
Philippine Copyright 2009 by DIWA LEARNING SYSTEMS INC
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ISBN 978-971-46-0103-1
reviewer
Bhazel Anne H. Rara-Pelicano has a bachelor’s and master’s degree in Physics from the
University of the Philippines–Diliman. She is currently pursuing her doctorate degree in Physics
in the same university. She has received awards and scholarships in the field of physics. Ms. Rara-
Pelicano is an instructor of the National Institute of Physics at the University of the Philippines–
Diliman.

3. P r e Fa c e
Discoveries in science and technology in recent years have had a profound impact on
our society. We are now able to communicate easier with the use of the Internet and cellular
phones. We have found ways to replace damaged body parts through prostheses and organ
transplants. People are continually developing new medicines to treat diseases that were
once fatal. Scientists have been able to clone animals, find alternative fuel sources, explore
the far reaches of outer space, and develop better materials for construction. Even the way
we entertain ourselves has been affected by discoveries in science.
With all these fascinating discoveries, it is important that you understand the
scientific principles behind such advancements. The High School Science Today series has
been developed with two objectives in mind: to explain key scientific concepts clearly and
accurately within a context of unifying themes; and to introduce you to the technology and
research techniques which have resulted from the application of these scientific concepts.
The topics in each textbook are organized to keep key science concepts in clear view.
In each chapter, you will find discussions on specific technological breakthroughs and the
implications these developments have on our global community.
Understanding science requires that you observe the things around you, perform
experiments to solve problems, and explain the reasons for your observation. Each
textbook contains activities that will help you develop the skills necessary in learning
science concepts meaningfully. These activities will provide you with hands-on learning
experiences. You will be asked to predict, hypothesize, describe, make models, form
conclusions, calculate, and measure with accuracy and precision.
As such, High School Science Today will enable you to keep pace with the ever-
evolving world of science and technology. We invite you to take this journey with us—into
the future and beyond.

4. Table oF conTenTS
uniT 1 energy in SocieTy
Chapter 1 An Introduction to Physics
1.1 Physics throughout Time .................................................................................... 2
1.2 Major Branches of Physics................................................................................... 4
1.3 Physicists and Their Attitudes ............................................................................ 7
1.4 Mathematics in Physics ....................................................................................... 11
Chapter 2 Physics, Technology, and Society
2.1 Physics and Technology in Daily Life .................................................................. 19
2.2 Energy and Society .............................................................................................. 23
uniT 2 energy and THe environmenT
Chapter 3 Light as a Wave
3.1 Wave and Its Characteristics ............................................................................... 30
3.2 Reflection ............................................................................................................. 34
3.3 Refraction ............................................................................................................. 40
3.4 Diffraction ............................................................................................................ 46
3.5 Interference .......................................................................................................... 48
3.6 Polarization .......................................................................................................... 49
Chapter 4 Light and Vision
4.1 How You See ......................................................................................................... 52
4.2 Eye Defects and Lenses........................................................................................ 60
4.3 The Eye and the Camera: A Comparison ............................................................. 63
4.4 Other Optical Instruments ................................................................................. 65
Chapter 5 Atomic Structure and Radioactivity
5.1 Atomic Physics ..................................................................................................... 70
5.2 Nuclear Physics .................................................................................................... 74
5.3 Matter-Energy Equivalence ................................................................................. 78
5.4 Nuclear Reactions ................................................................................................ 82
Chapter 6 Uses of Nuclear Radiation in Society
6.1 Effects of Nuclear Applications ........................................................................... 86
6.2 Uses of Radioisotopes .......................................................................................... 92
6.3 Radiation Safety ................................................................................................... 99
uniT 3 energy in THe Home
Chapter 7 Discovery of Electricity
7.1 The Discovery of Electricity ................................................................................. 106
7.2 Filipinos in the Field of Electricity ...................................................................... 112

5. Chapter 8 Electrical Circuits
8.1 Basic Parts of a Circuit ......................................................................................... 115
8.2 Electromotive Force, Current, and Resistance in a Circuit ................................ 117
8.3 Types of Electrical Circuit Connection ............................................................... 120
8.4 Transfer of Energy in Electrical Appliances ....................................................... 128
Chapter 9 Electrical Energy
9.1 Measure of Electrical Consumption.................................................................... 131
9.2 Electrical Conservation ....................................................................................... 136
9.3 Electrical Safety.................................................................................................... 140
uniT 4 energy and THe economy
Chapter 10 Energy Generation, Utilization, Management, and Conservation
10.1 Energy Resources and Development in the Philippines .................................... 146
10.2 Risks of Energy Development ............................................................................. 156
Chapter 11 Electricity and Magnetism
11.1 Magnetic Field...................................................................................................... 162
11.2 Electromagnetic Induction .................................................................................. 168
11.3 Generators and Transformers ............................................................................. 171
11.4 Motor .................................................................................................................... 175
11.5 Electrical Energy Generation, Transmission, and Distribution ........................ 178
uniT 5 energy in TranSPorTaTion
Chapter 12 Development of Transportation Technology
12.1 Transportation: Past to Present .......................................................................... 188
12.2 Modes of Transportation .................................................................................... 189
12.3 The Future of Transportation.............................................................................. 196
Chapter 13 Force and Motion: Applications in Land, Air, and Sea Transport
13.1 The Study of Motion ............................................................................................ 200
13.2 Newton’s Laws of Motion .................................................................................... 209
13.3 Law of Conservation of Momentum ................................................................... 220
13.4 Pressure ................................................................................................................ 228
Chapter 14 Interrelationship of Force, Power, Work, and Energy
14.1 Work, Kinetic Energy, and Potential Energy ..................................................... 243
14.2 Conservation of Mechanical Energy ................................................................... 252
14.3 Power .................................................................................................................... 258
14.4 Machines .............................................................................................................. 261
14.5 Temperature ......................................................................................................... 265
14.6 Mechanical Equivalent of Heat ........................................................................... 269
14.7 Expansion of Solids, Liquids, and Gases............................................................. 270
14.8 Specific Heat Capacity.......................................................................................... 276
14.9 Heat of Vaporization and Heat of Fusion ........................................................... 279
14.10 The Laws of Thermodynamics ............................................................................. 283

6. uniT 6 energy in icT
Chapter 15 Sound and the Development of Communication
15.1 Production of Sound ............................................................................................ 296
15.2 Vibration and Waves ............................................................................................ 297
15.3 Characteristics of Sound Waves .......................................................................... 298
15.4 Doppler Effect ...................................................................................................... 302
15.5 Standing Waves .................................................................................................... 306
15.6 Energy Transfer and Transformation in Communication ................................. 307
15.7 Development of Telecommunication .................................................................. 310
Chapter 16 Electromagnetic Theory
16.1 Producing Electromagnetic Waves ...................................................................... 318
16.2 Electromagnetic Spectrum .................................................................................. 321
16.3 Radio Waves in Focus .......................................................................................... 327
16.4 Laser and Fiber Optics ......................................................................................... 329
Chapter 17 Electronic Components
17.1 More on Resistors ................................................................................................ 335
17.2 Capacitor .............................................................................................................. 336
17.3 Conductors, Semiconductors, and Insulators .................................................... 343
17.4 Semiconductor Diodes ......................................................................................... 349
17.5 Transistors ........................................................................................................... 354
17.6 Simple Integrated Circuits................................................................................... 358
17.7 Logic Circuits ....................................................................................................... 360
Glossary .............................................................................................................................. 371
Bibliography .............................................................................................................................. 375
Index .............................................................................................................................. 376

7. Unit
1
EnErgy in SociEty
Physics is considered a basic science. It deals with universal laws and the study of the
behavior and relationships of physical phenomena. In addition to its intrinsic beauty, physics
also leads to an understanding of many practical applications and ideas in other areas of science.
The laws of physics govern many principles of chemistry, biology, astronomy, and geology, among
others.
The concepts and principles of physics constitute a major foundation of technology.
Significant technological developments have been made possible through physics. For example,
applications of physics in engineering and medicine have improved the quality of life. Physics
affects our daily lives in more ways than one.

8. Chapter 1
An introduction to PhySicS
Imagine a world without telephones, televisions, and computers. How would people
communicate with one another and acquire information? Achievements in modern
science and technology have made life more convenient for people. As a result, people
can communicate regardless of distance, order food and pay bills over the phone, send
messages electronically, and even replace a damaged internal organ.
Many tools, processes, and products have been invented and enhanced through
scientific research and discoveries. Technology refers to the practical application of science
upon which it is based. It is present in all sectors of society. The pace of technological
progress and innovation has reached such tremendous heights that one could wonder if
society can cope with these technological changes. It is important that you understand the
significance or relevance of technological developments and breakthroughs in your daily life.
1. PhySicS throughout timE
1
Physics is the study of the basic interactions of matter and energy and their
transformations. It is the study of the foundations of the universe from the macroscopic
level (such as the universe itself) to the microscopic level (like atoms and subatomic
particles). It also provides the framework in the study of other sciences. For example,
physics does not teach which atoms combine to form specific compounds, but it explains
why atoms behave the way they do. The study of physics can be very holistic, but you will
find that many explorations on specific concepts of physics can and has led to very practical
applications.
High School Science Today IV

9. The expansion of physics has
brought not only changes in ideas and
acquisitions of new ones, but also a
transformation of society.
Science began even before
the first account of history was
ever written. People learned to
make predictions when they
discovered patterns, regularities, and
relationships in nature.
In the early part of the 17th
century, Galileo Galilei agreed with
the Copernican view that Earth moved
Fig. 1.1 Development in the study of various sciences
leads to the improvement of life around the sun. He also debunked
Aristotle’s falling-body hypothesis.
Galileo disproved the long accepted theory of Aristotle, which states that heavy objects
would fall or accelerate faster than light objects. Galileo found out through his experiments
that objects of different weights, when released at the same time and at the same elevation,
would fall and hit the ground at the same time, except when air resistance is present. One
of his experiments included rolling balls of various weights down an incline. According to
legend, Galileo dropped two cannon balls from the Tower of Pisa to test his hypothesis.
At the end of the 17th century, Sir Isaac Newton made a remarkable achievement in
physics when he formulated the laws of motion and gravitation.
During the 18th and the 19th centuries, electricity and magnetism were studied.
In 1819, Hans Christian Oersted of Denmark discovered that a compass needle can
be deflected by a current-carrying wire. Andre Ampere of France carried out a similar
investigation and proved the same. A few years later, Michael Faraday of England and
Joseph Henry of the United States of America further validated that electricity and
magnetism are indeed related. It was during this time that James Clerk Maxwell related
electricity and magnetism in one coherent theory. The nature of light as an electromagnetic
wave was explained by Heinrich Hertz.
At the beginning of the 20th century, Albert Einstein’s development of the theory
of relativity and his ideas on quantum mechanics marked a historic milestone in physics.
Einstein’s theory of special relativity tells the nature of objects traveling at or near the
speed of light, while quantum mechanics studies the behavior of subatomic particles such
as electrons.
Energy in Society

10. 1.2 mAjor BrAnchES of PhySicS
During Einstein’s time, all fields of science were developing rapidly and their link
to physics was established. Scientists realized that there had been overlaps between the
different fields of science. Chemists and astronomers had to be knowledgeable about
physics. Biologists had to be familiar with chemistry and physics. The integration of
astronomy, chemistry, geology, and biology to physics thus became necessary.
The following are the major branches of physics:
• Astrophysics. This branch of physics deals with the physical and chemical nature
of celestial objects and events. It has sometimes been defined as the application of
physical laws concerning astronomical objects. Astrophysics applies the theories and
methods of physics to the study of stellar structure and evolution—the origin of the
solar system.
• Physical chemistry. This branch of physics combines the principles and methods
of physics and chemistry. The fundamental, theoretical, and experimental basis of
organic, inorganic, and analytical chemistry is provided by the principles of physical
chemistry. It is also the foundation of chemical engineering.
Physical chemistry focuses on the study of chemical equilibrium, reaction rates,
solutions, molecular weights and structure, and the properties of gases, liquids,
and colloids. This field considers the influence of turbulence of fluids, temperature,
pressure, electricity, and light.
There are three principal approaches involved in physical chemistry. Thermodynamics
involves large numbers of molecules in equilibrium. Kinetics involves chemical changes
in relation to time. Molecular structure involves the electronic and atomic arrangements
in which the quantum theory is applied.
• Geophysics. This is the
study of the structure,
composition, and dynamic
changes of Earth, its
lithosphere, hydrosphere,
atmosphere, and
magnetosphere based on the
principles of physics.
Some principles of
geophysics are applied
in locating subsurface Fig. 1.2 Application of geophysics in finding subsurface
petroleum and other mineral deposits
petroleum, mineral deposits,
High School Science Today IV

11. and water supplies. Geophysics is also used to understand the interactions of the
atmosphere and hydrosphere and how certain anomalies in the ocean’s circulation
affect the atmosphere. Geophysics also explains the relation of the layers of the
lithosphere to the amount and kind of subsurface water.
• Biophysics. This refers to the application of various methods and principles of
physical science to the study of biological problems. It has branched out to different
major divisions. In physiological biophysics, physical mechanism is used to explain
biological processes such as the transmission of the nerve impulses, the muscle
contraction mechanism, and the visual mechanism. Theoretical biophysics, on the
other hand, tries to use mathematical and physical models to explain life processes.
Radiation biophysics studies the response of organisms to various kinds of radiation
for diagnostic and treatment purposes. Medical physics is the application of concepts
and methods of physics to medicine, specifically, to diagnose and treat or cure human
diseases.
The principles of biophysics are applied in the study of organic molecules, which
play an important part in the biological processes. Paper chromatography, a direct
development of adsorption techniques, is widely used to analyze tissues for chemical
components. X-ray crystallography, on the other hand, is used to determine molecular
structures. It has also been useful in studying the complex structure of proteins.
lid
paper
solvent front
solvent
(a) (b)
Fig. 1.3 (a) Paper chromatography and (b) X-ray crystallography
The study of biological problems requires optical methods. Among these optical
methods are photochemistry, light scattering, absorption spectroscopy, and laser beams.
These methods allow biophysicists to determine the structure of molecules in plants
and animals to a degree not readily possible with ordinary chemical methods.
Energy in Society

12. The following are the other branches of physics.
• Atomic physics. This is the study of the properties and structure of atoms and the
forces that act between the positive nuclei and the negative electrons in orbit around
the nuclei.
• Electrodynamics. This is the study of the interactions between electric currents and
magnetic fields created by other electric currents.
• High energy physics or particle physics. This is the study of the structure,
properties, and interactions of elementary particles.
• Mechanics. This is the study of the behavior of physical systems in terms of their
position in space, under the action of external forces which may be equal to or
different from zero.
• Nuclear physics. This is the study of the structure of atomic nuclei and the forces
responsible for the stability or the degradation of atomic nuclei and their relation to
the formation of nuclear energy.
• Optics. This is the study of the phenomena associated with the generation,
transmission, and detection of electromagnetic radiation. Optics also studies light and
vision.
• Thermodynamics. This is the study of the mechanical properties of matter related to
energy transformations involving heat and mechanical work and how it affects matter.
ACTIVITY Physics and Other Sciences
Materials
small pieces of paper with the following labels: biophysics, astrophysics, physical
chemistry, geophysics, role-playing, song writing, panel discussion, and games
Procedure
1. The labels will be categorized into A and B. A should include biophysics,
astrophysics, physical chemistry, and geophysics, and B should contain role-
playing, song writing, panel discussion, and games.
2. The class will be divided into four groups and a representative from each
group will be chosen.
3. Each representative should pick one piece of paper from A and another from B.
4. Labels from B will be the activity to be completed by the group, and labels
from A will be the topic. For example, the group which has picked biophysics
and role-playing should perform a role-playing activity about biophysics.
5. Each group should present its activity to the class.
High School Science Today IV

13. Why is it important to be knowledgeable in physics if one is to study
astronomy, biology, geology, or chemistry?
Understanding the principles of physics and its applications in other fields will
help you cope with the demands of today’s highly technological world. Recent
developments in the field of optoelectronics, lasers, and alternative sources of
energy show the practical and useful applications of the principles of physics.
1.3 PhySiciStS And thEir AttitudES
Physicists must possess scientific attitudes that can be used in their continuous search
for knowledge about how and why things behave under different conditions. Attitudes
influence a physicist’s way of thinking and his/her actions. These attitudes are ways of
looking at things developed through years of experience.
Physicists should be creative and curious. They make accurate observations and have
the capacity to design experiments and develop hypotheses and models. They are also
willing to suspend judgment until they have proven a hypothesis to be true. They are honest
in reporting data and observations they have gathered. Physicists combine curiosity and
imagination to obtain answers by experimentation.
Physicists carefully study and validate observations instead of disputing them
right away. However, among physicists themselves and other scientists for that matter,
interpretation of certain observations may differ.
Physicists are open-minded. They are willing to accept new ideas and try them out.
They are also critical. They analyze and investigate the accuracy of new ideas before
accepting them fully.
These positive attitudes enabled the scientific giants—Galileo, Newton, and Einstein—
to discover scientific principles that improved and continues to improve human life. Today’s
physicists also possess these attitudes. It allows them to help mankind and improve the
quality of life. Who are some of these physicists and what are
their contributions to the modern world?
Filipino Physicists
Gregorio Y. Zara, D. Sc. Physics. His important
contributions include the invention of the two-way television
telephone, the invention of an airplane engine that runs on
alcohol, and other methods by which solar energy can be
harnessed. Fig. 1. Gregorio Y. Zara
Energy in Society

14. In 1930, he discovered a basic physical law—the law of kinetic electrical resistance or
the Zara effect. The law states:
“All contacts, turning or sliding, between metals, between carbon and metals, between
metals and mercury, or between conductors, produce a resistance to the passage of electric current
which may be kinetic and/or permanent electrical resistance. This is observed at currents of very
low amperage. Kinetic electrical resistance is the resistance to the passage of electric current when
contacts are in motion. Permanent electrical resistance manifests itself when contacts are at rest.”
Engr. Diosdado ‘Dado’ Banatao. His advanced chip
designs were among the information technology (IT) products
that helped popularize the California Silicon Valley. This chip
design became the basic building blocks of the three high-tech
companies he started. Among his companies are the following:
Mostron, Inc., a successful manufacturer of PC motherboards;
Chips and Technologies, a developer of chip-sets; and Silicon
SubSystems or S3, a pioneer of the world’s first single-chip
graphic user interface (GUI) accelerator. The GUI accelerator
eliminates the bottleneck of the graphics subsystem, thus
improving performance of computers.
He has been acclaimed for having developed the first-ever Fig. 1. Diosdado Banatao
Ethernet controller chip that has enabled computers to link
up and communicate with one another. This controller chip is designed to simplify the
complexity of the personal computer.
Banatao was awarded the Distinguished Leadership Award by the Asian Business
League, Entrepreneur Award by the Inc. Magazine, and the Ellis Island Medal of Valor by
the National Ethnic Coalition of Organizations.
Amador Muriel, Ph.D. He developed a theory addressing the turbulence observed
in fluids. This theory of turbulence considers the individual molecules in the fluid. It is
now being tested and examined in laboratories in France,
Russia, United States, Taiwan, and Hong Kong. If the theory
is proven and given practical applications, airline disasters and
air disturbances would decrease and safety in air travel would
be ensured. Also, understanding how turbulence works would
reduce airline fuel costs by billions of dollars annually.
For these breakthroughs, Muriel has been recognized
by the international scientific community. He was appointed
member of the Institute for Advanced Studies in Princeton in
1997. In 1999, he was chosen as one of the Ten Outstanding Fig. 1. Amador Muriel
Filipinos in Science.
High School Science Today IV

15. Foreign Physicists
Table 1.1 shows the list of the Nobel Prize Winners for physics from 1990 to
2008. Alfred Nobel, the scientist who invented dynamite in 1866, built companies and
laboratories in more than 20 countries all over the world. He held more than 350 patents
and even wrote poetry and drama. Nobel shared his fortune through the Nobel Foundation
which he established at the beginning of the 20th century. The Nobel Prize is acknowledged
as the most prestigious and the highest form of international recognition in the fields
of physics, chemistry, medicine, literature, peace, and economics. The Nobel Foundation
celebrated its 100th anniversary on 29 June 2000.
Table 1.1 Nobel Prize Winners for Physics from 1990 to 2008
Year Recipients Contribution
Yoichiro Nambu for the discovery of the mechanism of spontaneous
broken symmetry in subatomic physics
2008 Makoto Kobayashi for the discovery of the origin of the broken symmetry
Toshihide Maskawa which predicts the existence of at least three families of
quarks in nature
Albert Fert for the discovery of Giant Magnetoresistance
2007
Peter Grünberg
John C. Mather for their discovery of the blackbody form and
2006 George F. Smoot anisotropy of the cosmic microwave background
radiation
Roy J. Glauber for his contribution to the quantum theory of optical
coherence
2005 John L. Hall for their contributions to the development of laser-
Theodor W. Hänsch based precision spectroscopy, including the optical
frequency comb technique
David J. Gross for the discovery of asymptotic freedom in the theory
2004 H. David Politzer of the strong interaction
Frank Wilczek
Alexei A. Abrikosov for pioneering contributions to the theory of
2003 Vitaly L. Ginzburg superconductors and superfluids
Anthony J. Leggett
Raymond Davis Jr. for pioneering contributions to astrophysics, in
Masatoshi Koshiba particular for the detection of cosmic neutrinos
2002
Riccardo Giacconi for pioneering contributions to astrophysics, which
have led to the discovery of cosmic X-ray sources
Energy in Society

16. Eric A. Cornell for the achievement of Bose-Einstein condensation in
2001 Wolfgang Ketterle dilute gases of alkali atoms, and for early fundamental
Carl E. Wieman studies of the properties of the condensates
Zhores I. Alferov for developing semiconductor heterostructures used in
2000 Herbert Kroemer high-speed- and opto-electronics
Jack S. Kilby for his part in the invention of the integrated circuit
Gerardus ‘t Hooft for elucidating the quantum structure of electroweak
1999
Martinus J.G. Veltman interactions in physics
Robert B. Laughlin for their discovery of a new form of quantum fluid with
1998 Horst L. Störmer fractionally charged excitations
Daniel C. Tsui
Steven Chu for the development of methods to cool and trap atoms
1997 Claude Cohen-Tannoudji with laser light
William D. Phillips
David M. Lee for their discovery of superfluidity in helium-3
1996 Douglas D. Osheroff
Robert C. Richardson
Martin L. Perl the discovery of the tau lepton
1995
Frederick Reines the detection of the neutrino
Bertram N. Brockhouse for the development of neutron spectroscopy
1994 Clifford G. Shull for the development of the neutron diffraction
technique
Russell A. Hulse for the discovery of a new type of pulsar, a discovery
1993 Joseph H. Taylor Jr. that has opened up new possibilities in the study of
gravitation
Georges Charpak for his invention and development of particle detectors,
1992
in particular the multiwire proportional chamber
Pierre-Gilles de Gennes for discovering that methods developed for studying
order phenomena in simple systems can be generalized
1991
to more complex forms of matter, in particular to liquid
crystals and polymers
Jerome I. Friedman for their pioneering investigations concerning deep
Henry W. Kendall inelastic scattering of electrons on protons and bound
1990
Richard E. Taylor neutrons, which have been of essential importance for
the development of the quark model in particle physics
Source: Nobel Laureates in Physics (http://nobelprize.org/nobel_prizes/physics/laureates)
These people have made remarkable leaps in the realm of physics. Their discoveries led
to inventions and innovations which have improved and are continuously improving our
world.
10 High School Science Today IV

17. 1.4 mAthEmAticS in PhySicS
Physics is a science that can show relationships between and among quantities. These
relationships are expressed using mathematical equations.
Significant Figures
Significant figures include numbers which can be read clearly from the scales of
the measuring instrument plus a last uncertain number which is estimated between the
smallest scales of the instrument. It is important that measurements taken be expressed
in the proper number of significant figures. The following are rules to be followed in
determining the number of significant figures:
Rule 1. All nonzero digits are always significant.
Examples: 72 465 five significant figures
7 246.5 five significant figures
Rule 2. A zero between nonzero digits is always significant.
Examples: 903 three significant figures
90.3 three significant figures
Rule 3. A trailing zero after a decimal point is significant.
Examples: 4 625.0 five significant figures
462.50 five significant figures
0.610 three significant figures
0.6100 four significant figures
Rule 4. A zero used to fix a decimal point in a number less than 1 is not
significant.
Examples: 0.1256 four significant figures
0.01256 four significant figures
Rule 5. A zero ending a number more than 1 may or may not be significant.
Examples: 760 000 may have two to six significant figures
The ambiguity of this last rule can be resolved by expressing these numbers in
scientific notation.
7.6 × 105 two significant figures
7.600 × 10 5
four significant figures
Energy in Society 11

18. Scientific Notation and Measurement
Very large and very small numbers can be conveniently expressed as powers of 10. The
number written to the right and above the figure 10 is called an exponent. The scientific
notation is the system of expressing products with a number between 1 and 10 multiplied
by an appropriate power of 10. A positive exponent tells how many times a number must
be multiplied by 10 to obtain a certain number. For example, 1 × l03 means 1 should be
multiplied by 10 three times, i.e., 1 × 10 × 10 × 10 equals 1 000. Conversely, 1 × 10–5 means
to divide 1 by 10 five times. Therefore, 1 × 10–5 equals 0.00001. Note that 0.00001 should
contain the same number of significant figures as 1 × 10–5. The number to be multiplied by
10 should always be between 1 and 10.
Measurement is the process of comparing a specific quantity of matter with an
agreed standard. It is a method of describing physical phenomena. There are two kinds
of quantities of measurements: fundamental and derived. Fundamental quantities can be
measured directly using specific instruments. Derived quantities are based on fundamental
measurement. They can be a combination of fundamental quantities or a combination of
fundamental and other derived quantities.
In science, the system of measurement used is the International System of Units or the
SI (Systeme Internationale d’ Unites). It was adopted for worldwide use in 1960.
Precision and Accuracy
In measurement, accuracy and precision are required. The terms precision and accuracy
have different meanings. The precision of a measurement is the degree of agreement
between different values obtained under basically the same condition. It is a measure of the
degree to which measurements agree.
A measurement is said to have
a high degree of precision when
independently obtained values closely
agree. That is, when several trials are
done under the same condition, the
numerical data that are obtained are Accurate but imprecise Inaccurate but precise
very close to one another.
For example, three of your
classmates were asked to measure the
length of a pencil. They obtained the
following results: 9.60 cm, 9.70 cm, and
9.60 cm. You can say that the values
obtained are precise because the values
are close to one another. Inaccurate and imprecise Accurate and precise
Fig. 1. Accuracy versus precision
1 High School Science Today IV

19. The accuracy of a numerical result is the degree of agreement between the
experimental result and the true value. It is quite possible in duplicate measurements to
have highly similar results while at the same time both could be far from the true value. An
error of approximately the same measure may be involved in each.
For example, the length of a pencil is 9.65 cm. This is the true value. Our experimental
results are 9.60 cm, 9.70 cm, and 9.60 cm. If you get the average of these experimental
results, which is 9.63 cm, you will see that the results are accurate because it is close to the
true value.
Many factors affect the precision and accuracy of experimental results. These factors
include condition of equipment, quality of material used, and environmental conditions
such as temperature and pressure.
Fundamental Quantities of Measurement
Below are the seven fundamental quantities of measurement and the corresponding
SI units.
1. Length is the measure of distance from one point to another. The SI unit of length is
meter (m). Meter was redefined in 1983 as the distance that light traveled in a vacuum
1
during a time interval of 299 792 458
of a second. Rulers, metersticks, tape measures,
vernier calipers, and micrometer calipers are used to measure length.
2. Mass is the measure of the quantity of matter in a body. The SI unit used to express
mass is kilogram (kg). The standard kilogram is a block of platinum-iridium alloy,
which is preserved at the International Bureau of Weights and Measures in France.
A spring balance or scale can be used to measure mass.
3. Time is the measure of duration or the interval between two events or phenomena.
The SI unit of time is second (s). Instruments such as clocks and stopwatches are used
to measure time.
4. Temperature is the measure of the average kinetic energy of all molecules of a given
substance. The SI unit of temperature is Kelvin (K). Thermometers are used to measure
temperature.
5. Luminous intensity is the measure of radiant intensity in a given direction. It
also pertains to the brightness of light. Its SI unit is candela (cd). Radiometers and
photometers are used to measure luminous intensity.
6. Electric current is the measure of flow of electrical charges. The SI unit of electric
current is ampere (A). An ammeter is used to measure electric current.
7. Mole (mol) is the amount of substance which contains as many entities as there
are atoms in 0.12 kilogram of carbon 12. Specifically, it is defined using Avogadro’s
number, whose value is 6.02 × 1023 molecule/mol.
Energy in Society 1

20. Derived Quantities of Measurement
1. Area is the amount of surface usually expressed in square meters (m2).
Arectangle= lw Asquare= s2 Atriangle = 1 bh Acircle = r2
2
where A = area, l = length, w = width, s = side, b = base, h = height, and r = radius. The
symbol π (pi) has a value of 3.1416 (estimated to four decimal places).
2. Volume is the total space occupied by a body. Its SI unit is the cubic meter (m3).
Vrectangular prism = lwh Vcylinder = πr2h
where V = volume and r = radius
3. Density is the ratio of mass to volume of a given material. Its SI unit is kilogram per
cubic meter (kg/m3).
=m
V
where = density, m = mass, and V = volume
4. Speed is the distance traveled by an object per unit time. Its SI unit is meter per
second (m/s).
v= d
t
where v = speed, d = distance, and t = time
5. Acceleration is the rate at which the velocity (a rate of change in position in a
particular direction) of a moving body changes. The change in velocity may be in
magnitude (speed), direction, or both. It is measured in meter per second squared
(m/s2).
a = ∆v
∆t
where a = acceleration, ∆v = change in velocity, and ∆t = change in time
6. Weight is the pull of gravity in an object. It is expressed in newtons (N). One newton
is equal to 1 kg · m/s2.
w = mg
where w = weight, m = mass, and |g| = the magnitude of the acceleration due to
gravity which is equal to 9.8 m/s2.
SI provides prefixes which can be used with SI units. Table 1.1 lists the 20 approved
SI prefixes.
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21. Table 1.2 Prefixes for Powers of 10
Number Factor Name Symbol
1 000 000 000 000 000 000 000 000 1024 yotta Y
1 000 000 000 000 000 000 000 1021 zetta Z
1 000 000 000 000 000 000 1018 exa E
1 000 000 000 000 000 1015 peta P
1 000 000 000 000 1012 tera T
1 000 000 000 109 giga G
1 000 000 106 mega M
1 000 103 kilo k
100 102 hecto h
10 101 deca da
0.1 10–1 deci d
0.01 10–2 centi c
0.001 10–3 milli m
0.000 001 10–6 micro µ
0.000 000 001 10–9 nano n
0.000 000 000 001 10–12 pico p
0.000 000 000 000 001 10–15 femto f
0.000 000 000 000 000 001 10–18 atto a
0.000 000 000 000 000 000 001 10–21 zepto z
0.000 000 000 000 000 000 000 001 10–24 yocto y
The SI units were developed to replace the English system of measurement because
of the complexity in converting from one unit to another using the English system. Yards,
ounces, inches, and quarts are units in the English system.
Energy in Society 1

22. Today, we still use a few units from the English system such as inches, miles, and feet.
A conversion table was developed to facilitate conversion from the English system to the
metric system and vice versa. Table 1.3 lists common conversion factors for the two systems
of measurement.
Table 1.3 Conversion Factors of the English and
Metric Systems of Measurement
Length and Volume
1 in 2.54 cm
1 ft 0.3048 m
1m 39.37 in
1 mi 1.6093 km
1L 103 cm3 or 10–3 m3
Mass
1 kg 2.2 lb
Sample Problems:
1. Annie is 5 ft 4 in tall. What is her height in meters?
Solution:
12 in
5 ft × = 60 in
1 ft
5 ft 4 in = 5 ft + 4 in = 60 in + 4 in = 64 in
2.54 cm 1m
64 in × × = 1.6 m
1 in 100 cm
2. What is the equivalent of the density of aluminum (2.7 g/cm3) in kilogram
per cubic meter?
( 100 cm ) = 27 000 kg/ m3
3
2.7 g 1 kg
× ×
cm3 1 000 g 1 m3
= 2.7 × 10 4 kg/ m3
Observe that in problem 2, the answer has the same number of significant figures as
that of the given. This should be done in converting one unit of measure to another.
1 High School Science Today IV

23. Exercises:
1. Find the density of a book which measures 25 cm × 20 cm × 1.8 cm and has a mass
of 0.5 kg.
2. Elai is 180.02 cm tall. Express her height in meters.
You now see the reason why having a good background in mathematics is important in
physics. Many physicists excel in mathematics like Isaac Newton. His book Principia was
a pioneering work in the field of mathematical physics. Some of Newton’s contributions
include the law of gravitational attraction, the discovery of the nature of white light, and
the development of differential and integral calculus.
Using his discoveries, Newton was able to further work out the details of Earth’s
motion, accurately estimate the mass of the sun and Earth, prove that tides were the result
of the moon’s gravitational attraction, explain the orbits of comets, and lay the foundation
for the treatment of wave motion.
Accurate measurements are obtained when the instrument is properly calibrated and a
correct reading is made.
Energy in Society 1

24. Chapter Review
I. Enriching Your Science Vocabulary
Choose from the words inside the box the term that is being described in each
phrase below.
measurement biophysics accuracy speed
acceleration astrophysics technology volume
density weight precision scientific notation
__________ 1. deals with the physical and chemical nature of celestial objects and
events
__________ 2. refers to the application of various methods and principles of physical
science to the study of biological problems
__________ 3. process of comparing a specific quantity of matter with an agreed
standard
__________ 4. rate at which the velocity of a moving body changes
__________ 5. pull of gravity in an object
__________ 6. distance traveled by an object per unit time
__________ 7. ratio of mass to volume of a given material
__________ 8. degree of agreement between several values obtained basically
under the same conditions
__________ 9. practical application of science
__________ 10. extent to which a measured value agrees with the standard value
of a quantity
II. Assessing Your Knowledge
A. Match the scientist with his or her achievement. Write the letter of your answer.
_____ 1. Isaac Newton a. formulated the laws of motion and
gravitation
_____ 2. Albert Einstein
b. explained the nature of light as an
_____ 3. Galileo Galilei electromagnetic wave
_____ 4. Heinrich Hertz c. postulated the theory of relativity
_____ 5. James Clerk Maxwell d. combined electricity and magnetism
into one coherent theory
e. disproved the theory that heavy objects
fall or accelerate faster than light objects
B. Convert the following.
1. 10 mi to km 3. 86 km to m
2. 300 cm to ft 4. 45 in to cm
1 High School Science Today IV