FOCUS ON PHYSICAL SCIENCE (22)

Student Resources For Students and Parents/Guardians These resources are designed to help you achieve in science You will find useful information on laboratory safety, technology skills, and math skills In addition, some physical science reference materials are found in the Reference Handbook You’ll find the information you need to learn and sharpen your skills in these resources 570 Student Resources Student Resources Student Resources Table of Contents Science Safety Skill Handbook Safety Symbols 572 Safety in the Science Laboratory 573 General Safety Rules 573 Prevent Accidents .573 Laboratory Work 573 Laboratory Cleanup 574 Emergencies 574 Technology Skill Handbook Hardware Basics 575 Storing Your Data .575 Getting Started with Word Processing Programs .576 Getting Started with Spreadsheet Programs .576 Getting Started with Presentation Programs 577 Doing Research with the World Wide Web 578 Math Skill Handbook Math Review Use Fractions 579 Use Ratios 582 Use Decimals 582 Use Proportions 583 Use Percentages 584 Solve One-Step Equations 584 Use Statistics .585 Use Geometry .586 Science Application Measure in SI 589 Dimensional Analysis 589 Precision and Significant Digits 591 Scientific Notation .591 Make and Use Graphs 592 Reference Handbook Using a Calculator 594 Understanding Scientific Terms 595 Science Reference Guide 597 Physical Science Reference Tables 598 Periodic Table of Elements 600 Student Resources 571 Science Safety Skill Handbook Science Safety Skill Handbook These safety symbols are used in laboratory and field investigations in this book to indicate possible hazards Learn the meaning of each symbol and refer to this page often Remember to wash your hands thoroughly after completing lab procedures SAFETY SYMBOLS DISPOSAL HAZARD Special disposal procedures need to be followed EXAMPLES PRECAUTION REMEDY Do not dispose of these Dispose of wastes as materials in the sink or directed by your trash can teacher certain chemicals, living organisms Organisms or other bacteria, fungi, blood, biological materials that unpreserved tissues, might be harmful to plant materials humans Avoid skin contact with these materials Wear mask or gloves Notify your teacher if you suspect contact with material Wash hands thoroughly EXTREME TEMPERATURE Objects that can burn skin by being too cold or too hot boiling liquids, hot plates, dry ice, liquid nitrogen Use proper protection when handling Go to your teacher for first aid SHARP OBJECT Use of tools or glassware that can easily puncture or slice skin razor blades, pins, scalpels, pointed tools, dissecting probes, broken glass Practice common-sense Go to your teacher for behavior and follow first aid guidelines for use of the tool FUME Possible danger to respiratory tract from fumes ammonia, acetone, nail polish remover, heated sulfur, moth balls Make sure there is good ventilation Never smell fumes directly Wear a mask Leave foul area and notify your teacher immediately Double-check setup with teacher Check condition of wires and apparatus Use GFIprotected outlets Do not attempt to fix electrical problems Notify your teacher immediately BIOLOGICAL ELECTRICAL Possible danger from improper grounding, electrical shock or burn liquid spills, short circuits, exposed wires Substances that can irritate the skin or mucous membranes of the respiratory tract pollen, moth balls, steel Wear dust mask and wool, fiberglass, potas- gloves Practice extra care when handling sium permanganate these materials CHEMICAL Chemicals that can react with and destroy tissue and other materials bleaches such as hydrogen peroxide; acids such as sulfuric acid, hydrochloric acid; bases such as ammonia, sodium hydroxide Wear goggles, gloves, and an apron Immediately flush the affected area with water and notify your teacher TOXIC Substance may be poisonous if touched, inhaled, or swallowed mercury, many metal compounds, iodine, poinsettia plant parts Follow your teacher’s instructions Always wash hands thoroughly after use Go to your teacher for first aid FLAMMABLE Open flame may ignite flammable chemicals, loose clothing, or hair alcohol, kerosene, potassium permanganate, hair, clothing Avoid open flames and heat when using flammable chemicals Notify your teacher immediately Use fire safety equipment if applicable Tie back hair and loose clothing Follow teacher's instructions on lighting and extinguishing flames Always wash hands thoroughly after use Go to your teacher for first aid IRRITANT OPEN FLAME Open flame in use, may hair, clothing, paper, cause fire synthetic materials Eye Safety Proper eye protection must be worn at all times by anyone performing or observing science activities 572 Science Safety Skill Handbook Clothing Protection This symbol appears when substances could stain or burn clothing Go to your teacher for first aid Animal Safety Handwashing This symbol appears when safety of animals and students must be ensured After the lab, wash hands with soap and water before removing goggles Science Safety Skill Handbook Safety in the Science Laboratory The science laboratory is a safe place to work if you follow standard safety procedures Being responsible for your own safety helps to make the entire laboratory a safer place for everyone When performing any lab, read and apply the caution statements and safety symbol listed at the beginning of the lab General Safety Rules Never eat, drink, chew gum, apply cos- metics, or any personal grooming in the lab Never use lab glassware as food or drink containers Keep your hands away from your face and mouth Know the location and proper use of the safety shower, eye wash, fire blanket, and fire alarm Prevent Accidents Use the safety equipment provided to you Complete the Lab Safety Form or other safety contract BEFORE starting any science lab Study the procedure Ask your teacher any questions Be sure you understand safety symbols shown on the page Notify your teacher about allergies or other health conditions which can affect your participation in a lab Learn and follow use and safety procedures for your equipment If unsure, ask your teacher Goggles and a safety apron should be worn during investigations Do NOT use hair spray, mousse, or other flammable hair products Tie back long hair and tie down loose clothing Do NOT wear sandals or other open-toed shoes in the lab Remove jewelry on hands and wrists Loose jewelry, such as chains and long necklaces, should be removed to prevent them from getting caught in equipment Do not taste any substances or draw any material into a tube with your mouth Proper behavior is expected in the lab Practical jokes and fooling around can lead to accidents and injury Keep your work area uncluttered Laboratory Work Collect and carry all equipment and materials to your work area before beginning a lab Remain in your own work area unless given permission by your teacher to leave it Science Safety Skill Handbook 573 Science Safety Skill Handbook Introduction to Science Safety Science Safety Skill Handbook Dispose of chemicals and other materials Science Safety Skill Handbook as directed by your teacher Place broken glass and solid substances in the proper containers Never discard materials in the sink Clean your work area Wash your hands with soap and water thoroughly BEFORE removing your goggles Emergencies Report any fire, electrical shock, glassware Always slant test tubes away from yourself and others when heating them, adding substances to them, or rinsing them If instructed to smell a substance in a container, hold the container a short distance away and fan vapors towards your nose Do NOT substitute other chemicals/substances for those in the materials list unless instructed to so by your teacher Do NOT take any materials or chemicals outside of the laboratory Stay out of storage areas unless instructed to be there and supervised by your teacher Laboratory Cleanup Turn off all burners, water, and gas, and disconnect all electrical devices Clean all pieces of equipment and return all materials to their proper places 574 Science Safety Skill Handbook breakage, spill, or injury, no matter how small, to your teacher immediately Follow his or her instructions If your clothing should catch fire, STOP, DROP, and ROLL If possible, smother it with the fire blanket or get under a safety shower NEVER RUN If a fire should occur, turn off all gas and leave the room according to established procedures In most instances, your teacher will clean up spills Do NOT attempt to clean up spills unless you are given permission and instructions to so If chemicals come into contact with your eyes or skin, notify your teacher immediately Use the eyewash, or flush your skin or eyes with large quantities of water The fire extinguisher and first-aid kit should only be used by your teacher unless it is an extreme emergency and you have been given permission If someone is injured or becomes ill, only a professional medical provider or someone certified in first aid should perform first-aid procedures Technology Skill Handbook Computer Skills People who study science rely on computer technology to research, record experimental data, analyze results from investigations, and communicate with other scientists Whether you work in a laboratory or just need to write a lab report, good computer skills are necessary Desktop systems, like the one shown in Figure 2, typically have most of these components Notebook and tablet computers have most of the same components as a desktop computer, but the components are integrated into a single, book-sized portable unit Storing Your Data Technology Skill Handbook Figure Students and scientists rely on computers to When you save documents created on computers at your school, they probably are stored in a directory on your school’s network However, if you want to take the documents you have created home, you need to save them on something portable Removable media, like those shown in Figure 3, are disks and drives that are designed to be moved from one computer to another gather data and communicate ideas Hardware Basics Your personal computer is a system consisting of many components The parts you can see and touch are called hardware Monitor Speaker Keyboard Screen System unit Speaker Figure Removable data storage is a convenient way to carry your documents from place to place Mouse Figure Most desktop computers consist of the components shown above Notebook computers have the same components in a compact unit Removable media vary from floppy disks and recordable CDs and DVDs to small solid-state storage Tiny USB “keychain” drives have become popular because they can store large amounts of data and plug into any computer with a USB port Each of these types of media stores different amounts of data Be sure that you save your data to a medium that is compatible with your computer Technology Skill Handbook 575 Technology Skill Handbook Getting Started with Word Processing Programs A word processor is used for the composition, editing, and formatting of written material Word processors vary from program to program, but most have the basic functions shown in Figure Most word processors also can be used to make simple tables and graphics Technology Skill Handbook Menu bar ■ Use the spell-check function to check your spelling and grammar Remember that spell-check will not catch words that are misspelled to look like other words, such as cold instead of gold Reread your document to look for spelling and grammar mistakes ■ Graphics and spreadsheets can be added to your document by copying them from other programs and pasting them into your document ■ If you have questions about using your word processor, ask your teacher or use the program’s help menu Standard toolbar Cursor Formatting toolbar Getting Started with Spreadsheet Programs View choices Previous/next page buttons Status bar Drawing toolbar Figure Word processors have functions that easily allow you to edit, format, view, and save text, tables, and images, making them useful for writing lab reports and research papers A spreadsheet, like the one shown in Figure 5, helps you organize information into columns and rows Spreadsheets are particularly useful for making data tables Spreadsheets also can be used to perform mathematical calculations with your data Then, you can use the spreadsheet to generate graphs and charts displaying your results Cell number box Menu bar Standard toolbar Formatting toolbar Word Processor Tips ■ ■ As you type, text will automatically wrap to the next line Press Enter on your keyboard if you wish to start a new paragraph Cell Cell E5 You can move multiple lines of text around by using the cut and paste functions on the toolbar ■ If you make a typing or formatting error, use the undo function on the toolbar ■ Be sure to save your document early and often This will prevent you from losing your work if your computer turns off unexpectedly 576 Technology Skill Handbook Formula box Row Column E Worksheet tab scroll buttons Worksheet tabs Figure With formulas and graphs, spreadsheets help you organize and analyze your data Technology Skill Handbook Spreadsheet Tips Think about how to organize your data before you begin entering data ■ Each column (vertical) is assigned a letter and each row (horizontal) is assigned a number Each point where a row and column intersect is called a cell, and is labeled according to where it is located For example: column A, row is cell A1 ■ To edit the information in a cell, you must first activate the cell by clicking on it ■ ■ When using a spreadsheet to generate a graph, make sure you use the type of graph that best represents the data Review the Science Skill Handbook in this book for help with graphs Figure Video projectors and interactive whiteboards allow you to present information stored on a computer to an entire classroom They are becoming increasingly common in the classrooms Presentation Program Tips ■ Often, color and strong images will convey a point better than words alone But, be sure to organize your presentation clearly Don’t let the graphics confuse the message ■ Most presentation programs will let you copy and paste text, spreadsheets, art and graphs from other programs ■ Most presentation programs have built-in templates that help you organize text and graphics ■ As with any kind of presentation, familiarize yourself with the equipment and practice your presentation before you present it to an audience ■ Most presentation programs will allow you to save your document in html format so that you can publish your document on a Web site ■ If you have questions about using your presentation software or hardware, ask your teacher or use the program’s Help menu To learn more about using your spreadsheet program ask your teacher or use the program’s Help menu Getting Started with Presentation Programs There are many programs that help you orally communicate results of your research in an organized and interesting way Many of these are slideshow programs, which allow you to organize text, graphs, digital photographs, sound, animations, and digital video into one multimedia presentation Presentations can be printed onto paper or displayed on-screen Slideshow programs are particularly effective when used with video projectors and interactive whiteboards, like the one shown in Figure Although presentation programs are not the only way to communicate information publicly, they are an effective way to organize your presentation and remind your audience of major points Technology Skill Handbook ■ Technology Skill Handbook 577 Technology Skill Handbook World Wide Web Tips Technology Skill Handbook Doing Research with the World Wide Web The Internet is a global network of computers where information can be stored and shared by anyone with an internet connection One of the easiest ways to find information on the internet is by using the World Wide Web, a vast graphical system of documents written in the computer language, html (hypertext markup language) Web pages are arranged in collections of related material called “Web sites.” The content on a Web site is viewed using a program called a Web browser Web browsers, like the one shown in Figure 7, allow you to browse or surf the Web by clicking on highlighted hyperlinks, which move you from Web page to Web page Web content can be searched by topic using a search engine Search engines are located on Web sites which catalog key words on Web pages all over the World Wide Web Navigation buttons Address bar ■ Search the Web using specific keywords For example, if you want to research the element gold don’t type elements into the search engine ■ When performing a Web search, enclose multiple keywords with quotes to narrow your results to the most relevant pages ■ The first hit your Web search results in is not always the best Search results are arranged by popularity, not by relevance to your topic Be patient and look at many links in your search results to find the best information ■ Think critically when you science research on the Web Compared to a traditional library, finding accurate information on the Web is not always easy because anyone can create a Web site Some of the best places to start your research are websites for major newspapers and magazines, as well as U.S government (.gov) and university (.edu) Web sites ■ Security is a major concern when browsing the Web Your computer can be exposed to advertising software and computer viruses, which can hurt your computer’s data and performance Do not download software at your school unless your teacher tells you to so ■ Cite information you find on the Web just as you would books and journals An example of proper Web citation is the following: Loading indicator Menk, Amy J (2004) Urban Ecology Retrieved January 21, 2005, from McGraw-Hill Web site: http://www.mcgraw-hill.com/papers/urban.html ■ Link indicator Figure Web browsers have all the tools you need to navigate and view information on the Web 578 Technology Skill Handbook The World Wide Web is a great resource for information, but don’t forget to utilize local libraries, including your school library Math Skill Handbook Math Review Use Fractions ALG: 1.0 A fraction compares a part to a whole In the fraction 2ᎏ3, the represents the part and is the numerator The represents the whole and is the denominator Reduce Fractions To reduce a fraction, you must find the largest factor that is common to both the numerator and the denominator, the greatest common factor (GCF) Divide both numbers by the GCF The fraction has then been reduced, or it is in its simplest form Example Twelve of the 20 chemicals in the science lab are in powder form What fraction of the chemicals used in the lab are in powder form? Step part whole Step Step remainder are birds and insects How many are mammals? Step To find the GCF of the numerator and denominator, list all of the factors of each number Factors of 12: 1, 2, 3, 4, 6, 12 (the numbers that divide evenly into 12) Factors of 20: 1, 2, 4, 5, 10, 20 (the numbers that divide evenly into 20) ϩ ϭ (1 ϩ 3) ϭ ᎏ8 ᎏ8 ᎏ ᎏ8 Step Step ᎏ21 of the animals are mammals of the Earth is covered Example If ᎏ 16 of that is in glaciers, by freshwater, and ᎏ 16 how much freshwater is not frozen? Choose the greatest factor in the list The GCF of 12 and 20 is Step Divide the numerator and denominator by the GCF Step In the lab, 3ᎏ of the chemicals are in powder form Practice Problem At an amusement park, 66 of 90 rides have a height restriction What fraction of the rides, in its simplest form, has a height restriction? Divide the numerator and denominator by the GCF 4Ϭ4ϭ1 ᎏ ᎏ2 8Ϭ4 Step Find the GCF (GCF, 4) ᎏ8 List the common factors 1, 2, 12 Ϭ ϭ ᎏ ᎏ5 20 Ϭ Add the numerators Math Skill Handbook Step Example In the forest outside your house, 1ᎏ of the animals are rabbits, 3ᎏ are squirrels, and the Write the fraction 12 ᎏ ϭᎏ 20 Step Add and Subtract Fractions with Like Denominators To add or subtract fractions with the same denominator, add or subtract the numerators and write the sum or difference over the denominator After finding the sum or difference, find the simplest form for your fraction Subtract the numerators (7 Ϫ 1) Ϫ ϭ ϭᎏ ᎏ ᎏ ᎏ 16 16 16 16 Find the GCF (GCF, 2) ᎏ 16 Divide the numerator and denominator by the GCF 6Ϭ2 ϭᎏ ᎏ 16 Ϭ of the freshwater is not frozen ᎏ8 Practice Problem A bicycle rider is riding at a rate of 15 km/h for 4ᎏ of his ride, 10 km/h for 2ᎏ of his 9 ride, and km/h for the remainder of the ride How much of his ride is he riding at a rate greater than km/h? Math Skill Handbook 579 Math Skill Handbook Circumference of a Circle The diameter (d) of a circle is the distance across the circle through its center, and the radius (r) is the distance from the center to any point on the circle The radius is half of the diameter The distance around the circle is called the circumference (C) The formula for finding the circumference is: C ϭ 2␲r or C ϭ ␲d The circumference divided by the diameter is always equal to 3.1415926… This nonterminating and nonrepeating number is represented by the Greek letter ␲ (pi) An approximation often used for ␲ is 3.14 Example Find the circumference of a circle with a radius of m Step Step Step Step A ϭ ␲(4.0)2 Step Find the square of the radius A ϭ 16␲ Step Multiply the square of the radius by ␲ A ഠ 50 cm2 The area of the circle is about 50 cm2 Example Find the area of a circle with a radius of 225 m A ϭ ␲(225)2 Step Multiply times the radius C ϭ 6␲ Find the square of the radius A ϭ 50625␲ Step Multiply by ␲ C ഠ 19 m Multiply the square of the radius by ␲ A ഠ 159043.1 The area of the circle is about 159043.1 m2 Example Find the area of a circle whose diameter is 20.0 mm Step You know the formula for the circumference is the diameter times ␲ C ϭ ␲(24.0) Multiply the diameter by ␲ C ഠ 75.4 cm The circumference is about 75.4 cm Practice Problem Find the circumference of a circle with a radius of 19 cm Math Skill Handbook Step Example Find the circumference of a circle with a diameter of 24.0 cm Step Example Find the area of a circle with a radius of 4.0 cm You know the formula for the circumference is times the radius times ␲ C ϭ 2␲(3) The circumference is about 19 m Step Area of a Circle The formula for the area of a circle is: A ϭ ␲r You know the formula for the area of a circle is the square of the radius times ␲, and that the radius is half of the diameter ( )2 20.0 Aϭ␲ᎏ Step Find the radius A ϭ ␲(10.0)2 Step Find the square of the radius A ϭ 100␲ Step Multiply the square of the radius by ␲ A ഠ 314 mm2 The area of is about 314 mm2 Practice Problem Find the area of a circle with a radius of 16 m Math Skill Handbook 587 Math Skill Handbook Volume The measure of space occupied by a solid is the volume (V) To find the volume of a rectangular solid multiply the length times width times height, or V ϭ l ϫ w ϫ h It is measured in cubic units, such as cubic centimeters (cm3) Example Find the volume of a cylinder that has a base with a radius of 12.0 cm, and a height of 21.0 cm Step Example Find the volume of a rectangular solid with a length of 2.0 m, a width of 4.0 m, and a height of 3.0 m Step You know the formula for volume is the length times the width times the height V ϭ 2.0 m ϫ 4.0 m ϫ 3.0 m Step V ϭ (␲r 2) ϫ 21 V ϭ (␲122) ϫ 21 Step V ϭ 452 ϫ 21 Step The volume is 24 m3 Practice Problem Find the volume of a rectangular solid that is m long, m wide, and m high Math Skill Handbook To find the volume of other solids, multiply the area of the base times the height Example Find the volume of a solid that has a triangular base with a length of 8.0 m and a height of 7.0 m The height of the entire solid is 15.0 m Step [ Step ] [ ( Step Example Find the volume of a cylinder that has a diameter of 15 mm and a height of 4.8 mm Step Multiply the area of the base by the height of the solid [ (2 )] V ϭ ␲ 1ᎏ ϫ 15 ϫ 4.8 Vϭ Step (␲7.52) ϫ 4.8 Find the area of the base V ϭ 56.25␲ ϫ 4.8 ] ) You know that the base is a circle with an area equal to the square of the radius times ␲ The radius is one-half the diameter The volume is the area of the base times the height V ϭ (␲r2) ϫ 4.8 Find the area of the base V ϭ 1ᎏ (8 ϫ 7) ϫ 15 V ϭ 1ᎏ ϫ 56 ϫ 15 Multiply the area of the base by the height of the solid V ഠ 9,500 cm3 The volume is about 9,500 cm3 You know that the base is a triangle, and the area of a triangle is 1ᎏ the base times the height, and the volume is the area of the base times the height V ϭ 1ᎏ (b ϫ h) ϫ 15 Find the area of the base V ϭ 144␲ ϫ 21 Multiply the length times the width times the height V ϭ 24 m3 You know that the base is a circle, and the area of a circle is the square of the radius times ␲, and the volume is the area of the base times the height V ഠ 176.71 ϫ 4.8 Step Multiply the area of the base by the height of the solid V ഠ 848.2 V ϭ 28 ϫ 15 The volume is about 848.2 mm3 V ϭ 420 m3 Practice Problem Find the volume of a cylinder with a diameter of cm in the base and a height of 16 cm The volume is 420 m3 588 Math Skill Handbook Math Skill Handbook Science Applications Measure in SI Dimensional Analysis The metric system of measurement was developed in 1795 A modern form of the metric system, called the International System (SI), was adopted in 1960 and provides the standard measurements that all scientists around the world can understand The SI system is convenient because unit sizes vary by powers of 10 Prefixes are used to name units Look at Table for some common SI prefixes and their meanings Convert SI Units In science, quantities such as length, mass, and time sometimes are measured using different units A process called dimensional analysis can be used to change one unit of measure to another This process involves multiplying your starting quantity and units by one or more conversion factors A conversion factor is a ratio equal to one and can be made from any two equal quantities with different units If 1,000 mL equal L then two ratios can be made Table Common SI Prefixes Prefix Symbol 1,000 mL 1L ϭᎏ ϭ1 ᎏ 1L 1,000 mL thousandth One can convert between units in the SI system by using the equivalents in Table to make conversion factors hundred Example How many cm are in m? ten Step Meaning kilo- k 1,000 hecto- h 100 deka- da 10 deci- d 0.1 tenth Write conversion factors for the units given From Table 2, you know that 100 cm ϭ m The conversion factors are centi- c 0.01 hundreth 100 cm and m ᎏ ᎏ 1m 100 cm milli- m 0.001 thousandth Example How many grams equal one kilogram? Step Find the prefix kilo- in Table Step Using Table 2, determine the meaning of kilo- According to the table, it means 1,000 When the prefix kilo- is added to a unit, it means that there are 1,000 of the units in a “kilounit.” Step Apply the prefix to the units in the question The units in the question are grams There are 1,000 grams in a kilogram Practice Problem Is a milligram larger or smaller than a gram? How many of the smaller units equal one larger unit? What fraction of the larger unit does one smaller unit represent? Decide which conversion factor to use Select the factor that has the units you are converting from (m) in the denominator and the units you are converting to (cm) in the numerator Math Skill Handbook Step 100 cm ᎏ 1m Step Multiply the starting quantity and units by the conversion factor Cancel the starting units with the units in the denominator There are 400 cm in m cm m ϭ 100 ᎏ ϭ 400 cm 1m Practice Problem How many milligrams are in one kilogram? (Hint: You will need to use two conversion factors from Table 2.) Math Skill Handbook 589 Math Skill Handbook Table Unit System Equivalents Type of Measurement Equivalent Length in ϭ 2.54 cm yd ϭ 0.91 m mi ϭ 1.61 km Mass and weight* oz ϭ 28.35 g lb ϭ 0.45 kg ton (short) ϭ 0.91 tonnes (metric tons) lb ϭ 4.45 N Volume in3 ϭ 16.39 cm3 qt ϭ 0.95 L gal ϭ 3.78 L Area in2 ϭ 6.45 cm2 yd2 ϭ 0.83 m2 mi2 ϭ 2.59 km2 acre ϭ 0.40 hectares Temperature °C ϭ ᎏ 1.8 (°F Ϫ 32) K ϭ °C ϩ 273 Math Skill Handbook *Weight is measured in standard Earth gravity Convert Between Unit Systems Table gives a list of equivalents that can be used to convert between English and SI units Example If a meterstick has a length of 100 cm, how long is the meterstick in inches? Step Step Write the conversion factors for the units given From Table 3, in ϭ 2.54 cm Step Multiply the starting quantity and units by the conversion factor Cancel the starting units with the units in the denominator Round your answer to the nearest tenth in ϭ 39.37 in 100 cm ϫ ᎏ 2.54 cm The meterstick is about 39.4 in long cm in and 2.54 ᎏ ᎏ 2.54 cm in Practice Problem A book has a mass of lb What is the mass of the book in kg? Determine which conversion factor to use You are converting from cm to in Use the conversion factor with cm on the bottom Practice Problem Use the equivalent for in and cm (1 in ϭ 2.54 cm) to show how in3 ഠ 16.39 cm3 in ᎏ 2.54 cm 590 Math Skill Handbook Math Skill Handbook Precision and Significant Digits Scientific Notation When you make a measurement, the value you record depends on the precision of the measuring instrument This precision is represented by the number of significant digits recorded in the measurement When counting the number of significant digits, all digits are counted except zeros at the end of a number with no decimal point such as 2,050, and zeros at the beginning of a decimal such as 0.03020 When adding or subtracting numbers with different precision, round the answer to the smallest number of decimal places of any number in the sum or difference When multiplying or dividing, the answer is rounded to the smallest number of significant digits of any number being multiplied or divided Many times numbers used in science are very small or very large Because these numbers are difficult to work with scientists use scientific notation To write numbers in scientific notation, move the decimal point until only one non-zero digit remains on the left Then count the number of places you moved the decimal point and use that number as a power of ten For example, the average distance from the Sun to Mars is 227,800,000,000 m In scientific notation, this distance is 2.278 ϫ 1011 m Because you moved the decimal point to the left, the number is a positive power of ten The mass of an electron is about 0.000 000 000 000 000 000 000 000 000 000 911 kg Expressed in scientific notation, this mass is 9.11 ϫ 10Ϫ31 kg Because the decimal point was moved to the right, the number is a negative power of ten Example The lengths 5.28 and 5.2 are measured in meters Find the sum of these lengths and record your answer using the correct number of significant digits Step Find the sum 5.28 m digits after the decimal Step Example Earth is 149,600,000 km from the Sun Express this in scientific notation Step Move the decimal point until one non-zero digit remains on the left 1.496 000 00 Step Count the number of decimal places you have moved In this case, eight Step Show that number as a power of ten, 108 digit after the decimal Round to one digit after the decimal because the least number of digits after the decimal of the numbers being added is The sum is 10.5 m Practice Problem How many significant digits are in the measurement 7,071,301 m? How many significant digits are in the measurement 0.003010 g? Practice Problem Multiply 5.28 and 5.2 using the rule for multiplying and dividing Record the answer using the correct number of significant digits Math Skill Handbook ϩ 5.2 m 10.48 m ALG: 1.0 Earth is 1.496 ϫ 108 km from the Sun Practice Problem How many significant digits are in 149,600,000 km? How many significant digits are in 1.496 ϫ 108 km? Practice Problem Parts used in a high performance car must be measured to ϫ 10Ϫ6 m Express this number as a decimal Practice Problem A CD is spinning at 539 revolutions per minute Express this number in scientific notation Math Skill Handbook 591 Math Skill Handbook Distance v Time ALG: 6.0 Data in tables can be displayed in a graph—a visual representation of data Common graph types include line graphs, bar graphs, and circle graphs Line Graph A line graph shows a relationship between two variables that change continuously The independent variable is changed and is plotted on the x-axis The dependent variable is observed, and is plotted on the y-axis 50 40 Distance (km) Make and Use Graphs Math Skill Handbook Step Time (h) Distance (km) 0 16 24 32 40 Determine the x-axis and y-axis variables Time varies independently of distance and is plotted on the x-axis Distance is dependent on time and is plotted on the y-axis Step Determine the scale of each axis The x-axis data ranges from to The y-axis data ranges from to 50 Step Using graph paper, draw and label the axes Include units in the labels Step Draw a point at the intersection of the time value on the x-axis and corresponding distance value on the y-axis Connect the points and label the graph with a title, as shown in Figure 20 10 Example Draw a line graph of the data below from a cyclist in a long-distance race Table Bicycle Race Data 30 Time (h) Figure This line graph shows the relationship between distance and time during a bicycle ride Practice Problem A puppy’s shoulder height is measured during the first year of her life The following measurements were collected: (3 mo, 52 cm), (6 mo, 72 cm), (9 mo, 83 cm), (12 mo, 86 cm) Graph this data Find a Slope The slope of a straight line is the ratio of the vertical change, rise, to the horizontal change, run vertical change (rise) change in y Slope ϭ ᎏᎏ ϭ ᎏ horizontal change (run) change in x Example Find the slope of the graph in Figure Step You know that the slope is the change in y divided by the change in x change in y change in x Slope ϭ ᎏ Step Determine the data points you will be using For a straight line, choose the two sets of points that are the farthest apart (40 Ϫ 0) km (5 Ϫ 0) h Slope ϭ ᎏ Step Find the change in y and x km Slope ϭ 40 ᎏ 5h Step Divide the change in y by the change in x km Slope ϭ 8ᎏ h The slope of the graph is km/h 592 Math Skill Handbook Math Skill Handbook Bar Graph To compare data that does not change continuously you might choose a bar graph A bar graph uses bars to show the relationships between variables The x-axis variable is divided into parts The parts can be numbers such as years, or a category such as a type of animal The y-axis is a number and increases continuously along the axis Example A recycling center collects 4.0 kg of aluminum on Monday, 1.0 kg on Wednesday, and 2.0 kg on Friday Create a bar graph of this data Step Step Step Circle Graph To display data as parts of a whole, you might use a circle graph A circle graph is a circle divided into sections that represent the relative size of each piece of data The entire circle represents 100%, half represents 50%, and so on Example Air is made up of 78% nitrogen, 21% oxygen, and 1% other gases Display the composition of air in a circle graph Step Select the x-axis and y-axis variables The measured numbers (the masses of aluminum) should be placed on the y-axis The variable divided into parts (collection days) is placed on the x-axis Multiply each percent by 360° and divide by 100 to find the angle of each section in the circle 78% ϫ 360° ᎏ ϭ 280.8° 100 360° 21% ϫ ᎏ ϭ 75.6° 100 360° 1% ϫ ᎏ ϭ 3.6° 100 Step For each measured number, draw a vertical bar above the x-axis value up to the y-axis value For the first data point, draw a vertical bar above Monday up to 4.0 kg Use a compass to draw a circle and to mark the center of the circle Draw a straight line from the center to the edge of the circle Step Use a protractor and the angles you calculated to divide the circle into parts Place the center of the protractor over the center of the circle and line the base of the protractor over the straight line Aluminum Collected During Week Other 1% 4.0 Mass (kg) Math Skill Handbook Create a graph grid like you would for a line graph Include labels and units Oxygen 21% 3.0 2.0 Nitrogen 78% 1.0 Monday Wednesday Friday Day of collection Practice Problem Draw a bar graph of the gases in air: 78% nitrogen, 21% oxygen, 1% other gases Practice Problem Draw a circle graph to represent the amount of aluminum collected during the week shown in the bar graph to the left Math Skill Handbook 593 Reference Handbook Using a Calculator Solar cell Display Percent/Sign chamge Square root Off On/Clear Division Multiplication Clear entry Memory keys Subtraction Reference Handbook Decimal point Equals Addition • Read the problem very carefully Decide if you need the calculator to help you solve the problem • • • Clear the calculator by pressing the clear key when starting a new problem • If the number in the display is not one of the answer choices, check your work You may have to round the number in the display • Your calculator will NOT automatically perform the correct order of operations • When working with calculators, use careful and deliberate keystrokes, and always remember to check your answer to make sure that it is reasonable Calculators might display an incorrect answer if you press the keys too quickly • Check your answer to make sure that you have completed all of the necessary steps If you see an E in the display, clear the error before you begin If you see an M in the display, clear the memory and the calculator before you begin 594 Reference Handbook Reference Handbook Understanding Scientific Terms T his list of prefixes, suffixes, and roots is provided to help you understand science terms used throughout this textbook The list identifies whether the prefix, suffix, or root is of Greek (G) or Latin (L) origin Also listed is the meaning of the prefix, suffix, or root and a science word in which it is used MEANING EXAMPLE to, toward air without up male vessel flower against of water ancient jointed bag star self adaxial aerobic anaerobic anaphase androecium angiosperm anthophyte antibody aquatic archaebacteria arthropod ascospore Asteroidea autoimmune B bi (L) bio (G) two life bipedal biosphere C carn (L) cephalo (G) chlor (G) chroma (G) cide (L) circ (L) cocc/coccus (G) (L) cyte (G) flesh head light green pigmented to kill circular small and round together cell carnivore cephalopod chlorophyll chromosome insecticide circadian streptococcus convergent cytoplasm D de (L) dendron (G) dent (L) derm (G) di (G) remove tree tooth skin two decompose dendrite edentate epidermis disaccharide ORIGIN dia (G) dorm (L) MEANING apart sleep EXAMPLE diaphragm dormancy E echino (G) ec (G) endo (G) epi (G) eu (G) exo (G) spiny outer within upon true outside echinoderm ecosystem endosperm epidermis eukaryote exoskeleton F fer (L) to carry conifer G gastro (G) gen/(e)(o) (G) genesis (G) gon (G) gravi (L) gymn/o (G) gyn/e (G) stomach kind to originate reproductive heavy naked female gastropod genotype oogenesis archegonium gravitropism gymnosperm gynoecium H hal(o) (G) hapl(o) (G) hemi (G) hem(o) (G) herb/a(i) (L) heter/o (G) hom(e)/o (G) hom (L) hydr/o (G) salt single half blood vegetation different same human water halophyte haploid hemisphere hemoglobin herbivore heterotrophic homeostasis hominid hydrolysis I inter (L) intra (L) is/o (G) between within equal internode intracellular isotonic Reference Handbook Reference Handbook ORIGIN A ad (L) aero (G) an (G) ana (G) andro (G) angio (G) anth/o (G) anti (G) aqu/a (L) archae (G) arthro, artio (G) askos (G) aster (G) autos (G) 595 Reference Handbook ORIGIN K kary (G) kera (G) MEANING EXAMPLE nucleus hornlike eukaryote keratin L leuc/o (G) logy (G) lymph/o (L) lysis (G) white study of water break up leukocyte biology lymphocyte dialysis Reference Handbook M macr/o (G) meg/a (G) meso (L) meta (G) micr/o (G) mon/o (G) morph/o (G) large great in the middle after small only one form macromolecule megaspore mesophyll metaphase microscope monocotyledon morphology ORIGIN plasm/o (G) pod (G) poly (G) post (L) pro (G) (L) prot/o (G) pseud/o (G) MEANING to form foot many after before first false R re (L) rhiz/o (G) back to original reproduce root rhizoid S scope (G) some (G) sperm (G) stasis (G) syn (G) to look body seed remain constant mouthlike opening together stomata synapse T tel/o (G) terr (L) therm (G) thylak (G) trans (L) trich (G) trop/o (G) trophic (G) end of Earth heat sack across hair a change nourishment telophase terrestrial endotherm thylakoid transpiration trichome gravitropism heterotrophic U uni (L) one unicellular V vacc/a (L) vore (L) cow eat greedily vaccine omnivore X xer/o (G) dry xerophyte Z zo/o (G) zygous (G) living being two joined zoology homozygous stom (G) N nema (G) neuro (G) nod (L) nomy(e) (G) a thread nerve knot system of laws nematode neuron nodule taxonomy O olig/o (G) omni (L) orni(s) (G) oste/o (G) ov (L) small, few all bird bone formation an egg oligochaete omnivore ornithology osteocyte oviduct P pal(a)e/o (G) para (G) path/o (G) ped (L) per (L) peri (G) phag/o (G) phot/o (G) phyl (G) phyll (G) phyte (G) pinna (L) ancient beside suffering foot through around, about eating light race, class leaf plant feather paleontology parathyroid pathogen centipede permeable peristalsis phagocyte photosynthesis phylogeny chlorophyll epiphyte pinnate 596 Reference Handbook EXAMPLE plasmodium gastropod polymer posterior prokaryote protocells pseudopodium microscope lysosome gymnosperm homeostasis Reference Handbook Science Reference Guide Equations Average speed (v) ϭ distance ᎏ time Density (D) ϭ ᎏᎏ D ϭ m ᎏ V Force in newtons (F) ϭ mass (kg) ϫ acceleration (m/s2) F ϭ ma Pressure (P) ϭ ᎏ P f ϭ ᎏ A V ϭ ᐉϫwϫh v mass (g) Volume (cm ) force (N) area (m ) Volume (cm3) ϭ length (cm) ϫ width (cm) ϫ height (cm) ϭ dᎏt Units of Measure cm ϭ centimeter g ϭ gram kg ϭ kilogram m ϭ meter N ϭ newton s ϭ second Reference Handbook Reference Handbook 597 Reference Handbook Physical Science Reference Tables Standard Units Symbol Name Quantity m kg Pa K mol J s C V A V meter kilogram pascal kelvin mole joule second coulomb volt ampere ohm length mass pressure temperature amount of a substance energy, work, quantity of heat time electric charge electric potential electric current resistance Physical Constants and Conversion Factors Acceleration due to gravity Avogadro’s Number Electron charge Electron rest mass Gravitation constant Mass-energy relationship Speed of light in a vacuum Speed of sound at STP Standard Pressure g NA e me G 9.8 m/s/s or m/s2 6.02 1023 particles per mole 1.6 10219 C 9.11 10231 kg 6.67 10211 N m2/kg2 u (amu) 9.3 102 MeV 3.00 108 m/s c 331 m/s atmosphere 101.3 kPa 760 Torr or mmHg 14.7 lb/in.2 Reference Handbook Heat Constants Alcohol (ethyl) Aluminum Ammonia Copper Iron Lead Mercury Platinum Silver Tungsten Water (solid) Water (liquid) Water (vapor) Zinc 598 Reference Handbook Specific Heat (average) (kJ/kg °C) (J/g °C) Melting Point (°C) Boiling Point (°C) Heat of Fusion (kJ/kg) (J/g) Heat of Vaporization (kJ/kg) (J/g) 2.43 (liq.) 0.90 (sol.) 4.71 (liq.) 0.39 (sol.) 0.45 (sol.) 0.13 (sol.) 0.14 (liq.) 0.13 (sol.) 0.24 (sol.) 0.13 (sol.) 2.05 (sol.) 4.18 (liq.) 2.01 (gas) 0.39 (sol.) 2117 660 278 1083 1535 328 239 1772 962 3410 – – 420 79 2467 233 2567 2750 1740 357 3827 2212 5660 – 100 – 907 109 396 332 205 267 25 11 101 105 192 334 – – 113 855 10500 1370 4790 6290 866 295 229 2370 4350 – – 2260 1770 Reference Handbook &%%!%%% &%!%%% &!%%% &%% &% &#% %#& %#%& %#%%& %#%%%& %#%%%%& %#%%%%%& %#%%%%%%& %#%%%%%%%& %#%%%%%%%%& %#%%%%%%%%%& %#%%%%%%%%%%& %#%%%%%%%%%%%& N %#%%%%%%%%%%%%& 4UBOEBSE
6OJUT &%&(&%&' &%&& &%&% &%  &% - &% , &% + &% * &% ) &% ( &% ' &% & &% % &%& &% ' &% ( &% ) &% * MgVn B^XgdlVkZh JK K^h^WaZ G GVY^dlVkZh K^h^WaZA^\]i GZY ,#%m&%, *#.m&% )#.m&% DgVc\Z +#*m&%, NZaadl ,