A. meters
B. kilograms
C. kilometers
The units that best match the descriptions are:
A. meters - Height is typically measured in meters. Millimeters would be too small and kilometers too large.
B. kilograms - Mass of a person is typically measured in kilograms. Milligrams would be too small and grams too small for a person's total mass.
C. kilometers - Distance between cities is typically measured in kilometers as it would be a longer distance than meters or millimeters.
This document provides information on scientific notation and significant figures. It discusses how to write very large and very small numbers using scientific notation by moving the decimal place and using an exponent of 10. It provides examples of converting numbers to and from scientific notation. The document also covers significant figures, including which digits are significant when given a measurement with leading zeros, trailing zeros, or zeros between numbers. It explains how to determine the number of significant figures and how to properly round answers in calculations based on the least precise measurement.
This document discusses significant figures and how they are determined in measurements and calculations. It provides rules for identifying significant figures in measured values, including that non-zero digits, "sandwich zeros", and trailing zeros following a decimal point are significant. Calculated answers are rounded to the same number of significant figures as the least precise measurement used. Addition and subtraction are rounded to the least decimal places, while multiplication and division are rounded to the least significant figures.
This document provides an overview of scientific measurement and notation. It discusses the differences between accuracy and precision in measurements and how measurements are converted to scientific notation. It provides examples of multiplying, dividing, adding and subtracting numbers in scientific notation. Key points covered include moving the decimal place to determine the exponent, aligning decimals before adding/subtracting, and adding exponents when multiplying/subtracting them when dividing in scientific notation.
This document discusses key concepts in measurement including precision, accuracy, units, and significant figures. Precision refers to the reproducibility of measurements while accuracy refers to how close a measurement is to the true value. The SI system uses meters, grams, liters, and Celsius as standard units of measurement. When taking measurements, one should estimate one digit past the last readable digit to show uncertainty. Significant figures determine how many digits in a measurement are dependable based on rules for nonzero integers, leading/captive/trailing zeros, and decimal points. Mathematical operations and scientific notation are also discussed in regards to significant figures.
This document provides an overview of chapter 1 of an EdExcel functional skills pilot on working with whole numbers. The chapter covers reading and writing whole numbers, ordering and comparing numbers, rounding numbers, adding, subtracting, multiplying and dividing whole numbers, and working with negative numbers. It includes examples and practice problems for each skill, as well as tips for using different calculation methods like partitioning for addition.
This document discusses significant figures and rounding numbers to a specified number of significant figures. It provides examples and properties of significant figures, including:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Zeros following non-zero digits may or may not be significant depending on the context
- Zeros preceding non-zero digits in decimals are not significant
The document also demonstrates how to round numbers to a specified number of significant figures using guidelines for determining whether to round up or not. Finally, it provides practice problems for operations involving significant figures, like addition, subtraction, multiplication, and division. Learners are asked to state their answers to a specified number of significant figures
This document discusses significant figures and measurement uncertainty. It provides examples of exact vs measured numbers, rules for determining significant figures, and how to properly round measurements. Key points include:
- Measured numbers have uncertainty since the last digit is an estimate
- There are 4 rules for determining if a zero is significant
- Scientific notation makes it clear how many digits are significant
- Calculations should be rounded according to whether the first discarded digit is less than or greater than 5.
The document provides materials and instructions for assessing 2nd grade math skills related to number sense. It includes checklists of skills students should be able to demonstrate such as skip counting, placing numbers on a number line, using objects to add and subtract within 1000, explaining addition and subtraction strategies, and quickly performing single-digit addition and subtraction. Sample problems, checklists, and solutions are provided. Teachers are instructed to have students explain their thinking and use manipulatives to show their work, rather than just getting the numerical answer.
This document provides information on scientific notation and significant figures. It discusses how to write very large and very small numbers using scientific notation by moving the decimal place and using an exponent of 10. It provides examples of converting numbers to and from scientific notation. The document also covers significant figures, including which digits are significant when given a measurement with leading zeros, trailing zeros, or zeros between numbers. It explains how to determine the number of significant figures and how to properly round answers in calculations based on the least precise measurement.
This document discusses significant figures and how they are determined in measurements and calculations. It provides rules for identifying significant figures in measured values, including that non-zero digits, "sandwich zeros", and trailing zeros following a decimal point are significant. Calculated answers are rounded to the same number of significant figures as the least precise measurement used. Addition and subtraction are rounded to the least decimal places, while multiplication and division are rounded to the least significant figures.
This document provides an overview of scientific measurement and notation. It discusses the differences between accuracy and precision in measurements and how measurements are converted to scientific notation. It provides examples of multiplying, dividing, adding and subtracting numbers in scientific notation. Key points covered include moving the decimal place to determine the exponent, aligning decimals before adding/subtracting, and adding exponents when multiplying/subtracting them when dividing in scientific notation.
This document discusses key concepts in measurement including precision, accuracy, units, and significant figures. Precision refers to the reproducibility of measurements while accuracy refers to how close a measurement is to the true value. The SI system uses meters, grams, liters, and Celsius as standard units of measurement. When taking measurements, one should estimate one digit past the last readable digit to show uncertainty. Significant figures determine how many digits in a measurement are dependable based on rules for nonzero integers, leading/captive/trailing zeros, and decimal points. Mathematical operations and scientific notation are also discussed in regards to significant figures.
This document provides an overview of chapter 1 of an EdExcel functional skills pilot on working with whole numbers. The chapter covers reading and writing whole numbers, ordering and comparing numbers, rounding numbers, adding, subtracting, multiplying and dividing whole numbers, and working with negative numbers. It includes examples and practice problems for each skill, as well as tips for using different calculation methods like partitioning for addition.
This document discusses significant figures and rounding numbers to a specified number of significant figures. It provides examples and properties of significant figures, including:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Zeros following non-zero digits may or may not be significant depending on the context
- Zeros preceding non-zero digits in decimals are not significant
The document also demonstrates how to round numbers to a specified number of significant figures using guidelines for determining whether to round up or not. Finally, it provides practice problems for operations involving significant figures, like addition, subtraction, multiplication, and division. Learners are asked to state their answers to a specified number of significant figures
This document discusses significant figures and measurement uncertainty. It provides examples of exact vs measured numbers, rules for determining significant figures, and how to properly round measurements. Key points include:
- Measured numbers have uncertainty since the last digit is an estimate
- There are 4 rules for determining if a zero is significant
- Scientific notation makes it clear how many digits are significant
- Calculations should be rounded according to whether the first discarded digit is less than or greater than 5.
The document provides materials and instructions for assessing 2nd grade math skills related to number sense. It includes checklists of skills students should be able to demonstrate such as skip counting, placing numbers on a number line, using objects to add and subtract within 1000, explaining addition and subtraction strategies, and quickly performing single-digit addition and subtraction. Sample problems, checklists, and solutions are provided. Teachers are instructed to have students explain their thinking and use manipulatives to show their work, rather than just getting the numerical answer.
This document discusses uncertainty in measurement and significant figures. It explains that measurements have uncertainty due to limitations of instruments. Precision refers to the agreement between repeated measurements while accuracy is the agreement with the true value. There are two types of errors - random errors that can be high or low, and systematic errors that are always in the same direction. The document provides rules for determining the number of significant figures in measurements and calculations, including how significant figures are treated in addition, subtraction, multiplication and division.
This document discusses significant figures in measurements and calculations. It makes three key points:
1. Significant figures in a measurement include all known digits plus one estimated digit and indicate the precision or uncertainty in the measurement.
2. Rules are provided for determining which digits are significant, depending on their position relative to other digits and the decimal point.
3. Calculations must be rounded according to whether addition/subtraction or multiplication/division was used, and based on the least precise term (fewest significant figures).
The document provides an overview of different math topics including whole numbers, fractions, decimals, money, and percentage. It lists the key concepts and formulas for each topic. It also includes review questions to test memorization of important math facts related to time, length, mass, volume, and measurement units.
This document provides examples and explanations of significant figures, measurements, and calculations involving significant figures. It begins with converting between different units of measurement. It then discusses the definition of significant figures and whether certain digits, such as leading zeros, trailing zeros, or sandwiched zeros are significant. Examples are given for determining the number of significant figures in different measurements. The document concludes with rules for maintaining significant figures when adding, subtracting, multiplying, and dividing measurements, including examples of calculations and determining the correct number of significant figures for the answer.
Materi Bilangan Bulat Matematika Kelas 7
Terdiri dari :
Penjumlahan Bilangan Bulat
Pengurangan Bilangan Bulat
Perkalian Bilangan Bulat
Pembagian Bilangan Bulat
Pecahan Bilangan Bulat
Desimal
KPK dan FPB
Contoh Soal Bilangan Bulat
This document provides a pacing guide for kindergarten math curriculum organized by quarter. It outlines topics such as oral and object counting, subitizing, reasoning with numbers, reading and writing numbers, addition and subtraction modeling, problem writing and solving, and geometry, measurement, and data concepts to be covered each quarter. The guide includes recommended formative assessments and benchmarks beyond state standards.
This document provides an introduction to basic arithmetic concepts including the four fundamental operations of addition, subtraction, multiplication, and division. It discusses topics such as whole numbers, fractions, mixed numbers, and changing between numerical representations. Examples and exercises are provided to demonstrate key concepts like performing the four operations, reducing fractions, and converting between whole numbers and fractions. The goal is to lay the foundation for understanding modern mathematics.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses finding the area of irregular figures by breaking them into familiar geometric shapes. It provides examples of estimating the area of irregular figures using graph paper, as well as calculating the exact area by decomposing figures into components like rectangles, triangles, parallelograms, and semicircles. Students are shown how to write out the steps to find each area component and then add them together to get the total area of the irregular figure. The final example problem asks students to determine how much tile or wallpaper is needed to cover irregularly shaped surfaces.
The document compares and contrasts multiple methods for multiplying multi-digit numbers - the traditional method, distributive law, Chinese method, Egyptian method, and lattice method. All the methods are based on the distributive law and break the multiplication into a series of addition steps. The Chinese method uses place value and counting line intersections. The Egyptian method uses doubling and powers of two. The lattice method uses a grid layout to show the place value and distributive steps.
The document explains how to find the area of an unusual shape made up of two rectangles. It shows calculating the area of each rectangle and then adding them together to find the total area. The area of the blue rectangle is calculated as 45 x 35 = 1575 square units. The area of the pink rectangle is 22 x 20 = 440 square units. The total area is found by adding these numbers: 1575 + 440 = 2015 square units.
This document is the cover page and instructions for a 1 hour 45 minute GCSE Mathematics exam. It provides information such as the materials allowed, instructions for completing the exam, exam structure, and advice for students. The exam consists of 27 multiple choice and free response questions testing a variety of math skills, including algebra, geometry, statistics, and trigonometry. Students are advised to read questions carefully, watch the time, attempt all questions, and check their work. Calculators are not permitted.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The document provides information about the format and content of the GCE O-Level Mathematics examination. It consists of two papers, each lasting 2 hours. Paper 1 tests fundamental skills and concepts through 25 short answer questions. Paper 2 tests higher-order thinking through 10-11 longer questions. Calculators and geometrical instruments are allowed. Answers should be given to three decimal places, unless otherwise specified. Various mathematical formulae are provided.
This document provides instructions and examples for adding and subtracting decimals. It explains the basic steps of lining up the decimal point and filling in missing places with zeros before adding or subtracting. When subtracting across zeros, it notes to borrow from the first non-zero digit if needed. Several examples show evaluating decimal expressions by substituting values for variables and performing the indicated operations. The document concludes with a quiz to assess understanding of adding and subtracting decimals.
NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 4Future Managers
This slide show complements the learner guide NCV 3 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers. For more information visit our website www.futuremanagers.net
Scientific notation is a way of writing numbers as a product of two numbers: a coefficient and a power of 10. It is used to express very large and very small numbers in a way that is easier to work with. To write a number in scientific notation, the significant digits are rewritten as a number between 1 and 10, and the number of places the decimal is moved is written as the exponent. Positive exponents indicate places moved to the right, and negative exponents indicate places moved to the left. Significant figures, or sig figs, refer to the certain and estimated digits in a measurement. Rules for sig figs determine how calculations are carried out and final answers rounded.
This document provides a yearly scheme of work for Year 4 students covering topics in numbers, fractions, decimals, money, and time. It outlines the learning objectives, outcomes, and suggested teaching activities for each week. The topics include whole numbers, fractions, decimals, money up to RM 10,000, and telling time in hours and minutes. The learning objectives focus on skills like addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals. Suggested activities include using number lines, charts, and story problems. The scheme of work provides a full-year overview of the key mathematical concepts and skills to be taught each week.
This document discusses measured numbers and significant figures in measurements. It defines measured numbers as numbers provided from a measurement using a measuring tool. It explains that measured numbers have known digits that are certain, and may have estimated digits that are uncertain. All digits in a measured number, including estimated digits, are considered significant figures. The number of significant figures reported depends on the precision of the measuring tool used. It provides examples of how to determine the number of significant figures in various measurements.
The document discusses measured numbers and significant figures. It provides examples of reading measurement tools like metersticks and explains how to estimate digits. Measured numbers are obtained through measurement, while exact numbers come from counting or definitions. The document also distinguishes between exact and measured numbers, giving examples like temperature, length conversions, and counted items.
This document provides an overview of scientific measurement and units. It discusses qualitative vs quantitative measurements, scientific notation, accuracy and precision, significant figures, and the International System of Units (SI). Some key points covered include:
- Quantitative measurements provide numeric results with defined units, while qualitative measurements use descriptive terms.
- Scientific notation expresses numbers as a coefficient and exponent of 10.
- Accuracy refers to how close a measurement is to the accepted value, while precision describes how consistent repeated measurements are.
- Significant figures determine the precision expressed in a measurement based on the precision of the measuring tool.
- The SI system standardizes units of length, mass, volume, temperature and more based on powers of 10.
This document discusses uncertainty in measurement and significant figures. It explains that measurements have uncertainty due to limitations of instruments. Precision refers to the agreement between repeated measurements while accuracy is the agreement with the true value. There are two types of errors - random errors that can be high or low, and systematic errors that are always in the same direction. The document provides rules for determining the number of significant figures in measurements and calculations, including how significant figures are treated in addition, subtraction, multiplication and division.
This document discusses significant figures in measurements and calculations. It makes three key points:
1. Significant figures in a measurement include all known digits plus one estimated digit and indicate the precision or uncertainty in the measurement.
2. Rules are provided for determining which digits are significant, depending on their position relative to other digits and the decimal point.
3. Calculations must be rounded according to whether addition/subtraction or multiplication/division was used, and based on the least precise term (fewest significant figures).
The document provides an overview of different math topics including whole numbers, fractions, decimals, money, and percentage. It lists the key concepts and formulas for each topic. It also includes review questions to test memorization of important math facts related to time, length, mass, volume, and measurement units.
This document provides examples and explanations of significant figures, measurements, and calculations involving significant figures. It begins with converting between different units of measurement. It then discusses the definition of significant figures and whether certain digits, such as leading zeros, trailing zeros, or sandwiched zeros are significant. Examples are given for determining the number of significant figures in different measurements. The document concludes with rules for maintaining significant figures when adding, subtracting, multiplying, and dividing measurements, including examples of calculations and determining the correct number of significant figures for the answer.
Materi Bilangan Bulat Matematika Kelas 7
Terdiri dari :
Penjumlahan Bilangan Bulat
Pengurangan Bilangan Bulat
Perkalian Bilangan Bulat
Pembagian Bilangan Bulat
Pecahan Bilangan Bulat
Desimal
KPK dan FPB
Contoh Soal Bilangan Bulat
This document provides a pacing guide for kindergarten math curriculum organized by quarter. It outlines topics such as oral and object counting, subitizing, reasoning with numbers, reading and writing numbers, addition and subtraction modeling, problem writing and solving, and geometry, measurement, and data concepts to be covered each quarter. The guide includes recommended formative assessments and benchmarks beyond state standards.
This document provides an introduction to basic arithmetic concepts including the four fundamental operations of addition, subtraction, multiplication, and division. It discusses topics such as whole numbers, fractions, mixed numbers, and changing between numerical representations. Examples and exercises are provided to demonstrate key concepts like performing the four operations, reducing fractions, and converting between whole numbers and fractions. The goal is to lay the foundation for understanding modern mathematics.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
This document discusses finding the area of irregular figures by breaking them into familiar geometric shapes. It provides examples of estimating the area of irregular figures using graph paper, as well as calculating the exact area by decomposing figures into components like rectangles, triangles, parallelograms, and semicircles. Students are shown how to write out the steps to find each area component and then add them together to get the total area of the irregular figure. The final example problem asks students to determine how much tile or wallpaper is needed to cover irregularly shaped surfaces.
The document compares and contrasts multiple methods for multiplying multi-digit numbers - the traditional method, distributive law, Chinese method, Egyptian method, and lattice method. All the methods are based on the distributive law and break the multiplication into a series of addition steps. The Chinese method uses place value and counting line intersections. The Egyptian method uses doubling and powers of two. The lattice method uses a grid layout to show the place value and distributive steps.
The document explains how to find the area of an unusual shape made up of two rectangles. It shows calculating the area of each rectangle and then adding them together to find the total area. The area of the blue rectangle is calculated as 45 x 35 = 1575 square units. The area of the pink rectangle is 22 x 20 = 440 square units. The total area is found by adding these numbers: 1575 + 440 = 2015 square units.
This document is the cover page and instructions for a 1 hour 45 minute GCSE Mathematics exam. It provides information such as the materials allowed, instructions for completing the exam, exam structure, and advice for students. The exam consists of 27 multiple choice and free response questions testing a variety of math skills, including algebra, geometry, statistics, and trigonometry. Students are advised to read questions carefully, watch the time, attempt all questions, and check their work. Calculators are not permitted.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
The document provides information about the format and content of the GCE O-Level Mathematics examination. It consists of two papers, each lasting 2 hours. Paper 1 tests fundamental skills and concepts through 25 short answer questions. Paper 2 tests higher-order thinking through 10-11 longer questions. Calculators and geometrical instruments are allowed. Answers should be given to three decimal places, unless otherwise specified. Various mathematical formulae are provided.
This document provides instructions and examples for adding and subtracting decimals. It explains the basic steps of lining up the decimal point and filling in missing places with zeros before adding or subtracting. When subtracting across zeros, it notes to borrow from the first non-zero digit if needed. Several examples show evaluating decimal expressions by substituting values for variables and performing the indicated operations. The document concludes with a quiz to assess understanding of adding and subtracting decimals.
NCV 3 Mathematical Literacy Hands-On Support Slide Show - Module 4Future Managers
This slide show complements the learner guide NCV 3 Mathematical Literacy Hands-On Training by San Viljoen, published by Future Managers. For more information visit our website www.futuremanagers.net
Scientific notation is a way of writing numbers as a product of two numbers: a coefficient and a power of 10. It is used to express very large and very small numbers in a way that is easier to work with. To write a number in scientific notation, the significant digits are rewritten as a number between 1 and 10, and the number of places the decimal is moved is written as the exponent. Positive exponents indicate places moved to the right, and negative exponents indicate places moved to the left. Significant figures, or sig figs, refer to the certain and estimated digits in a measurement. Rules for sig figs determine how calculations are carried out and final answers rounded.
This document provides a yearly scheme of work for Year 4 students covering topics in numbers, fractions, decimals, money, and time. It outlines the learning objectives, outcomes, and suggested teaching activities for each week. The topics include whole numbers, fractions, decimals, money up to RM 10,000, and telling time in hours and minutes. The learning objectives focus on skills like addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals. Suggested activities include using number lines, charts, and story problems. The scheme of work provides a full-year overview of the key mathematical concepts and skills to be taught each week.
This document discusses measured numbers and significant figures in measurements. It defines measured numbers as numbers provided from a measurement using a measuring tool. It explains that measured numbers have known digits that are certain, and may have estimated digits that are uncertain. All digits in a measured number, including estimated digits, are considered significant figures. The number of significant figures reported depends on the precision of the measuring tool used. It provides examples of how to determine the number of significant figures in various measurements.
The document discusses measured numbers and significant figures. It provides examples of reading measurement tools like metersticks and explains how to estimate digits. Measured numbers are obtained through measurement, while exact numbers come from counting or definitions. The document also distinguishes between exact and measured numbers, giving examples like temperature, length conversions, and counted items.
This document provides an overview of scientific measurement and units. It discusses qualitative vs quantitative measurements, scientific notation, accuracy and precision, significant figures, and the International System of Units (SI). Some key points covered include:
- Quantitative measurements provide numeric results with defined units, while qualitative measurements use descriptive terms.
- Scientific notation expresses numbers as a coefficient and exponent of 10.
- Accuracy refers to how close a measurement is to the accepted value, while precision describes how consistent repeated measurements are.
- Significant figures determine the precision expressed in a measurement based on the precision of the measuring tool.
- The SI system standardizes units of length, mass, volume, temperature and more based on powers of 10.
The document discusses measured numbers and significant figures. It provides examples of measuring lengths using a meter stick and estimating digits. Measured numbers are obtained through measurement, while exact numbers come from counting or definitions. Numbers are classified as either exact or measured, with measured requiring a measuring tool and exact coming from counts or definitions.
- Scientific notation is a way of writing very large or small numbers as a product of a number between 1 and 10 and a power of 10.
- Prefixes are used to indicate the power of 10 being multiplied, with examples including mega (106) and micro (10-6).
- When measuring quantities, only a certain number of digits can be known with certainty based on the precision of the measuring instrument. Significant figures indicate the digits that are known precisely.
This document provides an introduction to CHEM 1101 and covers several key chemistry concepts. It introduces the instructor, Dr. Muhannad Amer, and discusses the scientific method and how it is used in chemistry. It also defines and compares scientific theories and laws. Additionally, it covers important topics such as the International System of Units (SI units), dimensional analysis, density, temperature scales, and significant figures.
Scientific Measurement can be summarized in 3 sentences:
Measurement involves assigning numerical values to properties of matter using standardized units. The units provide the numerical value and type of quantity being measured, with significant figures indicating the precision. Dimensional analysis allows conversion between different units by canceling unwanted units and introducing desired units using conversion factors derived from unit equality relationships.
This document discusses measurement, density, and temperature scales. It defines qualitative and quantitative measurements. It explains scientific notation and how to convert between standard and scientific notation. It discusses accuracy versus precision. It describes metric units and prefixes for length, mass, volume, and temperature. It provides examples of calculating density and solving density problems using dimensional analysis. Finally, it introduces the Fahrenheit, Celsius, and Kelvin temperature scales.
1. Significant figures indicate the precision or uncertainty of a measurement. Exact numbers are obtained by counting or definition while measured numbers use measuring devices and have uncertainty.
2. There are rules for determining which digits in a measured number are significant based on their position relative to the decimal point. Numbers should be rounded appropriately based on the number of significant figures.
3. Calculations with measured numbers must follow rules to avoid reporting more significant figures than the original measurements support, such as limiting digits in addition/subtraction and figures in multiplication/division.
1. Scientific notation is a way to write numbers as a product of a coefficient and a power of 10 to express very large and very small numbers.
2. A law is a statement of fact based on repeated observation that describes natural phenomena, while a theory is a well-substantiated explanation of such a law.
3. Significant figures indicate the precision or uncertainty of a measurement and are used to calculate the error in products and quotients of calculations.
The document discusses various measurement and calculation concepts in science including units, accuracy, precision, significant figures, and dimensional analysis. It provides examples of calculating percent error and guidelines for determining the number of significant figures in measurements and calculations. Various practice problems are included for converting between units and performing calculations while maintaining the appropriate number of significant figures.
1. Scientific notation is used to express very large or very small numbers in a standard way using a coefficient and power of 10.
2. Theories are explanations based on repeated experimentation and observation, while laws are rules of nature. Theories do not become laws.
3. Significant figures tell us how precisely a measurement or number is known and indicate the reliability of the last digits.
This document discusses various concepts related to measurement and errors in measurement. It defines physical quantities, units of measurement, and the classification of quantities into fundamental and derived quantities. It also explains the International System of Units (SI units), prefixes used with SI units, and rules for writing SI units. The document discusses the concepts of significant figures and counting significant figures in measurements. It describes different types of errors in measurement such as systematic errors, gross errors, and random errors. It also explains the concepts of absolute error, mean absolute error, relative error, percentage error, and least count error. Finally, it discusses the combination of errors in different mathematical operations.
The document discusses scientific measurement and units. It covers accuracy, precision, and significant figures when making measurements. Conversion factors allow measurements to be converted between different units through multiplication. Dimensional analysis uses the units of measurements to solve conversion problems by breaking them into steps. Complex problems are best solved by breaking them into manageable parts.
EOT 1 Sample questions and answers provide practice problems and worked examples related to chemistry concepts. The document contains questions on temperature conversions, classification of chemical formulas, the periodic table, properties of matter, unit prefixes, naming ions and ionic compounds, empirical formulas, significant figures, and calculations involving significant figures. Worked examples demonstrate how to perform unit conversions, classify formulas, name compounds, calculate empirical formulas, count significant figures, and properly round answers in calculations.
This document discusses significant figures and how they are used to convey the precision and uncertainty of measurements. It provides examples of how to determine the number of significant figures in a measurement, as well as rules for performing calculations while maintaining the proper number of significant figures in the final answer based on the least precise term. Calculations include addition, subtraction, multiplication, and division. The key points are that non-zero digits and zeros between non-zero digits are always significant, and that the final answer should be rounded based on the number of decimal places in the least precise measurement used.
This document discusses measurement units and conversions between metric and other systems. It covers:
- The fundamental SI units of mass, length, time, temperature and derived quantities.
- Using prefixes like kilo and centi to indicate multiples of ten in the metric system.
- Converting between metric units by moving the decimal place.
- Converting between metric and other systems like English units using conversion factors and unit cancellation.
- Applying significant figures rules to calculations to preserve measurement precision.
Significant figures are used to indicate the precision of a measurement or calculation. There are three types of zeros in numbers: leading zeros do not count as significant figures, captive zeros between nonzero digits do count, and trailing zeros count only if a decimal is present. When adding or subtracting measurements, the answer can have no more decimal places than the least precise measurement. When multiplying or dividing measurements, the result can have no more significant figures than the least reliable measurement.
1. The document provides an introduction to physics concepts including understanding physics, base and derived quantities, scalar and vector quantities, and measurements.
2. Key concepts discussed include the definition of physics, base units, derived units, scalar and vector quantities, and factors that affect the accuracy and sensitivity of measuring instruments.
3. Examples are provided to illustrate scientific notation, unit conversion, identifying systematic and random errors, and the proper use of instruments like the vernier caliper and micrometer screw gauge.
1. The scientific method involves making observations and measurements, formulating hypotheses to explain observations, and performing experiments to test hypotheses.
2. Scientific theories are sets of hypotheses that have been tested and provide explanations for natural phenomena, while scientific laws summarize repeated experimental observations of natural phenomena.
3. Scientific notation is used to conveniently express very large and small numbers and involves writing numbers in the form of M × 10n, where 1 ≤ M < 10 and n is an integer exponent.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
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A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
LAND USE LAND COVER AND NDVI OF MIRZAPUR DISTRICT, UPRAHUL
This Dissertation explores the particular circumstances of Mirzapur, a region located in the
core of India. Mirzapur, with its varied terrains and abundant biodiversity, offers an optimal
environment for investigating the changes in vegetation cover dynamics. Our study utilizes
advanced technologies such as GIS (Geographic Information Systems) and Remote sensing to
analyze the transformations that have taken place over the course of a decade.
The complex relationship between human activities and the environment has been the focus
of extensive research and worry. As the global community grapples with swift urbanization,
population expansion, and economic progress, the effects on natural ecosystems are becoming
more evident. A crucial element of this impact is the alteration of vegetation cover, which plays a
significant role in maintaining the ecological equilibrium of our planet.Land serves as the foundation for all human activities and provides the necessary materials for
these activities. As the most crucial natural resource, its utilization by humans results in different
'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
How to Setup Warehouse & Location in Odoo 17 InventoryCeline George
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
3. 3
Numbers in Scientific Notation
A number written in scientific notation contains a
• coefficient.
• power of 10.
Examples:
coefficient power of ten coefficient power of ten
1.5 x 102
7.35 x 10-4
4. 4
Writing Numbers in
Scientific Notation
To write a number in scientific notation,
• move the decimal point to give a number 1-9.
• show the spaces moved as a power of 10.
Examples:
52 000. = 5.2 x 104
0.00178 = 1.78 x 10-3
4 spaces left 3 spaces right
6. 6
Comparing Numbers in Standard
and Scientific Notation
Here are some numbers written in standard format
and in scientific notation.
Number in Number in
Standard Format Scientific Notation
Diameter of the Earth
12 800 000 m 1.28 x 107
m
Mass of a typical human
68 kg 6.8 x 101
kg
Length of a pox virus
0.000 03 cm 3 x 10-5
cm
7. 7
Study Tip: Scientific Notation
In a number 10 or larger, the decimal point
• is moved to the left to give a positive power of 10
In a number less than 1, the decimal point
• is moved to the right to give a negative power of 10
8. 8
Learning Check
Select the correct scientific notation for each.
A. 0.000 008 m
1) 8 x 106
m, 2) 8 x 10-6
m, 3) 0.8 x 10-5
m
B. 72 000 g
1) 7.2 x 104
g, 2) 72 x 103
g, 3) 7.2 x 10-4
g
10. 10
Learning Check
Write each as a standard number.
A. 2.0 x 10-2
L
1) 200 L, 2) 0.0020 L, 3) 0.020 L
B. 1.8 x 105
g
1) 180 000 g, 2) 0.000 018 g, 3) 18 000 g
14. 14
. l2
. . . . l . . . . l3
. . . . l . . . . l4
. . cm
• The markings on the meterstick at the end of the
orange line are read as:
the first digit 2
plus the second digit 2.7
• The last digit is obtained by estimating.
• The end of the line may be estimated between 2.7–
2.8 as half way (0.5) or a little more (0.6), which gives
a reported length of 2.75 cm or 2.76 cm.
Reading a Meterstick
15. 15
Known & Estimated Digits
If the length is reported as 2.76 cm,
• the digits 2 and 7 are certain (known).
• the final digit, 6, is estimated (uncertain).
• all three digits (2, 7, and 6) are significant, including
the estimated digit.
16. 16
. l8
. . . . l . . . . l9
. . . . l . . . . l10
. . cm
What is the length of the orange line?
1) 9.0 cm
2) 9.04 cm
3) 9.05 cm
Learning Check
17. 17
. l8
. . . . l . . . . l9
. . . . l . . . . l10
. . cm
The length of the orange line could be reported as
2) 9.04 cm
or 3) 9.05 cm
The estimated digit may be slightly different. Both
readings are acceptable.
Solution
18. 18
. l3
. . . . l . . . . l4
. . . . l . . . . l5
. . cm
• For this measurement, the first and second known
digits are 4 and 5.
• When a measurement ends on a mark, the estimated
digit in the hundredths place is 0.
• This measurement is reported as 4.50 cm.
Zero as a Measured Number
19. 19
Significant Figures in
Measured Numbers
Significant Figures
• obtained from a measurement include all
of the known digits plus the estimated
digit.
• reported in a measurement depend on the
measuring tool.
21. 21
All nonzero numbers in a measured number are
significant.
Number of
Measurement Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb 3
122.55 m 5
Counting Significant Figures
22. 22
Sandwiched Zeros
• occur between nonzero numbers.
• are significant.
Number of
Measurement Significant Figures
50.8 mm 3
2001 min 4
0.0702 lb 3
0.405 05 m 5
Sandwiched Zeros
23. 23
Trailing Zeros
• follow nonzero numbers in numbers without
decimal points.
• are usually placeholders.
• are not significant.
Number of
Measurement Significant Figures
25 000 cm 2
200 kg 1
48 600 mL 3
25 005 000 g 5
Trailing Zeros
24. 24
Leading Zeros
• precede nonzero digits in a decimal number.
• are not significant.
Number of
Measurement Significant Figures
0.008 mm 1
0.0156 oz 3
0.0042 lb 2
0.000 262 mL 3
Leading Zeros
25. 25
State the number of significant figures in each of
the following measurements.
A. 0.030 m
B. 4.050 L
C. 0.0008 g
D. 2.80 m
Learning Check
26. 26
State the number of significant figures in each of
the following measurements.
A. 0.030 m 2
B. 4.050 L 4
C. 0.0008 g 1
D. 2.80 m 3
Solution
27. 27
Significant Figures in
Scientific Notation
In scientific notation all digits in the coefficient
including zeros are significant.
Number of
Measurement Significant Figures
8 x 104
m 1
8.0 x 104
m 2
8.00 x 104
m 3
28. 28
Study Tip: Significant Figures
The significant figures in a measured number are
• all the nonzero numbers.
12.56 m 4 significant figures
• zeros between nonzero numbers.
4.05 g 3 significant figures
• zeros that follow nonzero numbers in a decimal
number.
25.800 L 5 significant figures
29. 29
A. Which answer(s) contain 3 significant figures?
1) 0.4760 2) 0.00476 3) 4.76 x 103
B. All the zeros are significant in
1) 0.00307. 2) 25.300. 3) 2.050 x 103
.
C. The number of significant figures in 5.80 x 102
is
1) one (1). 2) two (2). 3) three (3).
Learning Check
30. 30
A. Which answer(s) contain 3 significant figures?
2) 0.00476 3) 4.76 x 103
B. All the zeros are significant in
2) 25.300. 3) 2.050 x 103
.
C. The number of significant figures in 5.80 x 102
is
3) three (3).
Solution
31. 31
In which set(s) do both numbers contain the
same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000 015 and 150 000
Learning Check
32. 32
Solution
In which set(s) do both numbers contain the same
number of significant figures?
3) 0.000 015 and 150 000
Both numbers contain 2 significant figures.
33. 33
Examples of Exact Numbers
An exact number is obtained
• when objects are counted.
Counted objects
2 soccer balls
4 pizzas
• from numbers in a defined relationship.
Defined relationships
1 foot = 12 inches
1 meter = 100 cm
35. 35
Learning Check
A. Exact numbers are obtained by
1. using a measuring tool.
2. counting.
3. definition.
B. Measured numbers are obtained by
1. using a measuring tool.
2. counting.
3. definition.
36. 36
Solution
A. Exact numbers are obtained by
2. counting.
3. definition.
B. Measured numbers are obtained by
1. using a measuring tool.
37. 37
Learning Check
Classify each of the following as (1) exact or (2) measured
numbers.
A.__Gold melts at 1064 °C.
B.__1 yard = 3 feet
C.__The diameter of a red blood cell is 6 x 10-4
cm.
D.__There are 6 hats on the shelf.
E.__A can of soda contains 355 mL of soda.
38. 38
Classify each of the following as (1) exact or (2) measured
numbers.
A. 2 A measuring tool is required.
B. 1 This is a defined relationship.
C. 2 A measuring tool is used to determine
length.
D. 1 The number of hats is obtained by counting.
E. 2 The volume of soda is measured.
Solution
41. 41
Rounding Off Calculated
Answers
When the first digit dropped is 4 or less,
• the retained numbers remain the same.
45.832 rounded to 3 significant figures
drops the digits 32 = 45.8
When the first digit dropped is 5 or greater,
• the last retained digit is increased by 1.
2.4884 rounded to 2 significant figures
drops the digits 884 = 2.5 (increase by 0.1)
42. 42
Adding Significant Zeros
• Sometimes a calculated answer requires more
significant digits. Then, one or more zeros are
added.
Calculated Zeros Added to
Answer Give 3 Significant Figures
4 4.00
1.5 1.50
0.2 0.200
12 12.0
43. 43
Learning Check
Round off or add zeros to the following calculated
answers to give three significant figures.
A. 824.75 cm
B. 0.112486 g
C. 8.2 L
44. 44
Solution
Adjust the following calculated answers to give answers
with 3 significant figures.
A. 825 cm First digit dropped is greater than 5.
B. 0.112g First digit dropped is 4.
C. 8.20 L Significant zero is added.
46. 46
When multiplying or dividing
• the final answer must have the same number of
significant figures as the measurement with the
fewest significant figures.
• use rounding rules to obtain the correct number of
significant figures.
Example:
110.5 x 0.048 = 5.304 = 5.3 (rounded)
4 SF 2 SF calculator 2 SF
Multiplication and Division
47. 47
Select the answer with the correct number of
significant figures.
A. 2.19 x 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 =
1) 61.59 2) 62 3) 60
C. 2.54 x 0.0028 =
0.0105 x 0.060
1) 11.3 2) 11 3) 0.041
Learning Check
48. 48
A. 2.19 x 4.2 = 2) 9.2
B. 4.311 ÷ 0.07 = 3) 60
C. 2.54 x 0.0028 = 2) 11
0.0105 x 0.060
On a calculator, enter each number, followed by
the operation key.
2.54 x 0.0028 ÷ 0.0105 ÷ 0.060 = 11.28888889
= 11 (rounded)
Solution
49. 49
When adding or subtracting
• the final answer must have the same number of
decimal places as the measurement with the fewest
decimal places.
• use rounding rules to adjust the number of digits in
the answer.
25.2 one decimal place
+ 1.34 two decimal places
26.54 calculated answer
26.5 final answer with one decimal place
Addition and Subtraction
50. 50
For each calculation, round off the calculated answer
to give a final answer with the correct number of
significant figures.
A. 235.05 + 19.6 + 2 =
1) 257 2) 256.7 3) 256.65
B. 58.925 - 18.2 =
1) 40.725 2) 40.73 3) 40.7
Learning Check
53. 53
Prefixes
A prefix
in front of a unit increases or decreases the size of that unit.
makes units larger or smaller than the initial unit by one or more
factors of 10.
indicates a numerical value.
prefix = value
1 kilometer = 1000 meters
1 kilogram = 1000 grams
55. 55
Indicate the unit that matches the description.
1. A mass that is 1000 times greater than 1 gram.
1) kilogram 2) milligram 3) megagram
2. A length that is 1/100 of 1 meter.
1) decimeter 2) centimeter 3) millimeter
3. A unit of time that is 1/1000 of a second.
1) nanosecond 2) microsecond 3) millisecond
Learning Check
56. 56
Indicate the unit that matches the description.
1. A mass that is 1000 times greater than 1 gram.
1) kilogram
2. A length that is 1/100 of 1 meter.
2) centimeter
3. A unit of time that is 1/1000 of a second.
3) millisecond
Solution
57. 57
Select the unit you would use to measure
A. your height.
1) millimeters 2) meters 3) kilometers
B. your mass.
1) milligrams 2) grams 3) kilograms
C. the distance between two cities.
1) millimeters 2) meters 3) kilometers
D. the width of an artery.
1) millimeters 2) meters 3) kilometers
Learning Check
58. 58
A. your height.
2) meters
B. your mass.
3) kilograms
C. the distance between two cities.
3) kilometers
D. the width of an artery.
1) millimeters
Solution
59. 59
An equality
states the same measurement in two different units.
can be written using the relationships between two metric
units.
Example: 1 meter is the same as 100 cm and 1000 mm.
1 m = 100 cm
1 m = 1000 mm
Metric Equalities
63. 63
Indicate the unit that completes each of the following
equalities.
A. 1000 m = ___ 1) 1 mm 2) 1 km 2) 1 dm
B. 0.001 g = ___ 1) 1 mg 2) 1 kg 2) 1 dg
C. 0.1 s = ___ 1) 1 ms 2) 1 cs 2) 1 ds
D. 0.01 m = ___ 1) 1 mm 2) 1 cm 2) 1 dm
Learning Check
64. 64
Indicate the unit that completes each of the following
equalities.
A. 2) 1000 m = 1 km
B. 1) 0.001 g = 1 mg
C. 3) 0.1 s = 1 ds
D. 2) 0.01 m = 1 cm
Solution
65. 65
Complete each of the following equalities.
A. 1 kg = ___ 1) 10 g 2) 100 g 3) 1000 g
B. 1 mm = ___ 1) 0.001 m 2) 0.01 m 3) 0.1 m
Learning Check
66. 66
Complete each of the following equalities.
A. 1 kg = 1000 g (3)
B. 1 mm = 0.001 m (1)
Solution
68. 68
Equalities
• use two different units to describe the same measured
amount.
• are written for relationships between units of the metric
system, U.S. units, or between metric and U.S. units.
For example,
1 m = 1000 mm
1 lb = 16 oz
2.20 lb = 1 kg
Equalities
69. 69
Exact and Measured Numbers in
Equalities
Equalities between units in
• the same system of measurement are definitions
that use exact numbers.
• different systems of measurement (metric and U.S.)
use measured numbers that have significant figures.
Exception:
The equality 1 in. = 2.54 cm has been defined as an
exact relationship. Thus, 2.54 is an exact number.
72. 72
A conversion factor is
• obtained from an equality.
Equality: 1 in. = 2.54 cm
• written as a fraction (ratio) with a numerator and
denominator.
• inverted to give two conversion factors for every
equality.
1 in. and 2.54 cm
2.54 cm 1 in.
Conversion Factors
73. 73
Write conversion factors from the equality for each
of the following.
A. liters and mL
B. hours and minutes
C. meters and kilometers
Learning Check
74. 74
Write conversion factors from the equality for each of the
following.
A. 1 L = 1000 mL 1 L and 1000 mL
1000 mL 1 L
B. 1 h = 60 min 1 h and 60 min
60 min 1 h
C. 1 km = 1000 m 1 km and 1000 m
Solution
75. 75
A conversion factor
• may be obtained from information in a word problem.
• is written for that problem only.
Example 1:
The price of one pound (1 lb) of red peppers is $2.39.
1 lb red peppers and $2.39
$2.39 1 lb red peppers
Example 2:
The cost of one gallon (1 gal) of gas is $2.89.
1 gallon of gas and $2.89
Conversion Factors in a Problem
76. 76
A percent factor
• gives the ratio of the parts to the whole.
% = parts x 100
whole
• uses the same unit in the numerator and denominator.
• uses the value 100.
• can be written as two factors.
Example: A food contains 30% (by mass) fat.
30 g fat and 100 g food
100 g food 30 g fat
Percent as a Conversion Factor
78. 78
Smaller Percents: ppm and ppb
Small percents are shown as ppm and ppb.
• Parts per million (ppm) = mg part/kg whole
Example: The EPA allows 15 ppm cadmium in food
colors
15 mg cadmium = 1 kg food color
• Parts per billion ppb = µ g part/kg whole
Example: The EPA allows10 ppb arsenic in public
water
10 µ g arsenic = 1 kg water
79. 79
Arsenic in Water
Write the conversion factors for 10 ppb arsenic
in public water from the equality
10 µ g arsenic = 1 kg water.
Conversion factors:
10 µ g arsenic and 1 kg water
1 kg water 10 µ g arsenic
80. Study Tip: Conversion Factors
An equality
• is written as a fraction (ratio).
• provides two conversion factors that are the
inverse of each other.
80
81. 81
Learning Check
Write the equality and conversion factors for each of the
following.
A. meters and centimeters
B. jewelry that contains 18% gold
C. One gallon of gas is $2.89
82. 82
Solution
A. 1 m = 100 cm
1m and 100 cm
100 cm 1m
B. 100 g jewelry = 18 g gold
18 g gold and 100 g jewelry
100 g jewelry 18 g gold
C. 1 gal gas = $2.89
1 gal and $2.89
$2.89 1 gal
83. Risk-Benefit Assessment
A measurement of toxicity is
• LD50 or “lethal dose.”
• the concentration of the substance that causes death
in 50% of the test animals.
• in milligrams per kilogram (mg/kg or ppm) of body mass.
• in micrograms per kilogram (µ g/kg or ppb) of body
mass.
83
85. Solution
The LD50 for aspirin is 1100 ppm. How many grams of
aspirin would be lethal in 50% of persons with a body
mass of 85 kg?
B. 94 g
1100 ppm = 1100 mg/kg body mass
85
85 kg
1100 mg
×
kg
1 g
1000 mg
× = 94 g
87. 87
To solve a problem,
• identify the given unit.
• identify the needed unit.
Example:
A person has a height of 2.0 meters.
What is that height in inches?
The given unit is the initial unit of height.
given unit = meters (m)
The needed unit is the unit for the answer.
needed unit = inches (in.)
Given and Needed Units
88. 88
Learning Check
An injured person loses 0.30 pints of blood. How
many milliliters of blood would that be?
Identify the given and needed units given in this
problem.
Given unit = _______
Needed unit = _______
89. 89
Solution
An injured person loses 0.30 pints of blood. How
many milliliters of blood would that be?
Identify the given and needed units given in this
problem.
Given unit = pints
Needed unit = milliliters
90. 90
• Write the given and needed units.
• Write a plan to convert the given unit to the needed unit.
• Write equalities and conversion factors that connect the
units.
• Use conversion factors to cancel the given unit and
provide the needed unit.
Unit 1 x Unit 2 = Unit 2
Unit 1
Given x Conversion = Needed
unit factor unit
Problem Setup
91. 91
Study Tip: Problem Solving
Using GPS
The steps in the
Guide to Problem
Solving (GPS) are
useful in setting up
a problem with
conversion factors.
93. 93
A rattlesnake is 2.44 m long. How many cm long is
the snake?
1) 2440 cm
2) 244 cm
3) 24.4 cm
Learning Check
94. 94
A rattlesnake is 2.44 m long. How many cm long
is the snake?
2) 244 cm
Given Conversion Needed
unit factor unit
2.44 m x 100 cm = 244 cm
1 m
Solution
95. 95
• Often, two or more conversion factors are required
to obtain the unit needed for the answer.
Unit 1 Unit 2 Unit 3
• Additional conversion factors are placed in the
setup problem to cancel each preceding unit.
Given unit x factor 1 x factor 2 = needed unit
Unit 1 x Unit 2 x Unit 3 = Unit 3
Unit 1 Unit 2
Using Two or More Factors
96. 96
How many minutes are in 1.4 days?
Given unit: 1.4 days
Factor 1 Factor 2
Plan: days h min
Set Up Problem:
1.4 days x 24 h x 60 min = 2.0 x 103
min
1 day 1 h (rounded)
2 SF Exact Exact = 2 SF
Example: Problem Solving
97. 97
• Be sure to check the unit cancellation in the setup.
• The units in the conversion factors must cancel to
give the correct unit for the answer.
What is wrong with the following setup?
1.4 day x 1 day x 1 h
24 h 60 min
= day2
/min is not the unit needed
Units don’t cancel properly.
Study Tip: Check Unit
Cancellation
98. 98
A bucket contains 4.65 L of water. Write the setup
for the problem and calculate the gallons of water in
the bucket.
Plan: L qt gallon
Equalities: 1.06 qt = 1 L
1 gal = 4 qt
Set Up Problem:
4.65 L x x 1.06 qt x 1 gal = 1.23 gal
1 L 4 qt
Learning Check
99. 99
Given: 4.65 L Needed: gallons
Plan: L qt gallon
Equalities: 1.06 qt = 1 L; 1 gal = 4 qt
Set Up Problem:
4.65 L x x 1.06 qt x 1 gal = 1.23 gal
1 L 4 qt
3 SF 3 SF exact 3 SF
Solution
100. 100
If a ski pole is 3.0 feet in length, how long is the
ski pole in mm?
Learning Check
101. 101
Equalities:
1 ft = 12 in. 1 in. = 2.54 cm 1 cm = 10 mm
Set Up Problem:
3.0 ft x 12 in. x 2.54 cm x 10 mm =
1 ft 1 in. 1 cm
Calculator answer = 914.4 mm
Final answer = 910 mm
(2 SF rounded)
Check Factors in Setup: Units cancel properly
Check Final Unit: mm
Solution
102. 102
If your pace on a treadmill is 65 meters per minute,
how many minutes will it take for you to walk a
distance of 7500 feet?
Learning Check
103. 103
Solution
Given: 7500 ft 65 m/min Need: min
Plan: ft in. cm m min
Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm
1 min = 65 m (walking pace)
Set Up Problem:
7500 ft x 12 in. x 2.54 cm x 1m x 1 min
1 ft 1 in. 100 cm 65 m
= 35 min final answer (2 SF)
Given: 7500 ft 65 m/min Need: min
Plan: ft in. cm m
Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm
1 min = 65 m (walking pace)
Set Up Problem:
7500 ft x 12 in. x 2.54 cm x 1m x 1 min
1 ft 1 in. 100 cm 65 m
= 35 min final answer (2 SF)
105. 105
How many lb of sugar are in 120 g of candy if the
candy is 25% (by mass) sugar?
Learning Check
106. 106
Solution
How many lb of sugar are in 120 g of candy if the
candy is 25%(by mass) sugar?
percent factor
120 g candy x 1 lb candy x 25 lb sugar
454 g candy 100 lb candy
= 0.066 lb of sugar
108. 108
Density
• compares the mass of an object to its volume.
• is the mass of a substance divided by its
volume.
Density Expression
Density = mass = g or g = g/cm3
volume mL cm3
Note: 1 mL = 1 cm3
Density
110. 110
Osmium is a very dense metal. What is its density
in g/cm3
if 50.0 g of osmium has a volume of 2.22
cm3
?
1) 2.25 g/cm3
2) 22.5 g/cm3
3) 111 g/cm3
Learning Check
111. 111
Given: mass = 50.0 g volume = 2.22 cm3
Plan: Place the mass and volume of the osmium
metal
in the density expression.
2) D = mass = 50.0 g
volume 2.22 cm3
calculator answer = 22.522522 g/cm3
final answer = 22.5 g/cm3
Solution
114. 114
What is the density (g/cm3
) of 48.0 g of a metal if the
level of water in a graduated cylinder rises from 25.0
mL to 33.0 mL after the metal is added?
1) 0.17 g/cm3
2) 6.0 g/cm3
3) 380 g/cm3
Learning Check
object
33.0 mL25.0
mL
115. 115
Solution
Given: 48.0 g Volume of water = 25.0 mL
Volume of water + metal = 33.0 mL
Need: Density (g/mL)
Plan: Calculate the volume difference in cm3
and place
in density expression.
33.0 mL - 25.0 mL = 8.0 mL
8.0 mL x 1 cm3
= 8.0 cm3
1 mL
Set Up Problem:
Density = 48.0 g = 6.0 g = 6.0 g/cm3
8.0 cm3
1cm3
117. 117
Which diagram correctly represents the liquid layers
in the cylinder? Karo (K) syrup (1.4 g/mL); vegetable
(V) oil (0.91 g/mL); water (W) (1.0 g/mL)
1 2 3
K
K
W
W
W
V
V
V
K
Learning Check
119. 119
The density of octane, a component of gasoline, is
0.702 g/mL. What is the mass, in kg, of 875 mL of
octane?
1) 0.614 kg
2) 614 kg
3) 1.25 kg
Learning Check
120. 120
Density can be written as an equality.
• For a substance with a density of 3.8 g/mL, the
equality is
3.8 g = 1 mL
• From this equality, two conversion factors can be
written for density.
Conversion 3.8 g and 1 mL
factors 1 mL 3.8 g
Study Tip: Density as a
Conversion Factor
121. 121
Solution
1) 0.614 kg
Given: D = 0.702 g/mL V= 875 mL
Plan: mL → g → kg
Equalities: density 0.702 g = 1 mL
and 1 kg = 1000 g
Setup: 875 mL x 0.702 g x 1 kg = 0.614 kg
1 mL 1000 g
density metric
factor factor
122. 122
If olive oil has a density of 0.92 g/mL, how many
liters of olive oil are in 285 g of olive oil?
1) 0.26 L
2) 0.31 L
3) 310 L
Learning Check
123. 123
Solution
2) 0.31 L
Given: D = 0.92 g/mL mass = 285 g
Need: volume in liters
Plan: g → mL → L
Equalities: 1 mL = 0.92 g and 1 L = 1000 mL
Set Up Problem:
285 g x 1 mL x 1 L = 0.31 L
0.92 g 1000 mL
density metric
factor factor
inverted
124. 124
A group of students collected 125 empty aluminum
cans to take to the recycling center. If 21 cans
make 1.0 lb aluminum, how many liters of
aluminum (D=2.70 g/cm3
) are obtained from the
cans?
1) 1.0 L 2) 2.0 L 3) 4.0 L
Learning Check
125. 125
Solution
1) 1.0 L
125 cans x 1.0 lb x 454 g x 1 cm3
x 1 mL x 1 L
21 cans 1 lb 2.70 g 1 cm3
1000 mL
density
factor
inverted
= 1.0 L
126. 126
Which of the following samples of metals will displace
the greatest volume of water?
1 2 3
25 g of aluminum
2.70 g/mL
45 g of gold
19.3 g/mL
75 g of lead
11.3 g/mL
Learning Check
127. 127
Solution
25 g of aluminum
2.70 g/mL
1)
Plan: Calculate the volume for each metal and select
the metal sample with the greatest volume.
1) 25 g x 1 mL = 9.3 mL aluminum
2.70 g
2) 45 g x 1 mL = 2.3 mL gold
19.3 g
3) 75 g x 1 mL = 6.6 mL lead
11.3 g
density
factors