# Dimensions, Units, and Significant Digits Author: John M. Cimbala, Penn State University Latest revision, 06 January 2014

Save this PDF as:

Size: px
Start display at page:

Download "Dimensions, Units, and Significant Digits Author: John M. Cimbala, Penn State University Latest revision, 06 January 2014"

## Transcription

1 Dimensions, Units, and Significant Digits Author: John M. Cimbala, Penn State University Latest revision, 06 January 014 Dimensions and Units Primary (or Basic) Dimensions There are seven primary dimensions (also called basic dimensions). All other dimensions can be formed by combinations of these. The primary dimensions are: mass, length, time, temperature, current, amount of light, and amount of matter. Unit Systems Unit systems were invented so that numbers could be assigned to the dimensions. o There are three primary unit systems in use today: the International System of Units (SI units, from Le Systeme International d Unites, more commonly simply called the metric system of units) the English Engineering System of Units (commonly called English system of units) the British Gravitational System of Units (BG) o The latter two are similar, except for the choice of primary mass unit and use of the degree symbol. The two dominant unit systems in use in the world today are the metric system (SI) and the English system. [The BG system is no longer popular, and I do not recommend that you use it.] The table below shows each of the primary dimensions, along with their symbols and units in the SI, English, and BG unit systems: Primary dimension Symbol SI unit English unit BG unit mass m kg (kilogram) lbm (pound-mass) slug length L m (meter) ft (foot) ft (foot) time t s (second) s (second) s (second) thermodynamic temperature T K (kelvin) R (rankine) o R ( o Rankine) current I (or i) A (ampere) A (ampere) A (ampere) amount of light (luminous intensity) C (or I) cd (candela) cd (candela) cd (candela) amount of matter N mol (mole) mol (mole) mol (mole) All other dimensions and units can be derived as combinations of these seven. These are called secondary dimensions, with their corresponding secondary units. A few examples are given in the table below: Secondary Symbol SI unit English unit BG unit dimension force F N (newton = kgm/s ) lbf (pound-force) lbf or lb (pound) * acceleration a m/s ft/s ft/s pressure P (sometimes p) Pa (pascal = N/m ) lbf/in (psi) lbf/ft (psf) energy E J (joule = Nm) ftlbf (foot-pound) ftlbf (foot-pound) power W (sometimes P) W (watt = J/s) ftlbf/s ftlbf/s * Some users of the BG system use lb (pound) and do not distinguish between lbf and lbm. In this course we will never use lb, but will always use either lbf (pound force) or lbm (pound mass) to avoid confusion. Note: Some authors substitute force for mass in the list of primary dimensions. This is an alternative way to consider primary dimensions. We will not use this alternative method in this course, but you should be aware that it is sometimes used. The system using mass as a primary dimension is the more popular of the two.

2 Given: An engineer is measuring surface tension. To do: Express the dimensions of surface tension in terms of primary dimensions only. Solution: o Note: In this course, the notation {something} means the dimensions of something. o Surface tension has dimensions of force per unit length, or {F/L}. o Force has dimensions of mass times acceleration, or {ml/t }. o Hence, surface tension has dimensions of {(ml/t )/L}, or {m/t }. o The final result is thus {surface tension} = {m/t } There are many other units, both metric and English, in use today. For example, power is often expressed in units of Btu/hr, Btu/s, cal/s, ergs/s, or horsepower, in addition to the standard units of watt and ftlbf/s. There are conversion factors listed in handbooks to enable conversion from any of these units to any other. Even though the English system is much more difficult to use than the metric system, it is still widely in use in industry today. Therefore, we still have to learn both systems, and as engineers we must be comfortable using both systems. Quirks - There are quirks in both English and metric systems: o English - There are two standard units for mass: lbm and slug. Students are often confused by these. A lbm represents the mass that weighs one pound-force (lbf) on earth. It is not proper to say that a lbm is equal to a lbf since the former is a unit of mass and the latter is a unit of force. However, it is proper to say that a lbm weighs one lbf (on earth). A slug is much bigger than a lbm. In fact, a slug is lbm. A slug, then, weighs lbf (on earth). o Metric - The standard unit for mass is the kilogram (kg), and the standard unit for force is the newton (N). Unfortunately, most people use kg as a measure of weight, which is technically incorrect. Note that one kg weighs N (on earth). When you buy a box of cereal, the printing may say net weight 1 pound (454 grams). Technically, this means that the cereal inside the box weighs 1 lbf, and has a mass of 454 gm (0.454 kg). The actual weight of the cereal in the metric system is W = mg = (0.454 kg)(9.807 m/s )(Ns /kgm) = 4.45 N, but the manufacturer gives the weight in kg a quirk of the metric system. Unit system conversion is a common source of error, and has even led to catastrophic failures. Shown here is a newspaper article from 1999 showing how unit conversion errors led to the destruction of a NASA space probe:

3 Comment about the Gravitational Conversion Constant g c Some authors define the gravitational conversion constant g c, which is inserted into Newton s second law of motion. Instead of F = ma, they write F = ma/g c, where g c is defined in the English Engineering System of lbm ft kg m Units as g c and in SI units as g 1 lbf s c. N s I strongly discourage use of the gravitational conversion constant g c, since it leads to much confusion. Instead, Newton s law should remain in the fundamental form in which it was created, without an artificial constant thrown into the equation simply for unit s sake. There has been much confusion (and error!) because of the differences between lbf, lbm, and slug. The use of g c has complicated and further confused the issue, in my opinion, and should never have been invented. Relationship between Force and Mass units The relationship between force, mass, and acceleration can be clearly understood by applying Newton s second law. The following table is provided to avoid confusion, especially with English units. SI units: Relationship Newton s second law, F = ma. [Note: Bold notation indicates a vector.] By definition of the fundamental units, this yields 1 N = 1 kgm/s. Conversion Ns This is a unity conversion factor [equal to 1 and dimensionless]. kg m Discussion Terminology English units: Relationship Conversion Discussion Terminology This unity conversion factor simplifies the units and avoids confusion. How much force (in Newtons) is required to accelerate a mass of 13.3 kg at a constant acceleration of 1.0 m/s to F the right? mass, m m Ns Solution: F x=ma x = kg1. 0 = N s kg m to the right, since F x is the x-component of vector F, and a x is the x-component of acceleration vector a. It is not proper to say that 1.00 kg equals 9.81 N, but it is proper to say that 1.00 kg weighs 9.81 N (on earth). This is obtained by utilizing Newton s second law with gravitational acceleration: W=mg= m N s kg N s kg m =. Newton s second law, F = ma. [Note: Bold notation indicates a vector.] By definition of the fundamental units, this yields 1 lbf = 1 slugft/s or 1 lbf = lbmft/s. lbf s lbf s or slug ft slug or All are unity conversion factors lbm ft lbm This unity conversion factor simplifies the units and avoids confusion. How much force (in pounds-force) is required to accelerate a mass of 13.3 lbm at a constant acceleration of 1.0 ft/s to F the right? a mass, m Solution: ft lbf s F x=ma x = lbm1. 0 = lbf to the right, since F x is the s lbm ft x-component of vector F, and a x is the x-component of acceleration vector a. It is not proper to say that 1.00 lbm equals 1.00 lbf, but it is proper to say that 1.00 lbm weighs 1.00 lbf (on earth). This is obtained by utilizing Newton s second law with ft lbf s gravitational acceleration: W=mg= lbm lbf s lbm ft =. a

### A physical quantity is any quantity that can be measured with a certain mathematical precision. Example: Force

1 Unit Systems Conversions Powers of Physical Quantities Dimensions Dimensional Analysis Scientific Notation Computer Notation Calculator Notation Significant Figures Math Using Significant Figures Order

### US, Burma, Liberia are three countries that have not adopted the SI as the sole system of units (from Wikipedia)

1.2 System of Units A single system is efficient, convenient, economical, and makes sense. The US system units is difficult for the United States to give up because a lot of expert technical knowledge

### APPENDIX I SI AND ENGLISH UNITS AND CONVERSION FACTORS

APPENDIX I SI AND ENGLISH UNITS AND CONVERSION FACTORS The International System of Units (Systéme International d Unités, or SI) recognizes seven basic units from which all others are derived. They are:

### = 800 kg/m 3 (note that old units cancel out) 4.184 J 1000 g = 4184 J/kg o C

Units and Dimensions Basic properties such as length, mass, time and temperature that can be measured are called dimensions. Any quantity that can be measured has a value and a unit associated with it.

### Introduction to Engineering Calculations

Introduction to Engineering Calculations We usually deal with chemical manufacturing processes, genetic engineering, Semicondcutor manufacturing, pollution control, etc. We will see the basic princiles

### Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS

1 P a g e Physics Notes Class 11 CHAPTER 2 UNITS AND MEASUREMENTS The comparison of any physical quantity with its standard unit is called measurement. Physical Quantities All the quantities in terms of

### WEEK 1. Engineering Calculations Processes Process Variables

WEEK 1 Engineering Calculations Processes Process Variables 2.1 Units and Dimensions Units and dimensions are important in science and engineering A measured quantity has a numerical value and a unit (ex:

### 1. Dimensions and Units

1. Dimensions and Units 1-1. Dimensions 1-2. Dimensional Systems 1-3. Units 1-4. Scales 1-5. Mass Confusion and the Use of gc 1-6. Weight 1-7. Significant Figures This presentation surveys the dimensions

### Scientific Notation. Measurement Systems. How to Write a Number in Scientific Notation

Scientific Notation The star Proxima Centauri is 23,400,000,000,000 miles away from Earth. If we could travel in a spaceship at 5,000 miles/hour, it would take over 534,000 years to get there. Scientific

### Units represent agreed upon standards for the measured quantities.

Name Pd Date Chemistry Scientific Measurement Guided Inquiry Teacher s Notes Work with your group using your prior knowledge, the textbook (2.1 2.7), internet research, and class discussion to complete

### FE simulation: Consistent Units

March 3, 2010 Consistent System of Units Consistent System of Units 1 ABAQUS and most other simulation codes do not have a built-in unit system (except for rotation DOF & angles) Consistent System of Units

### Chapter 1 Lecture Notes: Science and Measurements

Educational Goals Chapter 1 Lecture Notes: Science and Measurements 1. Explain, compare, and contrast the terms scientific method, hypothesis, and experiment. 2. Compare and contrast scientific theory

### Ch.4 Forces. Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66

Ch.4 Forces Conceptual questions #1, 2, 12 Problem 1, 2, 5, 6, 7, 10, 12, 15, 16, 19, 20, 21, 23, 24, 26, 27, 30, 38, 39, 41, 42, 47, 50, 56, 66 Forces Forces - vector quantity that changes the velocity

### Pump Formulas Imperial and SI Units

Pump Formulas Imperial and Pressure to Head H = head, ft P = pressure, psi H = head, m P = pressure, bar Mass Flow to Volumetric Flow ṁ = mass flow, lbm/h ρ = fluid density, lbm/ft 3 ṁ = mass flow, kg/h

### Note that the terms scientific notation, exponential notation, powers, exponents all mean the same thing.

...1 1.1 Rationale: why use scientific notation or powers?...1 1.2 Writing very large numbers in scientific notation...1 1.3 Writing very small numbers in scientific notation...3 1.4 Practice converting

### Metric Conversion Factors

332 Metric Conversion Factors The following list provides the conversion relationship between U.S. customary units and SI (International System) units. The proper conversion procedure is to multiply the

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Numbers and Calculations

Numbers and Calculations Topics include: Metric System, Exponential Notation, Significant Figures, and Factor-Unit Calculations Refer to Chemistry 123 Lab Manual for more information and practice. Learn

### Chapter 1 Introduction to Physics. Copyright 2010 Pearson Education, Inc.

Chapter 1 Introduction to Physics Physics and the Laws of Nature Units of Length, Mass, and Time Dimensional Analysis Significant Figures Converting Units Order-of-Magnitude Calculations Scalars and Vectors

### TIME ESTIMATE FOR THIS LESSON One class period

TITLE OF LESSON Physical Science Unit 1 Lesson 2 Systéme Internationale aka the Metric System Nature of Matter: How do tribes standardize their lives? TIME ESTIMATE FOR THIS LESSON One class period ALIGNMENT

### Measurements. SI Units

Measurements When you measure something, you must write the number with appropriate unit. Unit is a standard quantity used to specify the measurement. Without the proper unit, the number you write is meaningless.

### Module 2.1. Introduction to S.I units

Module 2.1 Introduction to S.I units Learning Outcomes On successful completion of this module learners will be able to - Describe some of the S.I units relevant to energy use in buildings. S.I = The International

### Chem 115 POGIL Worksheet - Week 1 Units, Measurement Uncertainty, and Significant Figures

Chem 115 POGIL Worksheet - Week 1 Units, Measurement Uncertainty, and Significant Figures Why? All scientists the world over use metric units. Since 1960, the metric system in use has been the Système

### Chapter 1. Matter, Measurement and Problem Solving. Chapter 1. Helleur. Principles of Chemistry: A Molecular Approach 1 st Ed.

Why Clickers? to refresh the students during the lecture to assess student understanding of a topic to increase student participation in class to encourage student interaction in large lectures peer teaching

### Consistency of units. Units of Common Physical Properties

Introduction to Chemical Engineering Processes/Units Sept. 5 th, 2012 Consistency of units Most values that you'll run across as an engineer will consist of a number and a unit. Some do not have a unit

### The Importance of MEASUREMENT

Scientists use many skills as they investigate the world around them. They make observations by gathering information with their senses. Some observations are simple. For example, a simple observation

### Chapter 1 Chemical Foundations 1.3 Units of Measurement

Chapter 1 Chemical Foundations 1.3 Units of Measurement Copyright 2005 by Pearson Education, Inc. Publishing as Benjamin Cummings 1 Measurement You make a measurement every time you measure your height.

### 1.1 Thermodynamics and Energy

1.1 Thermodynamics and Energy What is Thermodynamics? Essentially, thermodynamics can be defined as the study of energy. Granted, this is a pretty broad definition, which suits it well, because thermodynamics

### Lecture Outline Chapter 1. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 1 Physics, 4 th Edition James S. Walker Chapter 1 Introduction to Physics Units of Chapter 1 Physics and the Laws of Nature Units of Length, Mass, and Time Dimensional Analysis

### APPENDIX H CONVERSION FACTORS

APPENDIX H CONVERSION FACTORS A ampere American Association of State AASHTO Highway & Transportation Officials ABS (%) Percent of Absorbed Moisture Abs. Vol. Absolute Volume ACI American Concrete Institute

### CHAPTER 8 UNITS, PREFIXES AND ENGINEERING NOTATION

CHAPTER 8 UNITS, PREFIXES AND ENGINEERING NOTATION EXERCISE 34 Page 62 1. State the SI unit of volume. The SI unit of volume is cubic metres, m 3 2. State the SI unit of capacitance. The SI unit of capacitance

### 2.2 Scientific Notation: Writing Large and Small Numbers

2.2 Scientific Notation: Writing Large and Small Numbers A number written in scientific notation has two parts. A decimal part: a number that is between 1 and 10. An exponential part: 10 raised to an exponent,

### Unified Lecture # 3 Measurement of physical quantities, Units and Systems of Units

Unified Lecture # 3 Measurement of physical quantities, Units and Systems of Units References [1] Editor: Barry N. Taylor. NIST Special Publication 330, 2001 Edition: The International System of Units

### Units of Measurement and Dimensional Analysis

POGIL ACTIVITY.2 POGIL ACTIVITY 2 Units of Measurement and Dimensional Analysis A. Units of Measurement- The SI System and Metric System T here are myriad units for measurement. For example, length is

### Unit Conversion and SI Units

Trigonometry Unit Conversion and SI Units Copyright This publication The Northern Alberta Institute of Technology 2002. All Rights Reserved. LAST REVISED June, 2007 Statement of Prerequisite Skills Complete

### PHYSICS 151 Notes for Online Lecture #1

PHYSICS 151 Notes for Online Lecture #1 Whenever we measure a quantity, that measurement is reported as a number and a unit of measurement. We say such a quantity has dimensions. Units are a necessity

### Chapter 2 Measurement and Problem Solving

Introductory Chemistry, 3 rd Edition Nivaldo Tro Measurement and Problem Solving Graph of global Temperature rise in 20 th Century. Cover page Opposite page 11. Roy Kennedy Massachusetts Bay Community

### MEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:

MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding

### Units and Dimensions in Physical Chemistry

Units and Dimensions in Physical Chemistry Units and dimensions tend to cause untold amounts of grief to many chemists throughout the course of their degree. My hope is that by having a dedicated tutorial

### Sample Exercise 1.1 Distinguishing Among Elements, Compounds, and Mixtures

Sample Exercise 1.1 Distinguishing Among Elements, Compounds, and Mixtures White gold, used in jewelry, contains gold and another white metal such as palladium. Two different samples of white gold differ

### JAMNABAI NARSEE SCHOOL ESTIMATION AND UNITS. Std 8

JAMNABAI NARSEE SCHOOL ESTIMATION AND UNITS Std 8 Order of magnitude Definition: The order of magnitude of a physical quantity is its magnitude in powers of ten when that physical quantity is expressed

### Metric System Math Review -Dimensional Analysis

Metric System Math Review -Dimensional Analysis In 1960 the International Bureau of Weights and Measures (Sevres, France) adopted the "International System of Units", also known as "SI" units. 7 base units

### MATH Fundamental Mathematics II.

MATH 10032 Fundamental Mathematics II http://www.math.kent.edu/ebooks/10032/fun-math-2.pdf Department of Mathematical Sciences Kent State University December 29, 2008 2 Contents 1 Fundamental Mathematics

### 5. Suppose you had to test how well two types of soap work. Describe your experiment using the terms control and variable.

Page # 31: 1. What is the scientific method? A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories supported by data.

### Lecture L1 - Introduction

S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L1 - Introduction Introduction In this course we will study Classical Mechanics and its application to aerospace systems. Particle motion in Classical

### Figure 1. A typical Laboratory Thermometer graduated in C.

SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES

### Abbreviations and Metric Conversion Factors

B Symbols, Abbreviations and Metric Conversion Factors Signs and Symbols + plus, or more than minus, or less than ± plus or minus Feet " nches > is greater than is greater than or equal to < is less than

### PHYSICS 1.2. BLACKBOARD COURSE (Developed by Dr. V.S. Boyko) PHYS SCI Core. 4 cl hrs, 2 lab hrs, 4 cr

BLACKBOARD COURSE (Developed by Dr. V.S. Boyko) PHYS 1433 PHYSICS 1.2 SCI Core 4 cl hrs, 2 lab hrs, 4 cr Basic concepts and principles of mechanics, heat and sound for liberal arts students and technology

### INTERIM UNITS OF MEASURE As suggested by Federal Standard 376B January 27, 1993. hectare (ha) Hundred for traffic buttons.

SI - The Metrics International System of Units The International System of Units (SI) is a modernized version of the metric system established by international agreement. The metric system of measurement

### Welcome to Physics 40!

Welcome to Physics 40! Physics for Scientists and Engineers Lab 1: Introduction to Measurement SI Quantities & Units In mechanics, three basic quantities are used Length, Mass, Time Will also use derived

### Work, Power & Conversions

Purpose Work, Power & Conversions To introduce the metric system of measurement and review related terminology commonly encountered in exercise physiology Student Learning Objectives After completing this

### General Physics 1. Class Goals

General Physics 1 Class Goals Develop problem solving skills Learn the basic concepts of mechanics and learn how to apply these concepts to solve problems Build on your understanding of how the world works

### Chapter 1 (Part 2) Measurements in Chemistry

Chapter 1 (Part 2) Measurements in Chemistry 1.7 Physical Quantities English Units Those of us who were raised in the US are very accustomed to these. Elsewhere in the world, these are very confusing.

### SCIENTIFIC MEASUREMENT

3 SCIENTIFIC MEASUREMENT Conceptual Curriculum Concrete concepts More abstract concepts or math/problem-solving Standard Curriculum Core content Extension topics Honors Curriculum Core honors content Options

### Mass. ) or the slug (lb f s²/ft)

MASS VS. FORCE Mass As stated elsewhere, statics is the study of forces on a stationary body. To this end, we must understand the difference between mass and force and how to calculate force if given the

### Accuracy, Precision and Uncertainty

Accuracy, Precision and Uncertainty How tall are you? How old are you? When you answered these everyday questions, you probably did it in round numbers such as "five foot, six inches" or "nineteen years,

### Why Chemistry? Why Chemistry?

Why Chemistry? Engineering Plastics - How does structure affect: Elasticity, Processability Composite Materials What additives make a material stronger, lighter, faster? Pulp and Paper What innovations

### SOLUTION MANUAL ENGLISH UNIT PROBLEMS CHAPTER 2 SONNTAG BORGNAKKE VAN WYLEN. FUNDAMENTALS of. Thermodynamics. Sixth Edition

SOLUTION MANUAL ENGLISH UNIT PROBLEMS CHAPTER 2 SONNTAG BORGNAKKE VAN WYLEN FUNDAMENTALS of Thermodynamics Sixth Edition CHAPTER 2 SUBSECTION PROB NO. Concept-Study Guide Problems 87-91 Properties and

### Preferred SI (Metric) Units

Quantity Unit Symbol LENGTH meter m Preferred SI (Metric) Units Metric-U.S. Customary Unit Equivalents 1 m = 1000 mm = 39.37 in. = millimeter mm 25.4 mm = 1 inch micrometer μm 1 μm = 10-6 m Remarks 3.281

### 2. List the fundamental measures and the units of measurement for each. 3. Given the appropriate information, calculate force, work and power.

Lab Activity 1 The Warm-Up Interpretations Student Learning Objectives After Completing this lab, you should be able to: 1. Define, explain and correctly use the key terms. 2. List the fundamental measures

### Emily is taking an astronomy course and read the following in her textbook:

6. EXPONENTS Emily is taking an astronomy course and read the following in her textbook: The circumference of the Earth (the distance around the equator) is approximately.49 0 4 miles. Emily has seen scientific

### AS Physics INDUCTION WORK XKCD. Student. Class 12 A / B / C / D Form

AS Physics 2014-15 INDUCTION WORK XKCD Student Class 12 A / B / C / D Form MCC 2014 1. Physical Quantities Maths and Physics have an important but overlooked distinction by students. Numbers in Physics

### Math 016. Materials With Exercises

Math 06 Materials With Exercises June 00, nd version TABLE OF CONTENTS Lesson Natural numbers; Operations on natural numbers: Multiplication by powers of 0; Opposite operations; Commutative Property of

### Lab 1: Units and Conversions

Lab 1: Units and Conversions The Metric System In order to measure the properties of matter, it is necessary to have a measuring system and within that system, it is necessary to define some standard dimensions,

### Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis

Numbers in Science Exploring Measurements, Significant Digits, and Dimensional Analysis OBJECTIVE Students will be introduced to correct measurement techniques, correct use of significant digits, and dimensional

### All the examples in this worksheet and all the answers to questions are available as answer sheets or videos.

BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Calculations 2 In this section we will look at - rounding numbers up or down - decimal places and significant figures - scientific notation - using

### Measurement. Chapter 1

Chapter 1 Measurement Figure 1.1 What s the difference between mass and weight? Figure 1.2 How did early clocks measure time? Figure 1.3 Why does a block of iron sink but an iron ship floats? Physics is

### Chapter 3 How Do We Make Measurements?

Chapter 3 How Do We Make Measurements? Chemistry, like all sciences, has its quantitative side. In this chapter, you will be introduced to the units and types of measurement in chemistry. 3.1 Background

### Newton s Laws of Motion

Chapter 4 Newton s Laws of Motion PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 4 To understand the meaning

### STATICS. Introduction VECTOR MECHANICS FOR ENGINEERS: Eighth Edition CHAPTER. Ferdinand P. Beer E. Russell Johnston, Jr.

Eighth E CHAPTER VECTOR MECHANICS FOR ENGINEERS: STATICS Ferdinand P. Beer E. Russell Johnston, Jr. Introduction Lecture Notes: J. Walt Oler Texas Tech University Contents What is Mechanics? Fundamental

### 2.6 Exponents and Order of Operations

2.6 Exponents and Order of Operations We begin this section with exponents applied to negative numbers. The idea of applying an exponent to a negative number is identical to that of a positive number (repeated

### CHEM 101 / 105 LECT 1

CHEM 101 / 105 LECT 1 Rules of the road: Your Loyola computer account (activate it). Class Web site (visit and send me an e-mail B4 Tues.) spavko1@luc.edu Chapter 1. Chemistry is... Matter is... Classifications

### What is the SI system of measurement?

ALE 3. SI Units of Measure & Unit Conversions Name CHEM 161 K. Marr Team No. Section What is the SI system of measurement? The Model the International System of Units (Reference: Section 1.5 in Silberberg

### A.P. Physics/Physics Notes Chapter 1 Physics is the study of the nature of matter and energy and its interactions in the

A.P. Physics/Physics Notes Chapter 1 Physics is the study of the nature of matter and energy and its interactions in the fields of mechanics (kinematics and dynamics), electricity and magnetism, waves

### General Physics (PHY 2130)

General Physics (PHY 2130) Lecture 8 Forces Newton s Laws of Motion http://www.physics.wayne.edu/~apetrov/phy2130/ Classical Mechanics Describes the relationship between the motion of objects in our everyday

### Introduction and Basic Concepts

Objectives MAE 320- Chapter 1 Identify the unique vocabulary associated with thermodynamics through the precise definition of basic concepts. Review the metric SI and the English unit systems. Introduction

### Dimensional Analysis #3

Dimensional Analysis #3 Many units of measure consist of not just one unit but are actually mixed units. The most common examples of mixed units are ratios of two different units. Many are probably familiar

### Chapter 4 Newton s Laws: Explaining Motion

Chapter 4 Newton s s Laws: Explaining Motion Newton s Laws of Motion The concepts of force, mass, and weight play critical roles. A Brief History! Where do our ideas and theories about motion come from?!

### Chapter 3: The Metric System. Metric System Basic Units

: The Metric System The English system was used primarily in the British Empire and wasn t very standardized. The French organized a committee to devise a universal measuring system. After about 10 years,

### Learning Centre CONVERTING UNITS

Learning Centre CONVERTING UNITS To use this worksheet you should be comfortable with scientific notation, basic multiplication and division, moving decimal places and basic fractions. If you aren t, you

### 3.2 Units of Measurement > Chapter 3 Scientific Measurement. 3.2 Units of Measurement. 3.1 Using and Expressing Measurements

Chapter 3 Scientific Measurement 3.1 Using and Expressing Measurements 3.2 Units of Measurement 3.3 Solving Conversion Problems 1 Copyright Pearson Education, Inc., or its affiliates. All Rights Reserved.

### Ch 7 Kinetic Energy and Work. Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43

Ch 7 Kinetic Energy and Work Question: 7 Problems: 3, 7, 11, 17, 23, 27, 35, 37, 41, 43 Technical definition of energy a scalar quantity that is associated with that state of one or more objects The state

### Reporting with Precision and Accuracy

COMMON CORE Locker LESSON Reporting with Precision and Accuracy Common Core Standards The student is expected to: COMMON CORE N-QA3 Choose a level of accuracy appropriate to limitations on measurement

### Review of Scientific Notation and Significant Figures

II-1 Scientific Notation Review of Scientific Notation and Significant Figures Frequently numbers that occur in physics and other sciences are either very large or very small. For example, the speed of

### Fractions and the Real Numbers

Fractions and the Real Numbers Many interesting quantities are not normally integer-valued: - the mass of a rocket payload - the batting average of a baseball player - the average score on an assignment

### 3.1.1 Decimals and Fractions

3.. Decimals and Fractions Learning Objective(s) Read and write numbers in decimal notation. 2 Write decimals as fractions. 3 Write fractions as decimals. Introduction In addition to fraction notation,

### 1. Introduction to Measurement Practice

1. Introduction to Measurement Practice Objectives Liquid-in-glass thermometer The objective of this experiment is to introduce some basic concepts in measurement, and to develop good measurement habits.

### Kosky, Wise, Balmer, Keat: Exploring Engineering, Second Edition

Chapter 2: Key Elements of Engineering Analysis To help get you in the habit of ing these elements, in the following exercises the students should be graded on use of all of the elements we have discussed

### Revision Notes Adult Numeracy Level 2

Revision Notes Adult Numeracy Level 2 Place Value The use of place value from earlier levels applies but is extended to all sizes of numbers. The values of columns are: Millions Hundred thousands Ten thousands

### Chapter 1 Chemistry: The Study of Change

Chapter 1 Chemistry: The Study of Change This introductory chapter tells the student why he/she should have interest in studying chemistry. Upon completion of this chapter, the student should be able to:

### Chapter 17. Quantity of Heat. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 17. Quantity of Heat A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Photo Vol. 05 Photodisk/Getty FOUNDRY: It requires about 289 Joules

### Changkat Changi Secondary School

Changkat Changi Secondary School UNIT 1 Measurement Name: Class: Date: 1 CONTENT PAGE Date Notes/Worksheets Marks Remarks Notes 1.1 Notes 1.2 Notes 1.3 Worksheet 1.1 Worksheet 1.2 Worksheet 1.3 "The whole

### Significant figures. Significant figures. Rounding off numbers. How many significant figures in these measurements? inches. 4.

Significant figures All non-zero numbers are always significant 2.38 has three significant figures 25 has two significant figures Are zeros significant? It depends on their position in the number. A zero

### CHAPTER 4 DIMENSIONAL ANALYSIS

CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.

### CH 2: SCIENTIFIC MEASUREMENT. Chemistry is a lot of math!

CH 2: SCIENTIFIC MEASUREMENT Chemistry is a lot of math! WARM UP 1.Name 3 tools used for measurement. 2.What is a unit? 3.Give an example of a unit. 4.Why are units important. CH 2 SCIENTIFIC MEASUREMENT

### 3.1 Force, Mass, and Acceleration

Sir Isaac Newton discovered one of the most important relationships in physics: the link between the force on an object, its mass, and its acceleration. In this section, you will learn about force and

### UNIT II: MATHEMATICS in CHEMISTRY Earland

Quantitative analysis used in Chemistry is not difficult, but it requires you to be able to toggle between different units and be accurate in your calculation. In other words, you must become extremely