Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section C

Size: px
Start display at page:

Download "Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section C"

Transcription

1 Section C.1: Significant Digits Significant digits The digits in a number that represents actual measurements and therefore have meaning are called significant digits. Significant digits: Nonzero digits. Zeros that follow a nonzero digit and lie to the right of the decimal point: Zeros between nonzero digits or other significant zeros: Not significant digits: Zeros to the left of the first nonzero digit: Zeros to the right of the last nonzero digit but before the decimal point: Ex pounds has 3 significant digits and implies a measurement to the nearest pound pounds has 5 significant digits and implies a measurement to the nearest hundredth of a pound students has 1 significant digit and implies a measurement to the nearest hundred students students has 3 significant digits and implies exactly 200 students. 1

2 Ex.2 Counting significant digits. State the number of significant digits and the implied meaning of the following numbers: (1) a time of seconds; (2) a length of meter; (3) a population reported as 240, 000; (4) a population reported as Section C.2: Rounding Significant digits The basic process of rounding numbers takes two steps: Step 1: Decide which decimal place (for example, tens, ones, tenths or hundredths) is the smallest that should be kept. Step 2: Look at the number in the nearest place to the right (for example, if rounding the tenths, look at hundredths). If the value in the next place is less than 5 round down, if it is 5 or greater than 5, round up. Ex rounded to the nearest thousandth is rounded to the nearest hundredth is rounded to the nearest tenth is rounded to the nearest one is rounded to the nearest ten is rounded to the nearest hundred is

3 Ex.4 Rounding with significant digits. For each of the following operations, give your answer with the specified number of significant digits: (1) 7.7 mm 9.92 mm; give your answer with 2 significant digits; (2) 240, , 106; give your answer with 4 significant digits. Section C.3: Understanding Errors Types of Error: Random and Systematic Types of error: random error and systematic error There are two types of error: Significant digits: Random errors occur because of random and inherently unpredictable events in the measurement process. We can minimize the effect of random errors by making many measurements and averaging them. Systematic errors occur when there is a problem in the measurement system that affect all measurements in the same way, such as making them all too low or too high by the same amount. If we discover a systematic error, we can go back and adjust the affected measurements. 3

4 Ex.5 Suppose you work in a pediatric office and use a digital scale to weigh babies. If you have ever worked with babies, you know that they usually aren t very happy about being put on a scale. Their thrashing and crying tends to shake the scale making the readout jump around. You could equally well record the baby s weight as anything between 14.5 and 15.0 pounds. The shaking of the scale introduces a random error. If you measure the baby s weight ten times, your measurements will probably be too high in some case and to low in other cases. When you average the measurements you are likely to get a value that better represents the true weight. Now, suppose you have weighed babies all day. At the end of the day, you notice that the scale reads 1.2 pounds when there is nothing on it. In that case, every measurement you made was too high by 1.2 pounds. Therefore, we have a systematic error. Now that you know about this systematic error, you can go back and adjust the affected measurements. Ex.6 Errors in global warming data. Scientists studying global warming need to know how the average temperature of the entire Earth, or the global average temperature, has changed with time. Consider two difficulties (among many others) in trying to interpret historical temperature data from the early 20th century: (1) temperatures were measured with simple thermometers and the data were recorded by hand; (2) most temperature measurements were recorded in or near urban areas, which tend to be warmer than surrounding rural areas because heat released by human activity. Discuss whether each of these two difficulties produces random or systematic errors, and consider the implications of these errors. 4

5 Ex.7 The Census. The constitution of the United States mandates a Census of the population every 10 years. The United State Census Bureau conducts the census by distributing house hold surveys through the mail and through personal visits. Suggest several sources of both random and systematic error in the census. 5

6 Size of Errors: Absolute versus Relative Sizes of error: absolute error and relative error There are two types of error: The absolute error describes how far a measured value lies from the true value: absolute error = measured value true value. The relative error compares the size of the error to the true value: absolute error measured value true value relative error = =. true value true value The absolute and the relative error are positive when the measured value is greater than the true value and negative when the measured value is less than the true value. Note that the above formula gives the relative error as a fraction which can be converted to a percentage. Ex.8 Suppose you go to a store and ask 6 pounds of hamburger. However, because the store s scale is poorly calibrated, you actually get 4 pounds. Suppose you buy a car which the owner s manual says weighs 3132 pounds, but you find that it really weighs 3130 pounds. Compute the absolute and relative error and discuss why you are disappointed in the first case but you don y care too much in the second case. 6

7 Ex.9 Find the absolute and relative error in each case. (1) Your true weight is 125 pounds, but a scale says you weigh 130 pounds. (2) The government claims that a program costs $49.0 billion, but an audit shows that the true cost is $50.0 billion. Describing Results: Accuracy and Precision Accuracy and precision Once a measurement is reported, we should evaluate it to see whether it is believable in light of any potential errors. In particular, we should consider two key ideas about any reported value: its accuracy and its precision. The term are often use interchangeably in English, but mathematically they are different. Accuracy describes how closely a measurement approximates a true value. An accurate measurement is very close to the true value. Precision describes the amount of detail in a measurement. Ex.10 Accuracy. If a census says that the population of your home town is 72, 453, but the true population is 96, 000, then the census report is not very accurate. In contrast, if a company projects sales of $7.30 billion and true sales turn out to be $7.32 billion, we would say that the projection is quite accurate. Ex.11 Precision. A distance given as kilometers is more precise than a distance given as 2.3 kilometers because the first number gives detail to the nearest kilometer and the second number gives detail only to the nearest 0.1 kilometer. Similarly, an income of $45, has greater precision than an income of $46, 000 because the first income is precise to the nearest penny and the second income is precise only to the nearest thousand dollars. 7

8 Ex.12 Accuracy and Precision in your Weight. Suppose your true weight is pounds. The scale at the doctor s office, which can be read only to the nearest quarter pound, says that you weigh puonds. The scale at the gym, which gives a digital readout to the nearest 0.1 pound says that you weigh Which scale is more precise? Which scale is more accurate? Summary: Dealing with Errors Summary Errors can occur in many ways, but generally can be classified as one of two basic types: random errors and systematic errors. Whatever the source of an error, its size can be described in two different ways: as an absolute error or as a relative error. Once a measurement is reported, we can evaluate it in terms of its accuracy and its precision. 8

9 Section C.3: Combining Measured Numbers Combining measured numbers In scientific or statistical work, researchers conduct careful analyses to determine how to combine numbers properly. We can use two simple rounding rules: Rounding rule for addition and subtraction: Rounding your answer to the same precision as the least precise number in the problem. Rounding rule for multiplication or division: Rounding your answer to the same number of significant digits as the measurement with the fewest significant digits. Note: to avoid errors, you should do the rounding only after completing all the operations, not during intermediate steps. Ex.13 Suppose that you live in a city with a population of 300, 000. One day, your best friend move to your city to share an apartment with you. What is the population of your city now? Ex.14 (1) A book written in 1962 states that the oldest Mayan ruins are 2000 years old. How old are they now? (2) The government in a town of 82, 000 people plans to spend $41.5 million this year. Assuming all this money must come from taxes, what average amount must the city collect from each resident? 9

Dealing with Uncertainty

Dealing with Uncertainty 3 C Page 1 Unit 3C Dealing with Uncertainty Significant Digits Understanding Error Type Random and Systematic Size Absolute and Relative Accuracy and Precision Combining Measured Numbers Significant Digits

More information

Section 2.2 ~ Dealing With Errors. Introduction to Probability and Statistics Fall 2015

Section 2.2 ~ Dealing With Errors. Introduction to Probability and Statistics Fall 2015 Section 2.2 ~ Dealing With Errors Introduction to Probability and Statistics Fall 2015 Objective To understand the difference between random and systematic errors, be able to describe errors by their absolute

More information

13. [Place Value] units. The digit three places to the left of the decimal point is in the hundreds place. So 8 is in the hundreds column.

13. [Place Value] units. The digit three places to the left of the decimal point is in the hundreds place. So 8 is in the hundreds column. 13 [Place Value] Skill 131 Understanding and finding the place value of a digit in a number (1) Compare the position of the digit to the position of the decimal point Hint: There is a decimal point which

More information

(Significant Digits are in BOLD type and the non-significant digits are underlined)

(Significant Digits are in BOLD type and the non-significant digits are underlined) Name Per. Date Significant Digits Worksheet Significant digits (or significant figures) are used to represent the accuracy of a measurement. In a measurement the significant digits represent all the reliable

More information

Section 4.7 Scientific Notation

Section 4.7 Scientific Notation Section 4.7 Scientific Notation INTRODUCTION Scientific notation means what it says: it is the notation used in many areas of science. It is used so that scientist and mathematicians can work relatively

More information

CHM101 Lab Math Review and Significant Figures Grading Rubric

CHM101 Lab Math Review and Significant Figures Grading Rubric Name CHM101 Lab Math Review and Significant Figures Grading Rubric Criteria Points possible Points earned Part A (0.25 each) 3.5 Part B (0.25 each) 2.5 Part C (0.25 each) 1.5 Part D (Q5 0.25 each, Q6 &

More information

Physics 12 Rules for Significant Digits and Rounding

Physics 12 Rules for Significant Digits and Rounding 1 Physics 12 Rules for Significant Digits and Rounding One mathematical aspect of problem-solving in the physical sciences that gives some students difficulty deals with the rounding of computed numerical

More information

CHAPTER TWO: MEASUREMENTS AND PROBLEM SOLVING

CHAPTER TWO: MEASUREMENTS AND PROBLEM SOLVING CHAPTER TWO: MEASUREMENTS AND PROBLEM SOLVING Measurements: Our Starting Point! Why should we begin our study of chemistry with the topic of measurement?! Much of the laboratory work in this course is

More information

A.0 SF s-uncertainty-accuracy-precision

A.0 SF s-uncertainty-accuracy-precision A.0 SF s-uncertainty-accuracy-precision Objectives: Determine the #SF s in a measurement Round a calculated answer to the correct #SF s Round a calculated answer to the correct decimal place Calculate

More information

Measurement 4: Scientific Notation

Measurement 4: Scientific Notation Q Skills Review The Decimal System Measurement 4: Scientific Notation Dr. C. Stewart We are so very familiar with our decimal notation for writing numbers that we usually take it for granted and do not

More information

Chapter 2 Measurements & Calculations. Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s)

Chapter 2 Measurements & Calculations. Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s) Chapter 2 Measurements & Calculations Quantity: A thing that can be measured. ex. Length (6.3 ft), mass (35 kg), and time (7.2 s) Measurements can be expressed in a variety of units: Example: length(cm,

More information

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?)

Warm-up: Are accuracy and precision the same thing? (If so do you want to bet the house on it?) Obj: Students will: 1. Distinguish between accuracy and precision. 2. Examine various pieces of lab equipment for their accuracy. 3. Define and identify significant figures. Warm-up: Are accuracy and precision

More information

AP Environmental Science Math Prep

AP Environmental Science Math Prep AP Environmental Science Math Prep This year in APES you will hear the two words most dreaded by high school students NO CALCULATORS! That s right, you cannot use a calculator on the AP Environmental Science

More information

Correlation Coefficient: the quantity, measures the strength and direction of a linear relationship between 2 variables.

Correlation Coefficient: the quantity, measures the strength and direction of a linear relationship between 2 variables. AFM Unit 9 Regression Day 1 notes A mathematical model is an equation that best describes a particular set of paired data. These mathematical models are referred to as models and are used to one variable

More information

Grade 5 Decimal Numbers

Grade 5 Decimal Numbers ID : ae-5-decimal-numbers [1] Grade 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer the questions (1) Which number is 0.26 less than the largest 2-digit number? (2) What is the

More information

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010

Chapter 1: Fundamentals of Algebra Lecture notes Math 1010 Section 1.1: The Real Number System Definition of set and subset A set is a collection of objects and its objects are called members. If all the members of a set A are also members of a set B, then A is

More information

5. Arrange the following decimal numbers in order from least to greatest

5. Arrange the following decimal numbers in order from least to greatest ( No Calculator Allowed) New material covered: F2.3-F2.4, F3.-F3.2, F4.-F4.2, and handouts Exercise Sets F3.2 & F4.2. Represent the shaded part of the 00 square grid a. as a fraction of the whole grid.

More information

Pre-Lab 0.2 Reading: Measurement

Pre-Lab 0.2 Reading: Measurement Name Block Pre-Lab 0.2 Reading: Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You

More information

Exam: practice test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam: practice test 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Exam: practice test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. ) Using the information in the table on home sale prices in

More information

Unit 8 Practice Problems Lesson 1

Unit 8 Practice Problems Lesson 1 Unit 8 Practice Problems Lesson 1 Problem 1 Find the area of each square. Each grid square represents 1 square unit. 17 square units. 0 square units 3. 13 square units 4. 37 square units Problem Find the

More information

3 Organizing Data. What is scientific notation? How are precision and accuracy different? How do scientists use graphs to show data?

3 Organizing Data. What is scientific notation? How are precision and accuracy different? How do scientists use graphs to show data? CHAPTER 1 Introduction to Science 3 Organizing Data SECTION KEY IDEAS As you read this section, keep these questions in mind: What is scientific notation? How are precision and accuracy different? How

More information

Everyday Conversion: Money

Everyday Conversion: Money Everyday Conversion: Money Everyday Measurement: Water Everyday Measurement: Water Everyday Accuracy: Weighing Scales The need to measure correctly and convert! Some Interesting Quantities Length Volume

More information

Measurement. Weight, height, and length are common measurements. List at least five things you can measure.

Measurement. Weight, height, and length are common measurements. List at least five things you can measure. chapter 32 Measurement section 1 Description and Measurement Before You Read Weight, height, and length are common measurements. List at least five things you can measure. What You ll Learn how to estimate

More information

Chapter 3 Scientific Measurement

Chapter 3 Scientific Measurement 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.

More information

3.1 Using and Expressing Measurements > 3.1 Using and Expressing Measurements >

3.1 Using and Expressing Measurements > 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.

More information

Measurements and Data Analysis

Measurements and Data Analysis Measurements and Data Analysis 1 Introduction The central point in experimental physical science is the measurement of physical quantities. Experience has shown that all measurements, no matter how carefully

More information

Reference Guide. Science Reference 9/25/ Copyright 1996 Gary Lewis Revisions 2007 by John Pratte

Reference Guide. Science Reference 9/25/ Copyright 1996 Gary Lewis Revisions 2007 by John Pratte Reference Guide Contents...1 1. General Scientific Terminology...2 2. Types of Errors...3 3. Scientific Notation...4 4. Significant Figures...6 5. Graphs...7 6. Making Measurements...8 7. Units...9 8.

More information

Numbers and Data Analysis

Numbers and Data Analysis Numbers and Data Analysis With thanks to George Goth, Skyline College for portions of this material. Significant figures Significant figures (sig figs) are only the first approimation to uncertainty and

More information

Class 6 Second quarter at school

Class 6 Second quarter at school ID : in6secondquarteratschool [] Class 6 Second quarter at school For more such worksheets visit wwwedugaincom Answer the questions () Find the value of the following : 7 () If the following figure represents

More information

Scientific Measurement

Scientific Measurement Scientific Measurement Sprint times are often measured to the nearest hundredth of a second (0.01 s). Chemistry also requires making accurate and often very small measurements. CHEMISTRY & YOU How do you

More information

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer.

Decimal Addition: Remember to line up the decimals before adding. Bring the decimal straight down in your answer. Summer Packet th into 6 th grade Name Addition Find the sum of the two numbers in each problem. Show all work.. 62 2. 20. 726 + + 2 + 26 + 6 6 Decimal Addition: Remember to line up the decimals before

More information

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding)

Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding) Tutorial 2: Expressing Uncertainty (Sig Figs, Scientific Notation and Rounding) Goals: To be able to convert quantities from one unit to another. To be able to express measurements and answers to the correct

More information

Name. Benchmark Test 1 Topics 1 4. Mark the best answer.

Name. Benchmark Test 1 Topics 1 4. Mark the best answer. Mark the best answer. 1. What is fifty-two billion in expanded form? A 50,000,000 2,000,000 B 5,000,000,000 2,000,000,000 C 50,000,000,000 200,000,000 D 50,000,000,000 2,000,000,000 2. Find 805.03 1,000.

More information

Physics 2020 Laboratory Manual

Physics 2020 Laboratory Manual Physics 00 Laboratory Manual Department of Physics University of Colorado at Boulder Spring, 000 This manual is available for FREE online at: http://www.colorado.edu/physics/phys00/ This manual supercedes

More information

1.5 Reporting Values from Measurements. Accuracy and Precision. 20 Chapter 1 An Introduction to Chemistry

1.5 Reporting Values from Measurements. Accuracy and Precision. 20 Chapter 1 An Introduction to Chemistry 20 Chapter 1 An Introduction to Chemistry 1.5 Reporting Values from Measurements All measurements are uncertain to some degree. Scientists are very careful to report the values of measurements in a way

More information

2 The Way Science Works

2 The Way Science Works CHAPTER 1 Introduction to Science 2 The Way Science Works SECTION KEY IDEAS As you read this section, keep these questions in mind: How can you use critical thinking to solve problems? What are scientific

More information

AP Environmental Science Math Prep

AP Environmental Science Math Prep AP Environmental Science Math Prep Courtesy of Kara House, Franklin Central High School, Indiana This year in APES you will hear the two words most dreaded by high school students NO CALCULATORS! That

More information

Work Session 2: Introduction to Measurements, Conversions, and Significant Figures

Work Session 2: Introduction to Measurements, Conversions, and Significant Figures Work Session 2: Introduction to Measurements, Conversions, and Significant Figures Measurements are made using tools. The tool can be as simple as a ruler or as complex as the Hubble Space Telescope. It

More information

Uncertainty in numbers

Uncertainty in numbers 1.03 Accuracy, Precision and Significant Figures Uncertainty in numbers Story: Taxi driver (13 years experience) points to a pyramid "...this here pyramid is exactly 4511 years old". After a quick calculation,

More information

EXPERIMENTAL UNCERTAINTY

EXPERIMENTAL UNCERTAINTY 3 EXPERIMENTAL UNCERTAINTY I am no matchmaker, as you well know, said Lady Russell, being much too aware of the uncertainty of all human events and calculations. --- Persuasion 3.1 UNCERTAINTY AS A 95%

More information

1 Measurement Uncertainties

1 Measurement Uncertainties 1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.

More information

Physics. Nov Title: Nov 3 8:52 AM (1 of 45)

Physics. Nov Title: Nov 3 8:52 AM (1 of 45) Physics Nov 3 2008 Title: Nov 3 8:52 AM (1 of 45) Physics Nov 3 2008 Physics is the branch of science that studies matter and energy, how they are related and how they interact. Physics covers everything

More information

Lesson 2: Exploring Quadratic Relations Quad Regression Unit 5 Quadratic Relations

Lesson 2: Exploring Quadratic Relations Quad Regression Unit 5 Quadratic Relations (A) Lesson Context BIG PICTURE of this UNIT: CONTEXT of this LESSON: How do we analyze and then work with a data set that shows both increase and decrease What is a parabola and what key features do they

More information

Contents Decimals Averages Percentages Metric Units Scientific Notation Dimensional Analysis

Contents Decimals Averages Percentages Metric Units Scientific Notation Dimensional Analysis This year in APES you will hear the two words most dreaded by high school students NO CALCULATORS! That s right, you cannot use a calculator on the AP Environmental Science exam. Since the regular tests

More information

Uncertainty in Measurements

Uncertainty in Measurements Uncertainty in Measurements! Two kinds of numbers " Exact! counted values " 2 dogs " 26 letters " 3 brothers! defined numbers " 12 inches per foot " 1000 g per kilogram " 2.54 cm per inch Metric Practice!

More information

Decimals Topic 1: Place value

Decimals Topic 1: Place value Topic : Place value QUESTION Write the following decimal numbers in expanded form. Hund- reds Tens U nits. Tenths Hundreths Thousandths a. 8 b. 6 c 8. 7 d. 8 9 e 7. 0 0 f 0 9. 0 6 QUESTION Write the following

More information

Group 1 Group 2. 1 meter = 100 cm 9.88 cm of Copper Wire 1 dollar = 4 quarters Room Temp is 22.7 C

Group 1 Group 2. 1 meter = 100 cm 9.88 cm of Copper Wire 1 dollar = 4 quarters Room Temp is 22.7 C NAME: DUE DATE: JUNE 11 TH AP Chemistry SUMMER REV: Sig Figs Why? The number of digits (significant figures) reported for a measured value conveys the quality of the measurement and hence, the quality

More information

1 Measurement Uncertainties

1 Measurement Uncertainties 1 Measurement Uncertainties (Adapted stolen, really from work by Amin Jaziri) 1.1 Introduction No measurement can be perfectly certain. No measuring device is infinitely sensitive or infinitely precise.

More information

Unit 1: Introduction to Variables

Unit 1: Introduction to Variables Section 1.1: Writing Algebraic Expressions Section 1.2: The Story of x Section 1.3: Evaluating Algebraic Expressions Section 1.4: Applications Section 1.5: Geometric Formulas KEY TERMS AND CONCEPTS Look

More information

Math Skills Needed For Chemistry

Math Skills Needed For Chemistry Lecture Presentation Chapter 1 Chemistry in Our Lives What is Chemistry? Chemistry is the study of composition, structure, properties, and reactions of matter. happens all around you every day. Antacid

More information

Lecture Presentation. Chapter 1. Chemistry in Our Lives. Karen C. Timberlake

Lecture Presentation. Chapter 1. Chemistry in Our Lives. Karen C. Timberlake Lecture Presentation Chapter 1 Chemistry in Our Lives What is Chemistry? Chemistry is the study of composition, structure, properties, and reactions of matter. happens all around you every day. Antacid

More information

Finding a Percent of a Number (page 216)

Finding a Percent of a Number (page 216) LESSON Name 1 Finding a Percent of a Number (page 216) You already know how to change a percent to a fraction. Rewrite the percent as a fraction with a denominator of 100 and reduce. 25% = 25 100 = 1 5%

More information

PRE-ALGEBRA SUMMARY WHOLE NUMBERS

PRE-ALGEBRA SUMMARY WHOLE NUMBERS PRE-ALGEBRA SUMMARY WHOLE NUMBERS Introduction to Whole Numbers and Place Value Digits Digits are the basic symbols of the system 0,,,, 4,, 6, 7, 8, and 9 are digits Place Value The value of a digit in

More information

LESSON 4-5 THE LAW OF COMMUTATIVITY

LESSON 4-5 THE LAW OF COMMUTATIVITY LESSON 4-5 THE LAW OF COMMUTATIVITY Axioms [AXE ee ums] are things we assume to be true because they seem obvious but we cannot prove them. Say with me: axiom. A. For example, if three plus four is seven,

More information

CHEM Chapter 1

CHEM Chapter 1 CHEM 1110 Chapter 1 Chapter 1 OVERVIEW What s science? What s chemistry? Science and numbers Measurements Unit conversion States of matter Density & specific gravity Describing energy Heat and its transfer

More information

SIGNIFICANT FIGURES. x 100%

SIGNIFICANT FIGURES. x 100% Page 1 SIGNIFICANT FIGURES ASSIGNED READING: Zumdahal, et.al, Chemistry (10 th ed.), Chapter 1, Sec. 4 and 5. I. Accuracy and Precision It is important to remember, here at the outset of this course, that

More information

Accelerated Chemistry Study Guide What is Chemistry? (Chapter 1)

Accelerated Chemistry Study Guide What is Chemistry? (Chapter 1) Accelerated Chemistry Study Guide What is Chemistry? (Chapter 1) Conversion factor Density Uncertainty Significant digits/figures Precision Accuracy Percent error September 2017 Page 1 of 32 Scientific

More information

Covers new Math TEKS!

Covers new Math TEKS! Covers new Math TEKS! 4 UPDATED FOR GREEN APPLE GRADE 4 MATH GREEN APPLE EDUCATIONAL PRODUCTS Copyright infringement is a violation of Federal Law. by Green Apple Educational Products, Inc., La Vernia,

More information

Review Numbers and Operations in Base Ten. What is the value of the expression? An equation is shown.

Review Numbers and Operations in Base Ten. What is the value of the expression? An equation is shown. 1. 2. 3. 4. 5. Review Numbers and Operations in Base Ten 3,400 x An equation is shown.? x = 0.034 What is the missing number? An equation is shown. 0.34 x? = 3.4 What is the value of the missing number?

More information

Grade 5 Decimal Numbers

Grade 5 Decimal Numbers ID : ww-5-decimal-numbers [1] Grade 5 Decimal Numbers For more such worksheets visit www.edugain.com Answer t he quest ions (1) At a construction site, there are 14.5 loads of bricks, and the total weight

More information

Math 9: Review for final

Math 9: Review for final Lesson 1.1: Square Roots of Perfect Squares 1. Use each diagram to determine the value of the square root. 1 a) b) 0.16 9 2. Which numbers below are perfect squares? How do you know? a) 25 121 b) 2.89

More information

6Of the 25 exotic animals to escape in the U.S. in the. 8Use what you ve learned about vision ratios (like (-4) = 0

6Of the 25 exotic animals to escape in the U.S. in the. 8Use what you ve learned about vision ratios (like (-4) = 0 Practice Test ISSUE SKILLS REVIEW Before heading to a mountain, a climber buys one 1 pair of shoes (s), one belay (b), and two carabiners (c). Which expression below describes the total amount of gear

More information

Algebra 1 FSA Mathematics Practice Test Questions

Algebra 1 FSA Mathematics Practice Test Questions Algebra 1 FSA Mathematics Practice Test Questions The purpose of these practice test materials is to orient teachers and students to the types of questions on paper-based FSA tests. By using these materials,

More information

Standards of the past

Standards of the past Metric Prefixes Measurement Must have a standard. A standard is an exact quantity people agree to use for comparison. A standard means two people using the same object should get close to the same results.

More information

WORKBOOK. MTH 01 - FUNDAMENTAL CONCEPTS AND SKILLS IN ARITHMETIC AND ALGEBRA. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE

WORKBOOK. MTH 01 - FUNDAMENTAL CONCEPTS AND SKILLS IN ARITHMETIC AND ALGEBRA. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE WORKBOOK. MTH 01 - FUNDAMENTAL CONCEPTS AND SKILLS IN ARITHMETIC AND ALGEBRA. DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE Contributors: M. Bates, U. N. Iyer Department of Mathematics and Computer Science,

More information

Chapter 2 Math Skills

Chapter 2 Math Skills Chapter 2 Math Skills 2.1 Measurements Measurement number with a unit Units are very important o A student wouldn t ask a teacher Could you please hand me 6? The student would instead ask, Could you please

More information

CHAPTER 9 : Motion Physics Intro to MEASUREMENTS

CHAPTER 9 : Motion Physics Intro to MEASUREMENTS CHAPTER 9 : Motion Physics Intro to MEASUREMENTS SIGNIFICANT FIGURES SCIENTIFIC NOTATION CALCULATIONS ACCURACY AND PRECICION ERRORS REVIEW OF METRIC SYSTEM Significant figures and calculations Significant

More information

Scientific Literacy & the Scientific Method

Scientific Literacy & the Scientific Method Scientific Literacy & the Scientific Method What does it mean to be? You ve probably hear that term before, and you might be thinking that literate means the ability to and. But what does it mean to be

More information

MATH 227 CP 7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 227 CP 7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. MATH 227 CP 7 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Find the mean, µ, for the binomial distribution which has the stated values of n and p.

More information

CHM Accuracy, Precision, and Significant Figures (r14) C. Taylor 1/10

CHM Accuracy, Precision, and Significant Figures (r14) C. Taylor 1/10 CHM 110 - Accuracy, Precision, and Significant Figures (r14) - 2014 C. Taylor 1/10 Introduction Observations are vitally important to all of science. Some observations are qualitative in nature - such

More information

Part One: Typical mistakes writing English numbers

Part One: Typical mistakes writing English numbers Typical Mistakes with English Numbers- Error Correction Task Find one mistake in each line of the three sections below. All have exactly one mistake (of many different kinds). Part One: Typical mistakes

More information

Rational Numbers. An Introduction to the Unit & Math 8 Review. Math 9 Mrs. Feldes

Rational Numbers. An Introduction to the Unit & Math 8 Review. Math 9 Mrs. Feldes Rational Numbers An Introduction to the Unit & Math 8 Review Math 9 Mrs. Feldes In this Unit, we will: Compare & order numbers using a variety of strategies. Strategies include: drawing pictures & number

More information

Co Curricular Data Analysis Review

Co Curricular Data Analysis Review Chapter Vocabulary Co Curricular Data Analysis Review Base Unit Second (s) Meter (m) Kilogram (kg) Kelvin (K) Derived unit Liter Density Scientific notation Dimensional analysis (Equality) not in book

More information

Appendix B: Skills Handbook

Appendix B: Skills Handbook Appendix B: Skills Handbook Effective communication is an important part of science. To avoid confusion when measuring and doing mathematical calculations, there are accepted conventions and practices

More information

Chemistry Day 39. Friday, December 14 th Monday, December 17 th, 2018

Chemistry Day 39. Friday, December 14 th Monday, December 17 th, 2018 Chemistry Day 39 Friday, December 14 th Monday, December 17 th, 2018 Do-Now: Reactions Quiz Do-Now 1. Write down today s FLT 2. Copy: KCl + H 2 O à? 3. Identify the type of reaction in #2. 4. Predict the

More information

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Sixth Edition by Charles H. Corwin Scientific Measurements by Christopher Hamaker 1 Uncertainty in Measurements A measurement is a number with a unit

More information

Name: Number: Number and Operations in Base Ten

Name: Number: Number and Operations in Base Ten Number and Operations in Base Ten 1.1 Multiplying and Dividing by Powers of Ten 8 x (6 + 3) = 12 (13-7) = 9 x (5 3) 2 = 3 x (2 + 4) (9-3) = Write the numbers in the table: 24,438. Thousands Ones Hundreds

More information

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS C O M P E T E N C Y 1 KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS SKILL 1.1 Compare the relative value of real numbers (e.g., integers, fractions,

More information

Section 2.5 from Precalculus was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website.

Section 2.5 from Precalculus was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. Section 2.5 from Precalculus was developed by OpenStax College, licensed by Rice University, and is available on the Connexions website. It is used under a Creative Commons Attribution-NonCommercial- ShareAlike

More information

AP Environmental Science Math Prep

AP Environmental Science Math Prep AP Environmental Science Math Prep This year in APES you will hear the two words most dreaded by high school students NO CALCULATORS! That s right, you cannot use a calculator on the AP Environmental Science

More information

Uncertainty: A Reading Guide and Self-Paced Tutorial

Uncertainty: A Reading Guide and Self-Paced Tutorial Uncertainty: A Reading Guide and Self-Paced Tutorial First, read the description of uncertainty at the Experimental Uncertainty Review link on the Physics 108 web page, up to and including Rule 6, making

More information

date: math analysis 2 chapter 18: curve fitting and models

date: math analysis 2 chapter 18: curve fitting and models name: period: date: math analysis 2 mr. mellina chapter 18: curve fitting and models Sections: 18.1 Introduction to Curve Fitting; the Least-Squares Line 18.2 Fitting Exponential Curves 18.3 Fitting Power

More information

Measurement & Lab Equipment

Measurement & Lab Equipment Measurement & Lab Equipment Abstract This lab reviews the concept of scientific measurement, which you will employ weekly throughout this course. Specifically, we will review the metric system so that

More information

Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section B

Chapter 3: Numbers in the Real World Lecture notes Math 1030 Section B Section B.1: Writing Large and Small Numbers Large and small numbers Working with large and small numbers is much easier when we write them in a special format called scientific notation. Scientific notation

More information

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS

KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS DOMAIN I. COMPETENCY 1.0 MATHEMATICS KNOWLEDGE OF NUMBER SENSE, CONCEPTS, AND OPERATIONS Skill 1.1 Compare the relative value of real numbers (e.g., integers, fractions, decimals, percents, irrational

More information

CHAPTER 1. Introduction

CHAPTER 1. Introduction CHAPTER 1 Introduction Engineers and scientists are constantly exposed to collections of facts, or data. The discipline of statistics provides methods for organizing and summarizing data, and for drawing

More information

Accuracy, Precision, and Significant Figures

Accuracy, Precision, and Significant Figures Accuracy, Precision, and Significant Figures Bởi: OpenStaxCollege A double-pan mechanical balance is used to compare different masses. Usually an object with unknown mass is placed in one pan and objects

More information

2. Place the following numbers in order from smallest to largest:

2. Place the following numbers in order from smallest to largest: MAT08 Final Exam Review Note to students: The final exam for this course will consist of 0 multiple-choice questions and a few open-ended questions. You may use a calculator on the exam, but no notes of

More information

Physics 11 Reading Booklet

Physics 11 Reading Booklet In Order complete the Physics 11 Substantive Assignment, you must read and complete the self-marking exercises in this booklet. 1. Read all the information provided. 2. Complete the Practice and Self Check

More information

Appendix C: Accuracy, Precision, and Uncertainty

Appendix C: Accuracy, Precision, and Uncertainty Appendix C: 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

More information

Name: Number: Number and Operations in Base Ten Key

Name: Number: Number and Operations in Base Ten Key Name: Number: Number and Operations in Base Ten Key 1.1 Multiplying and Dividing by Powers of Ten 8 x (6 + 3) = 72 12 (13-7) = 2 9 x (5 3) 2 = 9 3 x (2 + 4) (9-3) = 12 Write the numbers in the table: 24,438.

More information

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Seventh Edition by Charles H. Corwin

INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Seventh Edition by Charles H. Corwin Lecture INTRODUCTORY CHEMISTRY Concepts and Critical Thinking Seventh Edition by Charles H. Corwin Introduction to Chemistry by Christopher G. Hamaker Illinois State University Evolution of Chemistry The

More information

Destination Math California Intervention

Destination Math California Intervention Destination Math California Intervention correlated to the California Intervention 4 7 s McDougal Littell Riverdeep STANDARDS MAPS for a Mathematics Intervention Program (Grades 4-7) The standards maps

More information

Ch 1. The Language of Algebra

Ch 1. The Language of Algebra Ch 1 The Language of Algebra 1-1 Writing Expressions and Equations Writing Expressions Buying CDs: 1 CD = $15 2 CD = $15 x 2 3 CD = $15 x 3 n number of CDs? $15 x n Algebraic Expression Writing Expressions

More information

αα Measuring Global Temperatures 2.1 Measuring Global Temperatures Introductory Chemistry Fourth Edition Nivaldo J.

αα Measuring Global Temperatures 2.1 Measuring Global Temperatures Introductory Chemistry Fourth Edition Nivaldo J. Introductory Chemistry Fourth Edition Nivaldo J. Tro Chapter 2 Measurement and Problem Solving Dr. Sylvia Esjornson Southwestern Oklahoma State University Weatherford, OK 2.1 Measuring Global Temperatures

More information

UNIT 2 REASONING WITH LINEAR EQUATIONS AND INEQUALITIES Lesson 1: Creating Linear Equations and Inequalities in One Variable

UNIT 2 REASONING WITH LINEAR EQUATIONS AND INEQUALITIES Lesson 1: Creating Linear Equations and Inequalities in One Variable Guided Practice Example 1 James earns $15 per hour as a teller at a bank. In one week he pays 17% of his earnings in state and federal taxes. His take-home pay for the week is $460.65. How many hours did

More information

MEASUREMENT IN THE LABORATORY

MEASUREMENT IN THE LABORATORY 1 MEASUREMENT IN THE LABORATORY INTRODUCTION Today's experiment will introduce you to some simple but important types of measurements commonly used by the chemist. You will measure lengths of objects,

More information

Class 6 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks

Class 6 Decimals. Answer t he quest ions. Choose correct answer(s) f rom given choice. Fill in the blanks ID : in-6-decimals [1] Class 6 Decimals For more such worksheets visit www.edugain.com Answer t he quest ions (1) At a construction site, there are 19.5 loads of bricks, and the total weight of all the

More information

Astronomy 102 Math Review

Astronomy 102 Math Review Astronomy 102 Math Review 2003-August-06 Prof. Robert Knop r.knop@vanderbilt.edu) For Astronomy 102, you will not need to do any math beyond the high-school alegbra that is part of the admissions requirements

More information