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

Size: px
Start display at page:

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

Transcription

1 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 digits and the first digit with some uncertainty. RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT DIGITS When Reading a Measurement (Significant Digits are in BOLD type and the non-significant digits are underlined) Examples: 1) ALL non-zero digits are significant. Example: cm has 5 significant digits. 2) ALL zeros between two non-zero digits are significant. Example: kg has 8 significant digits. 3) ALL zeros to the left of an understood decimal point and to the right of a nonzero digit (place holding zeros) are not significant. Example: mm has 3 significant digits. 4) ALL zeros to the left of an expressed decimal point and to the right of a nonzero digit are significant. Example: m/s has 7 significant digits. 5) ALL zeros to the right of an expressed decimal point and to the right of a nonzero digit are significant. Example: cm has 5 significant digits. 6) ALL zeros to the right of an expressed decimal point and to the left of a nonzero digit are not significant. (place holding zeros) Example: cl has 3 significant digits. 1) s There are 4 significant digits. 5, 1, and 2 are significant by rule 1. The zero is significant by rule 2. 2) kg There are 4 significant digits. 4, 3, and 2 are significant by rule 1. The zero at the end is significant by rule 5. The two zeros after the decimal point an before the 4 are not significant by rule 6.

2 ml There are 3 significant digits. 1 and 2 are significant by rule 1. The zero between 1 and 2 is significant by rule 2. The three zeros after the 2 are not significant by rule cm There are 6 significant digits. 7, 8, and 9 are significant by rule 1. The three zeros at the end are significant by rule 4. RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT DIGITS When Taking a Measurement 1) Determine the accuracy of the instrument. (The value of the smallest separation between lines on a measuring device) example: 2) Take your measurement so that ALL certain digits are kept, They ARE significant. Example: It is certain that the measurement is greater than 10 cm and less than 11 cm. Therefore, the measurement has 2 certain digits 1 in the tens place and 0 in the ones place [10. cm]. (note: the 0 is significant because it was read from a line on the measuring device) Counting the lines between 10 cm and 11 cm, it is certain that 5 lines are passed but not 6. Thus another significant digit appears in the tenths place. [10.5 cm]. Thus, the measurement has 3 certain digits which ARE significant. 3) Estimate the last digit of the measurement. Divide the space between the known lines that the measurement falls, into tenths. Estimate this value one place beyond the accuracy of the instrument.

3 Example: It looks as if the measurement is less than half way between the lines, so it is possible to estimate a digit in the hundredths place. This digit is significant because the estimate was based on known lines and was not a blind guess. Thus there are 4 significant digits in the measurement. [10.53 cm] (Note: no digits in a place value smaller than the hundredths place would be significant, because the estimate would be based on two lines that are not on the measuring device. Hence, they would be blind guesses, which are NOT significant) 4) Record the measurement with ALL significant digits. Example: Length = cm There are no significant digits in place values higher than the tens place because the meter stick has a maximum length of 100 cm and there is no uncertainty that the item being measured is smaller than the meter stick. The digit 1 in the tens place is significant because there was a line on the measuring device that showed 1 ten and not 2. Thus, there is no uncertainty in the digit. The digit 0 in the ones place is significant because there was a line on the measuring device that showed 0 ones and not 1. Thus, there is no uncertainty in the digit. The digit 5 in the tenths place is significant because there was a line on the measuring device that showed 5 tenths and not 6. Thus, there is no uncertainty in the digit. The digit 3 in the hundredths place is significant because there is a line at the 5 tenths place and the 6 tenths place, so an estimate can be made on how far between these two lines that the measurement falls. Thus, there is some uncertainty in the digit but it was based on two visible reference marks and is not a blind guess. Any digits in place values smaller than the hundredths place would not be significant, because there are no lines on the measuring device to use as a reference point to make an estimation of the value. Thus, it would be a blind guess with no certainty at all!

4 Multiplication and Division Rule The general rule of thumb is that an answer can have only as many significant digits as the number with the least amount of significant digits used to calculate the answer. The following is a list of steps which will aid in calculating the number of significant digits for a multiplication or division problem. 1) Find the number of significant digits for each factor in the equation. 2) Determine which factor has the least number of significant digits. 3) Solve the equation 4) Round your answer so that it has the same number of significant digits as the factor found in step #2. Example: Step 1: Finding the number of significant digits in each term sig. figs sig. figs sig. figs. Step 2: Find the term with the fewest significant digits. Step 3: Do the math sig. figs. Step 4: Round the answer to number of digits determined in step 2. (3 significant digits) Start at the highest place value and move right rounds to 62.4 (Note: When rounding to a given place value (tenths place) look at the digit in the place value adjacent and to the right of that place value only (hundredths place) and truncate the rest of the digits. The general rule is if this digit is 0 to 4 leave it alone and if it is 5 to 9 round up.)

5 Addition and Subtraction Rule The general rule of thumb for adding and subtracting is that it is a place value rule. The answer cannot have a significant digit in a place value smaller than the smallest place value occupied by a significant digit of the terms to be added or subtracted. The following is a list of steps which will aid in calculating the number of significant digits for a addition or subtraction problem. 1) Find the significant digit occupying the smallest place value in each term and underline it. 2) Determine which of the underlined digits is in the highest place value. 3) Round each term to the place value determined in step 2 using the general rounding rule. 4) Solve the equation. This answer will have the proper number of significant digits. Example: Step 1: Finding the smallest place values Step 2: Determine which underlined digit is in the highest place value. 0 is in the thousandths place. 9 is in the ten thousandths place. 1 is in the hundredths place. 4 is in the millionths place. The hundredths place is greater than all the other place values. So the 1 in the third term occupies the highest place value. Step 3: Round each term to the place value found in step rounds to

6 Step 4: Do the math Significant digits are a way of determining how accurate measurements are and how accurate the quantities that are derived using the measurements are. Digits that are significant have meaning and dimension in the real world. While digits that are not significant are both dimensionless and meaningless. It is possible to divide to numbers and get an infinite number of digits on a calculator (3.0 m / 9.00 s). However only some of these digits have a physical meaning, the others are worthless ( repeating to infinity, only 2 digits are significant.33 m/s). Since science deals with real quantities and real measurements the use of significant digits is mandated.

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

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

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

Base unit-a defined unit of measurement based on an object or event in the physical world. Length

Base unit-a defined unit of measurement based on an object or event in the physical world. Length Base unit-a defined unit of measurement based on an object or event in the physical world Five base units: Temperature Mass Length Time Energy Derived unit-a unit of measurement defined by a combination

More information

Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific

Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific Unit 1 Part 1: Significant Figures and Scientific Notation. Objective understand significant figures and their rules. Be able to use scientific notation in calculations. Significant figures - consist of

More information

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision?

Section 3 Using Scientific Measurements. Look at the specifications for electronic balances. How do the instruments vary in precision? Lesson Starter Look at the specifications for electronic balances. How do the instruments vary in precision? Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?

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

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

Chemistry: The Study of Change Chang & Goldsby 12 th edition

Chemistry: The Study of Change Chang & Goldsby 12 th edition Chemistry: The Study of Change Chang & Goldsby 12 th edition modified by Dr. Hahn Chapter 1 Example 1.4 Determine the number of significant figures in the following measurements: (a)478 cm (b)6.01 g end

More information

Chemistry 1. Worksheet 3. Significant Figures in Calculations. 1 MathTutorDVD.com

Chemistry 1. Worksheet 3. Significant Figures in Calculations. 1 MathTutorDVD.com Chemistry 1 Worksheet 3 Significant Figures in Calculations 1 Report all answers on this worksheet with the correct number of significant figures. 1) How many significant figures does each of the following

More information

1. Scientific Notation A shorthand method of displaying very (distance to. Express in Scientific Notation

1. Scientific Notation A shorthand method of displaying very (distance to. Express in Scientific Notation Unit 2: MEASUREMENT 1. Scientific Notation 2. Metric System 3. Accuracy and Precision 4. Measuring & Counting Significant Figures 5. Calculations with Significant Figures 6. Density 1. Scientific Notation

More information

Measurement. Scientific Notation. Measurements and Problem Solving. Writing Numbers in Scientific Notation

Measurement. Scientific Notation. Measurements and Problem Solving. Writing Numbers in Scientific Notation Measurement Chapter 2 Measurements and Problem Solving Quantitative observation Comparison based on an accepted scale e.g. Meter stick Has 2 parts number and unit Number tells comparison Unit tells scale

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

CHM111 Lab Math Review Grading Rubric

CHM111 Lab Math Review Grading Rubric Name CHM111 Lab Math Review Grading Rubric Part 1. Basic Algebra and Percentages Criteria Points possible Points earned Question 1 (0.25 points each question) 2 Question 2 (0.25 points each question) 1

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

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

Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed.

Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed. Introductory Chemistry: A Foundation, 6 th Ed. Introductory Chemistry, 6 th Ed. Basic Chemistry, 6 th Ed. by Steven S. Zumdahl, Donald J. DeCoste University of Illinois Chapter 2 Measurements and Calculations

More information

CHM 130 Measurements, Significant Figures, Derived Quantities, and Unit Conversions

CHM 130 Measurements, Significant Figures, Derived Quantities, and Unit Conversions CHM 130 Measurements, Significant Figures, Derived Quantities, and Unit Conversions Objectives 1. Use measuring tools correctly 2. Read and record measurements correctly (significant digits and unit) 3.

More information

Physics and Physical Measurement. Topic 1.2 The Realm of Physics Range of magnitudes of quantities in our universe

Physics and Physical Measurement. Topic 1.2 The Realm of Physics Range of magnitudes of quantities in our universe Physics and Physical Measurement Topic 1.2 The Realm of Physics Range of magnitudes of quantities in our universe Range of Magnitudes Scientists are more concerned with the order of magnitude rather than

More information

The Rules of the Game

The Rules of the Game The Rules of the Game Over hundreds of years ago, physicists and other scientists developed a traditional way of expressing their observations. International System of Units (SI) metric system. The amount

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

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

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

Chapter 1. Chemistry and Measurements

Chapter 1. Chemistry and Measurements Chapter 1 Chemistry and Measurements Section 1-1 Chemistry: the study of matter and the changes it undergoes. macroscopic: relating to large-scale analysis, visible to the naked eye microscopic: not visible

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

Appendix A: Significant Figures and Error Analysis

Appendix A: Significant Figures and Error Analysis 1 Appendix A: Significant Figures and Error Analysis Every measurement of a physical quantity contains some amount of uncertainty or error. We often speak of a certain number or measurement as being precise

More information

Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER?

Metric Prefixes UNITS & MEASUREMENT 10/6/2015 WHY DO UNITS AND MEASUREMENT MATTER? UNITS & MEASUREMENT WHY DO UNITS AND MEASUREMENT MATTER? Chemistry In Action On 9/3/99, $15,000,000 Mars Climate Orbiter entered Mar s atmosphere 100 km (6 miles) lower than planned and was destroyed by

More information

Allows us to work with very large or small numbers more easily. All numbers are a product of 10.

Allows us to work with very large or small numbers more easily. All numbers are a product of 10. Unit 1: Measurements Scientific Notation : Allows us to work with very large or small numbers more easily. All numbers are a product of 10. M x 10n M= signif. digit [ 1 < M < 10 ] n = an integer move the

More information

Welcome to General Chemistry I

Welcome to General Chemistry I Welcome to General Chemistry I Chemistry Chemistry is a branch of science that studies the composition and properties of matter and the changes it undergoes H 2 O http://theresilientearth.com/?q=content/climate-models-blown-away-water-vapor

More information

Notes: Measurement and Calculation

Notes: Measurement and Calculation Name Chemistry-PAP Per. I. The Basics of Measurement Notes: Measurement and Calculation A. Measurement Most provide quantitative information, but because they are obtained experimentally, they are inexact.

More information

SPH3U Measurement and Analysis Mr. LoRusso Introduction

SPH3U Measurement and Analysis Mr. LoRusso Introduction Introduction Standard Unit: Metric is the preferred unit of measure in science. Metric is often referred to as S.I for Systèm Internatianale. Historically, S.I. has been referred to as MKS system for meters,

More information

Welcome to CHEM 1101

Welcome to CHEM 1101 Welcome to CHEM 1101 Lecture Times: Tuesday and Thursday 9 to 9:50 a.m. Instructor: Dr. Muhannad Amer Office Location: 44 staff Bldng Required Materials Text: Chemistry, 7th ed., Zumdahl Please see course

More information

Scientific Notation. Sig. Figs. Estimation Density. Unit cancelation

Scientific Notation. Sig. Figs. Estimation Density. Unit cancelation Unit cancelation Sig. Figs. Scientific Notation Estimation Density 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500 When doing unit conversions, this

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

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

How long is the arrow?

How long is the arrow? 1.2 Measurements Measuring We have all measured things before, but how would you define it? Measurement: comparing an unknown quantity to a standard unit (known quantity) How long is the arrow? Any measurement

More information

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4.

Summer Math Packet for Students Entering 6th Grade. Please have your student complete this packet and return it to school on Tuesday, September 4. Summer Math Packet for Students Entering 6th Grade Please have your student complete this packet and return it to school on Tuesday, September. Work on your packet gradually. Complete one to two pages

More information

Every time a measurement is taken, we must be aware of significant figures! Define significant figures.

Every time a measurement is taken, we must be aware of significant figures! Define significant figures. SCHM 103: FUNDAMENTALS OF CHEMISTRY Ch. 2: Numerical Side of Chemistry Types of data collected in experiments include: Qualitative: Quantitative: Making Measurements Whenever a piece of data is collected,

More information

Chem 140 Section C Instructor: Ken Marr. Chem 140 Section A Instructor: Ken Marr. Chem 140 Section E Instructor: Ken Marr. Day 1 Activities CHEMISTRY

Chem 140 Section C Instructor: Ken Marr. Chem 140 Section A Instructor: Ken Marr. Chem 140 Section E Instructor: Ken Marr. Day 1 Activities CHEMISTRY Chem 140 Section A Instructor: Ken Marr Weekly Schedule Lecture 9-10, MWF in STB-2 Lab 8-10, Tu in STB-2 8-10, Th in STB-5 Chem 140 Section C Instructor: Ken Marr Weekly Schedule Lecture 10 11, MWF in

More information

PHYSICS. Chapter 1 Review. Rounding Scientific Notation Factor Label Conversions

PHYSICS. Chapter 1 Review. Rounding Scientific Notation Factor Label Conversions PHYSICS Chapter 1 Review Rounding Scientific Notation Factor Label Conversions The Tools Of PHYSICS Metric Prefixes Prefix Symbol Meaning Kilo K 1000 Deci d tenth Centi c hundreth Milli m thousandth Prefix

More information

ECE 102 Engineering Computation

ECE 102 Engineering Computation ECE 102 Engineering Computation Phillip Wong Error Analysis Accuracy vs. Precision Significant Figures Systematic and Random Errors Basic Error Analysis Physical measurements are never exact. Uncertainty

More information

Measurement and Uncertainty

Measurement and Uncertainty Measurement and Uncertainty Name: Date: Block: There is uncertainty in every measurement due to of accuracy and precision. Accuracy: how close the instrument measures to an accepted. Precision: how closely

More information

Chapter 3 - Measurements

Chapter 3 - Measurements Chapter 3 - Measurements You ll learn it in the summer, If not, it ll be a bummer. You ll need to know conversions, For units, Euro version. Metrics are powers of ten, And you might cry when, You re forced

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

Measurements. October 06, 2014

Measurements. October 06, 2014 Measurements Measurements Measurements are quantitative observations. What are some kinds of quantitative observations you might make? Temperature Volume Length Mass Student A and Student B measured the

More information

Do Now: Use the ruler below to answer the following questions

Do Now: Use the ruler below to answer the following questions Chemistry Ms. Ye Name Date Block Do Now: Use the ruler below to answer the following questions 1. What is each tick mark worth on the ruler? 2. When measuring, to which decimal place should you estimate

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

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

More information

Notes: Unit 1: Math and Measurement

Notes: Unit 1: Math and Measurement Name: Regents Chemistry: Notes: Unit 1: Math and Measurement www.chempride.weebly.com Key Ideas Major Understandings: o Chemistry is the study of matter: Matter takes up space and has mass. (K- 4, 3.1a)

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

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

Unit 2. Scientific Measurement

Unit 2. Scientific Measurement Unit 2 Scientific Measurement Qualitative vs quantitative Qualitative measurementsgive results in a descriptive, non-numerical form Ex. Observations taken in the demo lab Quantitative measurementsgive

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

Significant Figures. CK12 Editor. Say Thanks to the Authors Click (No sign in required)

Significant Figures. CK12 Editor. Say Thanks to the Authors Click  (No sign in required) Significant Figures CK12 Editor Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,

More information

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit.

Significant Figures. Significant Figures 18/02/2015. A significant figure is a measured or meaningful digit. Significant Figures When counting objects, it is easy to determine the EXACT number of objects. Significant Figures Unit B1 But when a property such as mass, time, volume, or length is MEASURED, you can

More information

SCIENTIFIC MEASUREMENT C H A P T E R 3

SCIENTIFIC MEASUREMENT C H A P T E R 3 SCIENTIFIC MEASUREMENT C H A P T E R 3 WHAT IS MEASUREMENT? Comparing one object to a standard In science, we use SI Units meters, o C, grams NOT o F, pounds, ounces etc. TWO TYPES OF MEASUREMENTS 1.

More information

Lab 1: Measurement. PART 1: Exponential Notation: Powers of 10

Lab 1: Measurement. PART 1: Exponential Notation: Powers of 10 Lab 1: Measurement Equipment: 2 meter sticks You will find these websites useful for today s lab: SI Base Units: http://physics.nist.gov/cuu/units/units.html Metric prefixes: http://physics.nist.gov/cuu/units/prefixes.html

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

Uncertainties and Error Propagation Part I of a manual on Uncertainties, Graphing, and the Vernier Caliper

Uncertainties and Error Propagation Part I of a manual on Uncertainties, Graphing, and the Vernier Caliper Contents Uncertainties and Error Propagation Part I of a manual on Uncertainties, Graphing, and the Vernier Caliper Copyright July 1, 2000 Vern Lindberg 1. Systematic versus Random Errors 2. Determining

More information

Measurements and Calculations. Chapter 2

Measurements and Calculations. Chapter 2 Measurements and Calculations Chapter 2 Qualitative Observations: General types of observations. Easy to determine. Not necessarily precise. I have many fingers, the speed limit is fast, class is long,

More information

University of South Carolina. Stephen L Morgan. Tutorial on the Use of Significant Figures

University of South Carolina. Stephen L Morgan. Tutorial on the Use of Significant Figures University of South Carolina Stephen L Morgan Tutorial on the Use of Significant Figures All measurements are approximations--no measuring device can give perfect measurements without experimental uncertainty.

More information

Measurements and Calculations. Chapter 2

Measurements and Calculations. Chapter 2 Measurements and Calculations Chapter 2 Scientific Method Section 2-1 The Scientific Method The scientific method is a logical approach to solving problems by observing and collecting data, formulating

More information

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

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

More information

Chemistry Chapter 2 Data Analysis

Chemistry Chapter 2 Data Analysis Chemistry Chapter 2 Data Analysis I. Units of Measurement 2.1 (pages 25-30) A. The metric system (SI units) Why the metric system? B. Base Units of the SI System Based on an object or event of the of other

More information

The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class

The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class The AP Chemistry Summer assignment is meant to help prepare you for the first few weeks of class Part 1. Review the mole concept and how it s used. This includes mass (grams) to moles, moles-to-mass calculations,

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

Section 1 Scientific Method. Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations.

Section 1 Scientific Method. Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Section 1 Scientific Method Objectives Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Describe the differences between hypotheses, theories,

More information

Section 1 Scientific Method. Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations.

Section 1 Scientific Method. Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Section 1 Scientific Method Objectives Describe the purpose of the scientific method. Distinguish between qualitative and quantitative observations. Describe the differences between hypotheses, theories,

More information

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet.

Chemistry Basic Science Concepts. Observations: are recorded using the senses. Examples: the paper is white; the air is cold; the drink is sweet. Note Packet # 1 1 Chemistry: the study of matter. Chemistry Basic Science Concepts Matter: anything that has mass and occupies space. Observations: are recorded using the senses. Examples: the paper is

More information

Name Date Class. N 10 n. Thus, the temperature of the Sun, 15 million kelvins, is written as K in scientific notation.

Name Date Class. N 10 n. Thus, the temperature of the Sun, 15 million kelvins, is written as K in scientific notation. 53 MATH HANDBOOK TRANSPARENCY MASTER 1 Scientists need to express small measurements, such as the mass of the proton at the center of a hydrogen atom (0.000 000 000 000 000 000 000 000 001 673 kg), and

More information

Numbers and Uncertainty

Numbers and Uncertainty Significant Figures Numbers and Uncertainty Numbers express uncertainty. Exact numbers contain no uncertainty. They are obtained by counting objects (integers) or are defined, as in some conversion factors

More information

HW #1: 1.42, 1.52, 1.54, 1.64, 1.66, 1.70, 1.76, 1.78, 1.80, 1.82, 1.84, 1.86, 1.92, 1.94, 1.98, 1.106, 1.110, 1.116

HW #1: 1.42, 1.52, 1.54, 1.64, 1.66, 1.70, 1.76, 1.78, 1.80, 1.82, 1.84, 1.86, 1.92, 1.94, 1.98, 1.106, 1.110, 1.116 Chemistry 121 Lecture 3: Physical Quantities Measuring Mass, Length, and Volume; Measurement and Significant Figures; Scientific Notation; Rounding Review Sections 1.7-1.11 in McMurry, Ballantine, et.

More information

Accuracy and Precision of Laboratory Glassware: Determining the Density of Water

Accuracy and Precision of Laboratory Glassware: Determining the Density of Water Accuracy and Precision of Laboratory Glassware: Determining the Density of Water During the semester in the general chemistry lab, you will come into contact with various pieces of laboratory glassware.

More information

Chapter 2 - Measurements and Calculations

Chapter 2 - Measurements and Calculations Chapter 2 - Measurements and Calculations 2-1 The Scientific Method "A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating

More information

2 ways to write the same number: 6,500: standard form 6.5 x 10 3 : scientific notation

2 ways to write the same number: 6,500: standard form 6.5 x 10 3 : scientific notation greater than or equal to one, and less than 10 positive exponents: numbers greater than 1 negative exponents: numbers less than 1, (> 0) (fractions) 2 ways to write the same number: 6,500: standard form

More information

Assume that you have made n different measurements of a quantity x. Usually the results of these measurements will vary; call them x 1

Assume that you have made n different measurements of a quantity x. Usually the results of these measurements will vary; call them x 1 #1 $ http://www.physics.fsu.edu/users/ng/courses/phy2048c/lab/appendixi/app1.htm Appendix I: Estimates for the Reliability of Measurements In any measurement there is always some error or uncertainty in

More information

Chemistry Monday, January 23, 2017

Chemistry Monday, January 23, 2017 Chemistry Monday, January 23, 2017 Do-Now: Ch. 11 Quiz Review 1. Write down today s FLT 2. List three symbols used in chemical equations, and state their meaning. 3. Copy: S 8 + O 2 à SO 2 4. Identify

More information

Lesson 5: Significant Digits. AKA Significant Figures

Lesson 5: Significant Digits. AKA Significant Figures Lesson 5: Significant Digits AKA Significant Figures First, take HW out to be checked. Keep it out. In CJ, copy down info from board. Keep CJ open to today s date at the top corner of your desk. On your

More information

MEASUREMENT AND PROBLEM SOLVING. Chapter 3 & 4

MEASUREMENT AND PROBLEM SOLVING. Chapter 3 & 4 MEASUREMENT AND PROBLEM SOLVING Chapter 3 & 4 Importance of Measurements 1. Fundamental to all sciences 2. In chemistry you use the International System of Measurements (SI units). Qualitative vs. Quantitative

More information

2 Standards for Measurement. Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory!

2 Standards for Measurement. Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory! 2 Standards for Measurement Careful and accurate measurements of ingredients are important both when cooking and in the chemistry laboratory! Chapter Outline 2.1 Scientific Notation 2.2 Measurement and

More information

Measurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 -

Measurement. New Topics accuracy vs. precision rounding in chemistry significant figures determining uncertainty of a measurement % error moles - 1 - Measurement Unit Description In this unit we will focus on the mathematical tools we use in science, especially chemistry the metric system and moles. We will also talk about how to gauge the accuracy

More information

A Justification for Sig Digs

A Justification for Sig Digs A Justification for Sig Digs Measurements are not perfect. They always include some degree of uncertainty because no measuring device is perfect. Each is limited in its precision. Note that we are not

More information

Welcome to Chemistry! Sept 11, 2015 Friday

Welcome to Chemistry! Sept 11, 2015 Friday Welcome to Chemistry! Sept 11, 2015 Friday DO NOW: How many sig figs in this number? 2001.1109 Round this number to 3 sig figs...... Objectives: 1. Quantitative Tools for Chemistry: complete calculations

More information

Chapter 2: Standards for Measurement. 2.1 Scientific Notation

Chapter 2: Standards for Measurement. 2.1 Scientific Notation Chapter 2: Standards for Measurement 2.1 Scientific Notation A measurement (quantitative observation) consists of two parts: o Numerical value which gives magnitude, and o Unit which gives the scale used

More information

Chemistry 11. First Assignment Scientific Notation

Chemistry 11. First Assignment Scientific Notation First Assignment Scientific Notation This First Assignment may take between 1 hours depending on your background and prior knowledgeplease follow the instructions carefully. a. Read all the information

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

Uncertainties in Measurement

Uncertainties in Measurement Uncertainties in Measurement Laboratory investigations involve taking measurements of physical quantities. All measurements will involve some degree of experimental uncertainty. QUESTIONS 1. How does one

More information

Unit 3 - Physics. Motion. Intro to Measurements

Unit 3 - Physics. Motion. Intro to Measurements Unit 3 - Physics Motion Intro to Measurements Motion Physics Intro to MEASUREMENTS SIGNIFICANT FIGURES SCIENTIFIC NOTATION CALCULATIONS ACCURACY AND PRECISION ERRORS REVIEW OF METRIC SYSTEM Significant

More information

Every physical or chemical change in matter involves a change in energy.

Every physical or chemical change in matter involves a change in energy. Sec. 2.1 Energy Objectives: 1. Explain that physical and chemical changes in matter involve transfers of energy 2. Apply the law of conservation of energy to analyze changes in matter 3. Distinguish between

More information

Introduction to 1118 Labs

Introduction to 1118 Labs Name: Partner(s): 1118 section: Desk # Date: Introduction to 1118 Labs Introductory materials are at: www.langaraphysics.com/lab.html. You may find following 3 links useful for this lab: Measurements:

More information

Example 3: 4000: 1 significant digit Example 4: : 4 significant digits

Example 3: 4000: 1 significant digit Example 4: : 4 significant digits Notes: Measurement and Math 1 Accuracy and Precision Precision depends on the precision of the measuring device o For example a device that can measure to the ten thousands place (1.6829 grams) is a more

More information

Chemistry Unit 1. Chapter 1 Chemical Overview

Chemistry Unit 1. Chapter 1 Chemical Overview Chemistry Unit 1 Chapter 1 Chemical Overview Chemistry Unit 1 Section 1 Overview Scientific Method Measurement Significant Figures Dimensional Analysis A main challenge of chemistry is to understand the

More information

Measurements in Chemistry Chapter 2

Measurements in Chemistry Chapter 2 Measurements in Chemistry Chapter 2 Problem-Set Solutions 2.1 It is easier to use because it is a decimal unit system. 2.2 Common measurements include mass, volume, length, time, temperature, pressure,

More information

percent, since the ratio5/540 reduces to (rounded off) in decimal form.

percent, since the ratio5/540 reduces to (rounded off) in decimal form. percent, since the ratio5/540 reduces to 0.0093 (rounded off) in decimal form. Significant Digits The accuracy of a measurement is often described in terms of the number of significant digits used in expressing

More information

General Chemistry I Introductory Concepts. Units, dimensions, and mathematics for problem solving

General Chemistry I Introductory Concepts. Units, dimensions, and mathematics for problem solving General Chemistry I Introductory Concepts Units, dimensions, and mathematics for problem solving Unit Conversion What is the value of S in cm per second? S = 5x10 3 furlongs fortnight Conversion Factor:

More information

CHAPTER 2: SCIENTIFIC MEASUREMENTS

CHAPTER 2: SCIENTIFIC MEASUREMENTS CHAPTER 2: SCIENTIFIC MEASUREMENTS Problems: 1-26, 37-76, 80-84, 89-93 2.1 UNCERTAINTY IN MEASUREMENTS measurement: a number with attached units To measure, one uses instruments = tools such as a ruler,

More information

Tools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus

Tools of Chemistry. Measurement Scientific Method Lab Safety & Apparatus Tools of Chemistry Measurement Scientific Method Lab Safety & Apparatus Scientific Notation Scientific Notation a number described as a power of 10 (used for very large or small numbers) 1000 = 1 X 10

More information

Chapter 1: Chemical Foundations A Summary

Chapter 1: Chemical Foundations A Summary Chapter 1: Chemical Foundations A Summary 1.1 Chemistry: An Overview A. Reaction of hydrogen and oxygen 1. Two molecules of hydrogen react with one molecule of oxygen to form two molecules of water 2H

More information

POGIL: Sig Figs in Calculations

POGIL: Sig Figs in Calculations Name: Date: Period: Chemistry POGIL: Sig Figs in Calculations WHY? Many of the measurements a scientist makes in lab are further analyzed or used to calculate derived units, such as area, speed, and pressure.

More information