ENVIRONMENTAL PROTECTION AGENCY APTI 435: Atmospheric Sampling Course. Student Manual

Similar documents
Air Quality Measurement Methods. Tim Morphy Regional Manager Thermo Electron October 20 th, 2006

CHAPTER 2 - Air Quality Trends and Comparisons

Stack Sampling. requires airflow through the sampling probe to be at the same rate as that flowing in the waste gas stream isokinetic

Particulate Monitors and Samplers

2016 Particulate Matter Summary

Zhongchao Tan. Air Pollution and Greenhouse Gases. From Basic Concepts to Engineering. Applications for Air Emission Control.

EVALUATION OF THE TEOM METHOD FOR THE MEASUREMENT OF PARTICULATE MATTER FROM TEXAS CATTLE FEEDLOTS. A Thesis STEWART JAMES SKLOSS

Atmospheric Disperssion

REAL-TIME DUST MONITOR TEOM 1405-F

ABSTRACT INTRODUCTION

Methods for determination of mercury in LP gas

METHOD BERYLLIUM SCREENING METHOD. Analyte CAS No. Sensitivity Beryllium (Be) Dependent upon analytical procedure used

ASME PTC Flow Measurement

Pipe Flow Hydraulics

Indoor Air Quality Solutions

1. Overview 2 2. Definitions 2 3. Laboratory Testing Criteria 2. A. Laboratory Qualifications 2. B. Analysis of TSS Samples 2. C.

METHOD 3 - GAS ANALYSIS FOR THE DETERMINATION OF DRY MOLECULAR WEIGHT. NOTE: This method does not include all of the

Contents. Preface XI Nomenclature XIII. Part I Basic Concepts and Principles 1

AIR POLLUTION. History of Clean Air Act Clean Air Update The Role of APCD

PM 2.5 Continuous Monitoring. Program Objectives, History, Requirements, and Flexibility. National Ambient Air Monitoring Conference Atlanta 2014

EMISSION MEASUREMENT TECHNICAL INFORMATION CENTER NSPS TEST METHOD. Method 10 - Determination of Carbon Monoxide Emissions from Stationary Sources

STATE UNIVERSITY OF NEW YORK COLLEGE OF TECHNOLOGY CANTON, NEW YORK COURSE OUTLINE CONS 322 HYDRAULICS

METHOD 201A - DETERMINATION OF PM EMISSIONS. 1.1 Applicability. This method applies to the in-stack measurement of

Australian/New Zealand Standard

Gas Dehydration Field Manual

SOP SMPS BaltimorePM supersite Version 2 November 20, 2000 Page 1 of 1. SEAS Chemistry

CEM Gilles Gonnet Ecomesure, B.P. 13, F Briis Sous Forges, France telephone: fax:

Contents. 1 Gas Measurement Fundamentals Head Meters Turbine Meters Other Meters Orifice Meters... 5.

Air Monitoring Directive Chapter 4: Monitoring Requirements and Equipment Technical Specifications

DETERMINATION OF CONCENTRATION AND MASS FLOW OF PARTICULATE MATTER IN FLUE GAS FOR STATIONARY SOURCE EMISSIONS

2011 Particulate Summary

Streamflow Measurement

GUJARAT TECHNOLOGICAL UNIVERSITY, AHMEDABAD, GUJARAT. Course Curriculum. FLUID FLOW OPERATION (Code: ) Chemical Engineering

Air pollution Measurements and Emission Estimates. Dr. Ahmed Abu Foul

This document is a preview generated by EVS

Title: Standard Operating Procedure for Measurement of Ozone in Ambient Air by Ultraviolet (UV) Photometry

The Paradigm Case Method of Flowmeter Selection

Audit Report of SIMAT Particle Monitoring Network

AIRBORNE PARTICULATE MATTER WITHIN 100 RANDOMLY SELECTED OFFICE BUILDINGS IN THE UNITED STATES (BASE)

TABLE OF CONTENTS CHAPTER 1 INTRODUCTION A DESCRIPTION OF THE PROBLEM OBJECTIVE METHODOLOGY 5

Method No.: 8.06/2.0/M Effective Date: January 4, 2012 Location: ###

METHOD 4 - DETERMINATION OF MOISTURE CONTENT IN STACK GASES. NOTE: This method does not include all the

Worldwide Pollution Control Association

Can your unit pass a Particulate Emission Compliance Test?

WBEA Standard Operating Procedure

Provläsningsexemplar / Preview INTERNATIONAL STANDARD ISO First edition

SANTA BARBARA COUNTY APCD GUIDANCE DOCUMENT FOR EMISSION VERIFICATION OF CONTAMINATED SOIL/GROUNDWATER CLEANUP (CSC) PROCESSES

Ambient Air Quality and noise Measurements Report Gas pipeline network at Farshout- Naqada, Waqf, and Qeft - Qena governorate

Ambient Air Monitoring. Bray. 21st October th May 2006

WEATHER MONITORING. Competitive rates available for long term hire. Hire rate Per week Per month

Sampling for particulates

New Developments in Thermal Desorption (TD) Tube & Canister Technologies for Collection & Analysis of Soil Gas

Distinguish between different types of numerical data and different data collection processes.

SURFER (the Surfaces Analyzer) Draft product specifications

Sampling for particulates

Setting The Standard

Air Sampling Instruments for Evaluation of Atmospheric Contaminants (9th ed)

Ambient Air Quality Monitoring

Efficacy of Novaerus NV 1050 System against NO 2 and Formaldehyde Gases

ENVIRONMENTAL ENGINEERING 343

Appendix B: Minimum Monitoring Requirements and 2016 Monitor Classifications in AQS

Ecologix Environmental Systems, LLC

Chapter 15. Air Monitoring. Source Sampling

GE 2211 Environmental Science and Engineering Unit III Air Pollution. M. Subramanian

Ambient Air Monitoring. Wexford. 10 th March st March 2006

Ambient Air Quality and noise Measurements Report Gas pressure reduction station in Marsa Matrouh Governorate

SAMPLING FOR ENVIRONMENTAL MONITORING

Stephenson CO-GENERATION PLANT STACK EMISSION TESTING TOOHEYS PTY LTD LIDCOMBE, NSW PROJECT NO.: 5648/S24184/16 DATE OF SURVEY: 24 MARCH 2016

2004 Network Summary

ENGINEERING DESIGN GUIDE UNITHERM...

CHAPTER 6 : GAS SAMPLING SYSTEMS

NCASI METHOD CI/SG/PULP CHILLED IMPINGER TEST METHOD FOR USE ON PULP MILL SOURCES TO QUANTIFY METHANOL EMISSIONS

Laboratory Testing of Safety Relief Valves

Physical pharmacy. dr basam al zayady

Paper 4: Environmental Chemistry Paper 23: Air pollution controls, their chemistry and continuous monitoring instruments

PM Compliance Options for MACT and MATS Rules. Ed McCall PCME

Title: Standard Operating Procedure for Ambient Air Sampling Using a Versatile Air Pollution Sampler (VAPS) with Annular Denuder System (ADS)

Model 140MX Flowmeter Functional Overview

Title: Standard Operating Procedure for Measurement of CO in Ambient Air by Gas Filter Correlation (GFC)

COMMONWEALTH OF VIRGINIA STATE AIR POLLUTION CONTROL BOARD REGULATIONS FOR THE CONTROL AND ABATEMENT OF AIR POLLUTION

Table of Contents. Preface...

Stephenson CO-GENERATION PLANT STACK EMISSION TESTING TOOHEYS PTY LTD LIDCOMBE, NSW PROJECT NO.: 5522/S23794/15 DATE OF SURVEY: 15 JULY 2015

PRODUCT INFORMATION. Model 140MX Flowmeter Functional Overview. PI 14-1 Rev: 1 March 2002

Analysis of skewness and kurtosis for ambient air quality monitoring data Neyveli thermal plants

Index for Labs under Chemical Engineering

Table of Contents. iii. vi Tables. Figures. viii Foreword. ix Acknowledgments

Title: Operation of ACCU System Particulate Matter sampler in Ambient Air in conjunction with the Tapered Element Oscillating Microbalance (TEOM)

DustCheck DPM-16. Previous Go to PM10-2,5 sampling adding the Wins impactor 9 of 75 Next Go to DustCheck DPM-5. Sequential sampler

Lab. Analytical Services

Draft for comments only Not to be cited as East African Standard

Field Tests of Chloroform Collection/Analysis Methods

STATE OF CALIFORNIA AIR RESOURCES BOARD AIR MONITORING QUALITY ASSURANCE VOLUME V AUDIT PROCEDURES FOR AIR QUALITY MONITORING APPENDIX V

Treatment & Control of Air Pollutants

Flow Conditioning Why, What, When and Where. Gas Flow Conditioning Why, What, When and Where

Contents. Preface to the Third Edition Preface to the Fourth Edition. Part I Air Pollution Essentials

Proposed Guidelines for the Reduction of Nitrogen Oxide Emissions from Natural Gas fuelled Stationary Combustion Turbines

2018 ANNUAL NETWORK PLAN DIVISION OF NATURAL RESOURCES AND ENVIRONMENTAL MANAGEMENT AMBIENT AIR QUALITY MONITORING PROGRAM CITY OF HUNTSVILLE, ALABAMA

Sorbents Evaluation Testing Facilities. 95% removal efficiency or an emission standard of lbs/gw h by 2012, while

Performance Standards for Continuous Ambient Air Quality Monitoring Systems. Environment Agency Version 8 June 2012

2001 Air Monitoring Network

Transcription:

ENVIRONMENTAL PROTECTION AGENCY APTI 435: Atmospheric Sampling Course Student Manual

Table of Contents Chapter 1: An Introduction to Atmospheric Sampling... 1-1 1.1 Introduction... 1-2 1.2 Sampling Train Design... 1-2 References... 1-5 Chapter 2: Basic Gas Properties and Mathematical Manipulations... 2-1 2.1 Temperature... 2-1 The Fahrenheit and Celsius Scales... 2-1 Absolute Temperature... 2-1 2.2 Pressure... 2-3 Definition of Pressure... 2-3 Barometric Pressure... 2-3 Torricelli Barometer... 2-4 Fortin Barometer... 2-4 Aneroid Barometer... 2-7 Pressure Transducers... 2-8 Gauge Pressure... 2-10 Absolute Pressure... 2-10 The Concept of Pressure-Head... 2-12 Dalton s Law of Partial Pressure... 2-12 2.3 The Ideal Gas Laws... 2-13 Boyle s Law... 2-13 Charles Law... 2-13 The Law for Ideal Gases... 2-13 Molar Volume... 2-14 2.4 Gas Density... 2-15 Standard Conditions for Atmospheric Sampling... 2-16 Origin and Definition of Viscosity... 2-16 Kinematic Viscosity... 2-17 Liquid Viscosity versus Gas Viscosity... 2-18 2.5 Reynolds Number... 2-20 2.6 Summary of Useful Equations... 2-22 Temperature... 2-22 i

Pressure... 2-22 Ideal Gas Law... 2-23 Gas Density... 2-23 Viscosity, µ... 2-23 Reynolds Number... 2-23 2.7 Units of Measurements... 2-24 Recommended Units... 2-24 Conversion Problems... 2-26 References... 2-29 Chapter 3: Air Measuring Instruments... 3-1 3.1 Introduction to Air Movers... 3-1 Relationship of Air Movers to Other Sampling System Components... 3-1 Air Mover Classification... 3-2 3.2 Air Mover Selection Criteria... 3-2 Pollutant Concentration and Sampling Time... 3-2 Sampling Rate Required... 3-3 Physical and Chemical Nature of Air to be Sampled... 3-3 Portability of Air Mover... 3-3 Air Mover Noise... 3-3 Air Mover Maintenance... 3-4 Resistance... 3-4 Constant Flow Rate... 3-4 3.3 Pumps... 3-5 Definition and Classification... 3-5 Positive Displacement Pumps... 3-5 Centrifugal Pumps... 3-7 Driving Forces for Pumps... 3-9 Characterisitic Curves... 3-9 Selecting a Pump... 3-10 Pump Gauges... 3-11 3.4 Ejectors... 3-12 Principle of Operation... 3-12 Driving Forces... 3-13 Sampling Use of Ejectors... 3-13 3.5 Liquid Displacers... 3-13 Principle of Operation... 3-13 Sampling by Use of Liquid Displacement... 3-14 3.6 Air Displacers... 3-14 ii

Evacuated Flasks: Principle of Operation... 3-14 Sampling by Use of Evacuated Flasks... 3-15 Plastic Bags: Principle of Operation... 3-14 Sampling by Use of Plastic Bags... 3-15 3.7 Flow Rate Control... 3-15 Control by Diversion... 3-15 Resistance Control... 3-16 Driving Force Control... 3-16 3.8 Flow Rate for Sampling... 3-16 Need for Control... 3-16 Control Mechanisms... 3-17 3.9 Air Measuring Instruments... 3-18 Introduction... 3-18 Types of Air Measuring Devices... 3-18 Calibration... 3-19 3.10 Volume Meters... 3-20 The Spirometer (or Bell Prover ) Primary Standard... 3-20 Displacement Bottle Technique Primary Standard... 3-22 Frictionless Pistons Primary Standard... 3-23 Automated Bubble Flowmeters... 3-27 Automated Dry-Piston Flowmeters... 3-28 Wet Test Meter (WTM) Secondary Standard... 3-28 Roots Meter Secondary Standard... 3-31 Dry Test Meter Secondary Standard... 3-33 3.11 Rate Meters... 3-35 Variable-Pressure Meters Head Meters... 3-35 Variable Area Meters... 3-38 Mass Flow Meters Heat Transfer Meters Hot-Wire Meters 3-40 3.12 Velocity Meters... 3-41 Pitot Tube Primary Velocity Standard... 3-42 Standard Pitot Tube Secondary Velocity Standard... 3-43 S-Type Pitot Tube Secondary Velocity Standard... 3-45 Thermal Anemometer Secondary Velocity Standard... 3-46 3.13 Sample Problems... 3-47 Problem 1: Volume Conversion to Standard Conditions... 3-47 Problem 2: Orifice Conversion When Used at Other Calibration Conditions... 3-47 Problem 3: Conversion for Different Gas Used with a Rotameter... 3-48 Problem 4: Pump Capacity... 3-49 iii

3.14 Additional PM 2.5 Flowmeters and Devices... 3-50 Bubble Flowmeters... 3-50 Piston Flowmeters... 3-50 Mass Flowmeters... 3-50 Orifice Devices... 3-50 Laminar Flow Elements... 3-51 Wet Test Meters... 3-51 Dry Gas Meters... 3-51 References... 3-52 Chapter 4: Particulate Matter Sampling... 4-1 4.1 Introduction... 4-1 Principles of Inertial Collection... 4-5 4.2 Inertial Sampling Devices... 4-6 Impaction Devices... 4-6 Impingement Devices... 4-14 Centrifugal Separation Devices... 4-14 Virtual Impactors Dichotomous Sampler... 4-16 4.3 Collection Efficiency and Penetration Efficiency of Inertial Sampling Devices... 4-21 Definition of Collection Efficiency and Penetration Efficiency 4-21 Impactor Performance Characteristics... 4-22 Properties of Aerosols Affecting Inertial Collection Efficiency... 4-22 Properties of the Collecting Device Influencing Collection Efficiency... 4-23 4.4 Limitations and Sources of Error in Inertial Collection 4-24 Inherent Errors in Sample Collection... 4-24 Errors Associated with the Calibration of Collection Devices... 4-25 Errors in Sample Analysis... 4-25 Size-Selective Inlets and Devices for Aerosol Sampling... 4-25 4.5 Filtration Sampling... 4-32 Introduction... 4-32 General Considerations... 4-32 The Theory of Filtration... 4-33 Collection Efficiency of Filters... 4-34 Characteristics of Filter Media... 4-38 Sample Problems... 4-54 4.6 Gravitational Sampling... 4-55 Dustfall Bucket or Jar... 4-55 Precipitation Collectors... 4-55 iv

4.7 Electrostatic Precipitators... 4-56 Introduction... 4-56 Principles of Electrostatic Precipitation... 4-56 Collection Efficiency... 4-57 Specific Applications... 4-57 4.8 Thermal Precipitators... 4-58 Introduction... 4-58 Collection Efficiency and Depostion Pattern... 4-58 Advantages and Disadvantages of Thermal Precipitators... 4-59 4.9 Summary... 4-59 References... 4-60 Chapter 5: Methodologies and Instrumentation for Particulate Matter Sampling... 5-1 5.1 Introduction... 5-1 5.2 High-Volume Sampling for Suspended Particulate Matter (SPM) and Air Toxics... 5-1 5.3 High-Volume Air Sampling... 5-3 Introduction... 5-3 Development of the High-Volume Sampler... 5-3 Sampler-Shelter Combination... 5-5 Filter Media for High-Volume Sampler... 5-6 Precautions in Filter Handling... 5-8 Calibration... 5-10 U.S. EPA High-Volume Sampling Procedure for TSP... 5-18 Sample Problems... 5-22 Analysis of High-Volume Filters... 5-24 Sampling Accuracy and Precision... 5-25 Accuracy... 5-25 Precision... 5-30 Maintenance... 5-30 Summary... 5-32 5.4 FRM for the Determination of Particulate Matter as PM 10... 5-32 Applicability... 5-32 Principle... 5-32 Range... 5-34 Precision... 5-34 Accuracy... 5-35 Potential Sources of Error... 5-36 v

PM 10 Sampler Apparatus... 5-37 Filter Media... 5-38 Calculations... 5-38 Sample Problems... 5-39 5.5 FRM and FEM for the Determination of Fine Particulate Matter as PM 2.5... 5-41 Reference Methods for PM 2.5 (FRM)... 5-41 Designated Methods for PM 2.5... 5-45 Equivalent Methods for PM 2.5 (FEM)... 5-46 Limitations of PM 2.5 Reference and Class I Equivalent Methods5-47 Approved Regional Methods (ARMs)... 5-48 Calculations... 5-48 Sample Problems... 5-48 5.6 FRM and FEM for the Determination of Coarse Particles (PM 10 -PM 2.5 )... 5-50 5.7 PM 2.5 Speciation Sampling... 5-51 5.8 Continuous in situ Monitoring for Particulate Matter.. 5-55 National Core (NCore)... 5-56 State and Local Air Monitoring Stations (SLAMS)... 5-56 5.9 Automated Federal Equivalent Monitors... 5-56 Beta Attenuation Monitor (BAM)... 5-57 Tapering Element Oscillating Microbalance (TEOM )... 5-58 5.10 Other Automated PM Methods... 5-59 Mass and Mass Equivalent... 5-60 Visible Light Scattering... 5-61 Visible Light Absorption... 5-64 Electrical Mobility... 5-66 Multi-Elemental Analyzer... 5-69 References... 5-74 Chapter 6: Gaseous Sampling... 6-1 6.1 Principles of Absorption... 6-1 Introduction... 6-1 Types of Absorption... 6-1 Physical Absorption... 6-2 Chemical Absorption... 6-2 6.2 Collection Efficiency... 6-3 Factors Affecting Collection Efficiency... 6-3 Absorber Characteristics... 6-3 Chemical Characteristics... 6-4 vi

Physical Characteristics... 6-5 6.3 Determination of Collection Efficiency... 6-5 Absorption Devices... 6-5 Fritted-Glass Absorbers... 6-6 Impingers... 6-9 Summary... 6-10 Current Applications of Absorption in Atmospheric Sampling... 6-10 6.4 Principles of Adsorption... 6-10 Basic Principles... 6-10 Types of Adsorption... 6-11 Variables Affecting Gas Adsorption... 6-12 Adsorption Isotherms... 6-13 Adsorbate Characteristics... 6-14 Adsorbent Characteristics... 6-16 Typical Adsorbents... 6-17 Adsorption Losses in Air Sampling... 6-19 Current Applications of Adsorption in Atmospheric Sampling... 6-19 Summary... 6-22 6.5 Selection and Performance of Wet Collector Media.. 6-23 Introduction... 6-23 Solubility of Pollutant... 6-23 Rate of Reaction... 6-25 Collection Efficiency... 6-25 Retention Characteristics of Absorbent (Solvent)... 6-26 Retention of Gases and Vapor by Chemical Reaction... 6-28 Retention of Particulate Matter... 6-29 6.6 Principles of Grab Sampling... 6-29 Introduction... 6-29 Evacuated Containers... 6-29 Air Displacement or Purging... 6-33 Liquid Displacement... 6-34 Inflation Plastic Bag Sampling... 6-34 Syringes... 6-36 Grab Sampling Techniques... 6-36 Current Applications of Whole Air (Grab and Integrated) Sampling in Ambient Air... 6-36 6.7 Principles of Cryogenic (Freezeout) Sampling... 6-36 Introduction... 6-36 Concept... 6-37 Equipment... 6-37 vii

Single-Stage Units... 6-38 Multistage Units... 6-38 Efficiency... 6-40 Current Applications of Cryogenic (Freezeout) Sampling in Ambient Air... 6-41 Summary... 6-42 References... 6-43 Chapter 7: Standard Methods for Criteria Pollutants... 7-1 7.1 Introduction... 7-1 7.2 Reference Method and Equivalent Method... 7-1 Criteria Pollutants and Measurement Methods... 7-2 Particulate Matter... 7-4 Ozone... 7-6 Carbon Monoxide... 7-7 Nitrogen Dioxide... 7-7 Sulfur Dioxide... 7-8 Lead... 7-10 References... 7-11 Chapter 8 : Introduction to Ambient Air Sampling for Air Toxics... 8-1 8.1 Introduction... 8-1 What are Toxic Air Pollutants?... 8-1 Clean Air Act of 1990... 8-2 Timeline for Air Toxics Monitoring... 8-3 8.2 What is Risk?... 8-5 What is a Risk Assessment?... 8-6 Hazard Identification... 8-7 Weight of Evidence for Health Problems of Concern... 8-7 Exposure Assessment... 8-8 Dose-Response Assessment... 8-8 Dose-Response Relationships... 8-9 Risk Characterization... 8-9 8.3 Introduction to Air Toxics Methods... 8-10 Monitoring Program Goal and Objectives... 8-10 Description of the Methods... 8-13 Compendium Method TO-11A... 8-14 viii

Compendium Method TO-13A... 8-16 Compendium Method TO-15A... 8-18 Compendium Method IO-3.5... 8-20 References... 8-23 Appendix A: Statistical Techniques Employed in Atmospheric Sampling...A-1 A.1 Introduction... A-1 A.2 The Data Quality Objective (DQO) Process... A-2 The Seven Steps of the DQO Process... A-2 Outputs of the DQO Process... A-3 A.3 Data Collection Design... A-3 Data Plotting... A-3 A.4 Graphical Analysis... A-4 Frequency Tables... A-4 The Frequency Polygon... A-6 The Histogram... A-6 The Cumulative Frequency Distribution... A-8 Distribution of Data... A-9 Transformation of Data... A-9 The Logarithmic Transformation... A-10 Probability Graph Paper... A-11 Least-Square Linear Regression... A-12 A.5 Measures of Central Tendency... A-14 Arithmetic Average, or Mean... A-14 Median... A-15 Geometric Mean... A-16 A.6 Measures of Dispersion... A-17 The Range... A-17 Standard Deviation... A-18 Coefficient of Variation... A-19 Standard Geometric Deviation... A-20 A.7 Distribution Curves... A-22 The Normal Distribution... A-22 Lognormal Distributions... A-24 References... A-26 Appendix B: Glossary and Acronyms...B-1 B.1 Glossary... B-1 ix

B.2 Acronyms... B-28 Appendix C: Conversion Factors and Useful Information... C-1 Appendix D: Compendium of Methods for the Determination of Toxic Organic Compounds in Ambient Air, Second Edition... D-1 Appendix E: Compendium of Methods for the Determination of Inorganic Compounds in Ambient Air... E-1 Appendix F: Theory and Calibration Procedures for the Use of a Rotameter... F-1 F.1 Nomenclature... F-1 F.2 Description of a Rotameter... F-2 F.3 Development of Flow Equations... F-3 General Flow Rate Equations... F-3 Computation of Reynolds Number... F-5 F.4 Common Practices in the Use of a Rotameter for Gas Flow Measurement... F-6 Procedures for the Calibration of a Rotameter... F-7 A Universal Calibration Curve... F-8 Development of a Universal Calibration Curve... F-9 F.5 Use of the Universal Calibration Curve for a Rotameter... F-11 To Determine an Existing Flow Rate... F-11 To Establish a Required Sampling Rate... F-11 To Predict Calibration Curves... F-12 Appendix G: Significant Figures and Rounding Off... G-1 G.1 Working with Numbers Intro Problems... G-2 G.2 Approximate Numbers... G-2 Rule 1 (General)... G-3 Rule 2 (General)... G-3 x

G.3 Rounding Approximate Numbers... G-3 Rule for Rounding Approximate Numbers... G-3 G.4 Adding and Subtracting Approximate Numbers... G-4 Truncating Approximate Numbers Following Addition or Subtraction... G-4 G.5 Multiplying and Dividing Approximate Numbers... G-5 Significant Digits... G-5 Truncating Approximate Numbers Following Multiplication or Division... G-6 G.6 Reasonability... G-8 Rule to Meet the Conditions of Reasonability... G-8 G.7 Practice Exercises... G-9 G.8 Answers to Intro Problems... G-10 G.9 Answers to Practice Exercises... G-11 xi