Forensic Chemistry



Forensic Chemistry
Third Edition

Suzanne Bell


Third edition published 2022
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ISBN: 9781138339842 (hbk)
ISBN: 9781032246567 (pbk)
ISBN: 9780429440915 (ebk)
DOI: 10.4324/9780429440915
Typeset in Minion
by codeMantra


To all the dedicated forensic science and chemistry educators and practitioners I have known over my career



Contents
Notes to Readers and Instructorsxv
Acknowledgmentsxvii

SECTION 1  Metrology and Measurement1
1 Making Good Measurements3
Chapter Overview3
1.1 Good Measurements and Good Numbers3
1.2
Significant Figures, Rounding, and Uncertainty4
1.3
Fundamentals of Statistics10
1.4
Accuracy, Precision, and Beyond17
1.4.1
Types of Analytical Errors18
1.5

Hypothesis Testing20
1.5.1
Overview20
1.5.2
Outliers and Other Statistical Significance Tests21
Chapter Summary27
Key Terms and Concepts27
Questions and Exercises28
Further Reading29
Selected Open Source Resources and Articles29
References30
2 Assuring Good Measurements31
Chapter Overview31
2.1
Quality Assurance and Quality Control31
2.1.1
W ho Makes the Rules? International Organizations, Accreditation, and Certification32
2.1.2
Traceability34
2.1.3
Calibration and Control Charts36
2.1.3.1
Calibration36
2.1.3.2
Control Charts37
2.1.3.3
Concentration and Response38
2.2
Method Validation47
2.2.1

Figures of Merit47
2.2.2
Figures of Merit for Qualitative Methods51
2.3
Sampling52
2.3.1
Overview52
2.3.2
Hypergeometric Sampling54
2.4
Measurement Uncertainty (MU)57
2.4.1
Overview57
2.4.2
Identifying Contributing Factors59
2.4.3
Uncertainty Budgets64
2.4.4
Complex Procedures and Measurement Assurance Samples68
2.5
Integration70
Chapter Summary73
Section Summary73
Key Terms and Concepts74

vii


viii    Contents


Questions and Exercises76
Further Reading79
Selected Open Source Articles and Resources79
Articles79
References80

SECTION 2  Chemical Foundations81
3 Chemical Fundamentals: Partitioning, Equilibria, and Acid-Base Chemistry83
Chapter Overview83
3.1
General Considerations83
3.2
An Introductory Example84
3.3
The Special K’s88
3.3.1
Equilibrium Constants88
3.3.2
Solubility Equilibrium Constant Ksp90
3.3.3
Octanol-Water Partition Coefficient Kow (logP)91
3.3.4
Partition Coefficients92
3.3.5
Ka/K b94
3.4
Partitioning96
3.4.1
Solvent and Liquid-Liquid Extractions96
3.4.2

Water Solubility and Partitioning98
3.4.3
Ionization Centers (Ionizable Centers)98
3.4.4
Ionizable Centers, Drug Salts, and Solubility102
3.4.5
Degrees of Ionization104
3.4.6
Integrating Ionizable Centers and Solubility107
3.4.7
Summary A/B, Ionizable Centers, and Solubility108
3.5
Partitioning with a Solid Phase112
3.5.1
Overview112
3.5.2
Solid Phase Partitioning112
3.5.3
Partition and Extractions117
3.6
Partitioning with a Moving Phase119
Chapter Summary122
Key Terms and Concepts122
Questions and Exercises123
Further Reading125
Selected Open Source Resources and Articles125
References125
4 Chromatography and Mass Spectrometry127
Chapter Overview127
Overview of Chromatography127

4.1
Gas Chromatography128
4.2
4.2.1
Overview128
Instrumental Systems129
4.2.2
4.2.3
Efficiency Measures130
4.2.4
Theory131
Retention Index133
4.2.5
GC Columns136
4.2.6
Gas Chromatography Detectors136
4.2.7
4.3
Liquid Chromatography137
4.3.1
HPLC and UPLC137
4.3.2
Liquid Chromatography Detectors141
Mass Spectrometry141
4.4


Contents   ix

4.4.1

Overview141
4.4.2
GC-MS and Quadrupole Mass Filters141
4.4.3
ICP-MS145
4.4.4
Ambient Pressure Ionization Sources147
4.4.5
Tandem Mass Spectrometry150
4.4.6
High-Resolution Mass Spectrometry (HRMS)154
4.4.7
DART-MS161
4.4.8
Isotope Ratio Mass Spectrometry (IRMS)162
4.5
Electrophoresis166
Chapter Summary168
Key Terms and Concepts169
Questions and Exercises171
Further Reading172
Selected Open Source Articles and Resources172
References172
5 Spectroscopy175
Chapter Overview175
5.1
Electromagnetic Energy176
5.2
Spectroscopy177
5.2.1

The Basics177
5.2.2
Instrument Components180
5.2.3
Detectors184
5.2.4
Instrument Designs185
5.2.5
Bandwidth and Resolving Power185
5.3
Types of Spectroscopy188
5.3.1
U V/VIS Spectroscopy188
5.3.2
Infrared Spectroscopy192
Raman Spectroscopy197
5.3.3
5.3.4
NMR Spectroscopy200
5.3.5
X-Ray Spectroscopy and Scanning Electron Microscopy203
Chapter Summary207
Section Summary207
Key Terms and Concepts208
Questions and Exercises210
Further Reading210
Selected Open Source Resources and Articles210
References210

SECTION 3  Drugs and Poisons211

6 Overview of Drug Analysis215
Chapter Overview215
6.1
Classification215
6.2
Legislation and Regulation217
6.3
Data Sources221
6.4
Drugs as Physical Evidence226
6.4.1
Five P’s226
6.4.2
Adulterants, Cutting Agents, and Impurities228
6.4.3
Clandestine Synthesis229
6.4.4
Profiling234
6.5
Overview of Chemical Analysis of Illicit Drugs239
6.5.1
W hat Is Definitive Identification?241


x    Contents

6.5.2
Chemistry of Color Tests242
6.6
Current Issues: Marijuana248

Chapter Summary254
Key Terms and Concepts254
Questions and Exercises256
Further Reading257
Selected Open Source Articles and Resources257
Articles257
References258
7 Novel Psychoactive Substances263
Chapter Overview263
7.1
History264
7.2
Legislation, Regulation, and Chemical Similarity265
7.3
Categories of NPSs269
7.3.1
Cannabinoids269
7.3.2
Stimulants and Hallucinogens273
7.3.3
Opioids279
7.4
Laboratory Approach for NPSs283
7.4.1
Analytical Schemes283
7.4.2
Non-target Analysis288
7.5
Case Examples291
Summary

300
Key Terms and Concepts300
Review Questions and Exercises301
Selected Open Source Articles and Resources302
References302
8 Fundamentals of Toxicology307
Chapter Overview307
Pharmacokinetics308
8.1
8.1.1
Ingestion308
Absorption309
8.1.2
8.1.2.1
Oral Ingestion311
8.1.2.2
Bioavailability313
Distribution317
8.1.3
Metabolism and Elimination: Kinetics319
8.1.4
Summary of ADME with Calculations and Applications321
8.1.5
Metabolism: Biochemical Aspects324
8.1.6
Tracking a Dose332
8.1.7
8.1.8
Endogenous vs Exogenous Substances333
8.2

Dosage Considerations and Lethal Concentrations333
8.3
Mechanism of Action335
Chapter Summary339
Key Terms and Concepts340
Questions and Exercises342
Further Reading343
Selected Open Source Articles and Resources343
References343
9 Applications of Forensic Toxicology345
Chapter Overview345
9.1
Types of Forensic Toxicology345
9.2
Sample Types348


Contents   xi

9.2.1
Blood and Plasma348
9.2.2
Urine349
9.2.3
Vitreous Fluid350
9.2.4
Tissues and Other Samples352
9.2.5
Hair352
9.2.6

Oral Fluid352
9.2.7
Ion Trapping and Relative Concentrations353
9.3
Analytical Methods356
9.3.1
Immunoassay357
9.3.2
MS methods359
9.4
Forensic Toxicology in Practice360
9.4.1
Ethanol360
9.4.1.1
A lcohol Metabolism361
9.4.1.2
Absorption, Distribution, and Elimination361
9.4.1.3
Breath Alcohol368
9.4.1.4
BAC Laboratory Analysis369
9.4.2
Postmortem Toxicology370
9.4.2.1
Postmortem Redistribution370
9.4.2.2
Tracking Doses across Tissues and Fluids371
9.5
Integrated Examples and Cases372
9.5.1

Heroin372
9.5.2
Bupropion373
9.5.3
NPS Mixed Drug Fatality377
Chapter and Section Summary379
Key Terms and Concepts380
Questions and Exercises382
Further Reading382
Selected Open Source Articles and Resources382
References383

SECTION 4  Combustion Evidence387
10 Overview of Combustion Chemistry389
Chapter Overview389
10.1
Combustion Basics389
Overview389
10.1.1
Reaction Mechanisms and Kinetics391
10.1.2
Types of Combustion394
10.1.3
Smoldering394
10.1.3.1
Flames and Ignition398
10.1.3.2
Thermodynamics of Combustion Reactions401
10.2
General Considerations401

10.2.1
10.2.2
Stoichiometry404
Mass and Heat Transfer408
10.2.3
Propagation411
10.3
Deflagration to Detonation413
10.3.1
10.4
Fire Behavior416
10.4.1
Propagation over Liquids417
Walls and Inclined Surfaces418
10.4.2
Ceiling Jets and Flashover423
10.4.3
Chapter Summary426
Key Terms and Concepts426
Review Questions and Exercises428


xii    Contents

Further Reading428
Selected Open Source Resources and Articles429
References429
11 Fire Investigation and Fire Debris Analysis431
Chapter Overview431
11.1

Fire Investigation431
11.2
Fire Debris Analysis434
11.2.1
Preconcentration Methods435
11.2.2
Data Analysis and Interpretation437
11.2.2.1
Chemical Pattern Evidence437
11.2.2.2
Detection Limits440
11.2.2.3
Matrix and Substrates440
11.2.2.4
Weathering and Environmental Degradation442
11.3
Forensic Investigation of Fire Deaths453
11.3.1
Mechanism of Toxicity456
11.3.2
Analytical Methods458
11.3.3
Integration with Autopsy462
Chapter Summary464
Key Terms and Concepts464
Review Questions and Exercises465
Further Reading466
Selected Open Source Articles and Resources466
References466
12 Explosives469

Chapter Overview469
12.1
Explosions and Explosive Power469
12.1.1
Types of Power469
12.1.2
Classification Schemes470
Chemical and Thermodynamic Considerations472
12.2
12.2.1
Balancing Equations472
Oxygen Balance476
12.2.2
12.2.3
Explosive Power and Thermodynamic Calculations478
12.2.4
Balancing Summary482
Explosive Devices482
12.3
Pipe Bombs482
12.3.1
Other Types of IEDs and Explosives487
12.3.2
Forensic Analysis of Explosives487
12.4
Stand-off Detection488
12.4.1
12.4.1.1
Vapor Phase Detection488
12.4.1.2

Spectroscopy491
12.4.2
Laboratory Analysis of Explosives494
12.4.2.1
Overview494
12.4.2.2
Ion Chromatography496
12.4.2.3
Mass Spectrometry498
12.5
Integrated Example502
Chapter Summary508
Key Terms and Concepts508
Questions and Exercises509
Further Reading509
References509


Contents   xiii

13 Firearms and Firearms Discharge Residue513
Chapter Overview513
13.1
How Guns Work513
13.2
Primers and Propellants517
13.3
Forensic Analysis of FDR and GSR525
13.3.1
Color Tests and Distance Estimations526

13.3.2
GSR529
13.3.3
Organic Gunshot Residue537
13.3.4
Time Since Discharge539
13.3.5
Implications541
13.4
Serial Number Restoration545
Chapter Summary552
Section Summary552
Key Terms and Concepts552
Questions and Exercises554
Further Reading554
Selected Open Source Resources and Articles555
References556
14 Forensic Chemistry and Trace Evidence Analysis559
Chapter Overview559
14.1
Trace Evidence Overview559
14.1.1
Chemical Pattern Evidence Revisited560
14.1.2
Example Scenario560
14.2
Successive Classification563
14.3
Characterizing Color567
14.3.1

Making Color Quantitative567
14.3.2
CIE System568
14.3.3
Munsell System577
14.3.4
Other Systems and Conversions578
14.3.5
Colorants579
14.4
Example Types of Trace Evidence581
14.4.1
Fibers581
14.4.2
Paint587
14.4.3
Glass592
Chapter Summary595
Key Terms and Concepts595
Questions and Exercises597
Further Reading598
Selected Open Source Resources and Articles598
References598
Appendix 1: Glossary of Terms
599
Appendix 2: Abbreviations
619
Appendix 3: Tables for Statistical Testing
629
Appendix 4: Selected Thermodynamic Quantities

631
Appendix 5: Selected and Characteristic Infrared Group Frequencies
633
Appendix 6: Selected 1H NMR Chemical Shifts
635
Appendix 7: Periodic Table of the Elements
637
Index639



Notes to Readers and Instructors
So much has changed in the field since the second edition was published a decade ago that this edition consists of
mostly new or completely revamped sections and material. The sections remain the same although the multiple chapters regarding materials and trace evidence have been condensed to one chapter. A new chapter on novel psychoactive
substances is included in the four sections that cover drug analysis (seized drugs and toxicology).
Additional pages have been devoted to the rapid advances in mass spectrometry as applied in forensic chemistry
and there are now two chapters covering instrumental methods, one on chromatography, mass spectrometry, and
capillary electrophoresis, and the other on spectroscopy including a new section on nuclear magnetic resonance.
Additional emphasis has been placed on statistical methods and treatments.
The introductory chapters have been condensed to two to allow readers to dive into chemistry quickly. You will find
a new post-chapter section on open access resources and articles that anyone can access and download. An effort
has been made to provide links to web resources most referenced by forensic chemists and the text reflects the field’s
growing reliance on electronic resources over hard copy reference books.
Finally, it is critical to note that this book is not meant to be a definitive treatment of any one area of forensic chemistry. It is meant to introduce the topic, provide a foundational background of the chemistry involved, and illustrate
how it is applied. Similarly, it is not intended as a primary reference in a judicial setting. For working professionals, it
is well suited as a reference guide and to refresh skills and knowledge, but it is not a manual.

xv




Acknowledgments
I am grateful to Mark Listewnik of Taylor & Francis/CRC Press for welcoming the text and giving it a new home. I
am indebted to Fred Coppersmith who organized such thorough reviews and to all the reviewers who assisted him
in that task. The development team provided in-depth feedback and summaries that were immeasurably helpful in
­developing this work. I had invaluable assistance from Colby Ott, Joseph Cox, and Erica Maney, PhD students in the
Department of Forensic and Investigative Sciences at West Virginia University. Their careful review and sharp eyes
were invaluable.

xvii



Section 1
Metrology and Measurement

1

Forensic chemistry is analytical chemistry, and analytical chemistry is about making measurements. The
data produced by a forensic chemist is data that has consequences. Decisions are made based on this data
that can impact society and lives. The responsibility of the forensic analytical chemist is to make the best
measurements possible. Accordingly, that is where we will begin our journey through forensic chemistry.
How do you know that your data is as good as it can be? How do you ensure that your data is reported and
interpreted with all the necessary information? By applying the principles that underlie measurement science. Figure I.1 presents an overview of this section and the topics covered in the next two chapters.

Figure I.1  Overview figure for this section. Our focus will be on events and procedures that occur within the l­aboratory.
The unifying themes are metrology, statistics, and ensuring the goodness of data.

DOI: 10.4324/9780429440915-11



2    Forensic Chemistry

This book focuses on the analysis of evidence once it enters the doors of the laboratory (Figure I.1). As soon as the
evidence is received, a paper (and digital) trail begins that will ensure that the evidence is protected by a clear chain of
custody. This means that every transfer of the evidence is documented, and a responsible person identified. Subsamples
may be needed for large seizures, a topic we explore in this chapter. The next section goes into detail on sample preparation and the analytical methods. Our focus in this section is the foundation of these procedures including selection
and validation of analytical methods, establishing the limits and performance of methods (figures of merit), and how
we ensure methods are operating as expected (quality assurance and quality control). Integrated into any chemical
analysis is evaluation, interpretation, and reporting of results. The entity that submitted the evidence needs specific,
clear, and complete information. Providing it requires more than outputs and values. Sufficient information and context are essential, and this includes more than a number. We will address this using the NUSAP system.
Underlying the section topics are principles of measurement science. These concepts extend beyond chemistry and
include any situation in which human beings make a measurement. Because we design instruments and equipment
for this purpose, significant figures must be considered. Hopefully, you will find the treatment of this subject here less
daunting that you may be used to. We will see how statistics is integrated into any measurement process and how all
these factors come together to ensure the “goodness” of data which can be thought of as its pedigree.
Forensic data has consequences and laboratory results can impact lives (far right of Figure I.1). Accordingly, forensic
chemists must produce good data. How do we evaluate the goodness of data? In the context of forensic chemistry, we
first evaluate its utility and reliability. Does it answer the question pertinent to the issue at hand? Does it provide the
information needed by the decision makers (law enforcement or the legal system)? Is the data correct and complete?
We summarize these considerations based on utility and reliability. The other criteria we will use in the evaluation of
data and methods are reasonable-defensible-fit-for-purpose. Suppose a blood sample is submitted for blood alcohol
analysis. The method used must be reasonable, defensible to scientists and laypeople, and it must answer the question:
What is the blood alcohol concentration? If it does, then the method is fit-for-purpose.
The first chapter in this section explores measurement science or metrology. Metrology is based on an understanding
of making measurements and characterizing them using the appropriate tools and techniques. Key among these tools
are significant figures and statistics. We will cover that in Chapter 1, and with this background, we will introduce
terms such as error and other associated terms vital to metrology. You will find that definitions used in everyday conversation for terms such as accuracy, precision, error, and uncertainty are incorrect or incomplete in a metrological
and analytical context. Once the section is complete, you will understand how forensic chemists produce reasonable,
defensible, and reliable data. In other words, you will know what is meant by “good data” and how to generate it.



Chapter 1
Making Good Measurements

CHAPTER OVERVIEW
Forensic data has consequences for individuals and society. The measurements generated in forensic chemistry must
be acquired with care and expressed properly, neither over- nor understated, and with all necessary descriptors and
qualifiers. How measurements are generated and reported is critical. Understanding how measurements are made
starts with significant figures. We will not go through dry rules and exercises; rather, we will explore where significant figures come from and how they are used. What a number means and how it should be interpreted involves basic
statistics. We will review foundational concepts, but it is assumed that you are already familiar with the basics. If not,
now is a good time to do a quick review before delving into the chapter. The chapter will conclude with a discussion
of hypothesis testing, which is a useful tool to add to your measurement science toolkit.

1.1 GOOD MEASUREMENTS AND GOOD NUMBERS
Metrology is the study of measurement and producing good numbers, but how do we judge if a number is “good?” In
the forensic context, we can describe goodness as a function of utility and reliability. Does the data answer, or provide
the information needed to answer, the relevant question(s)? Do we trust this data? How much do we trust it? We will
add to this utility/reliability criteria as we move through this and the next chapter.
It is difficult to encompass the depth and breadth of metrology, given that it spans many disciplines, trades, and industries. The topic can seem daunting even to experienced forensic and analytical chemists but fear not. As we move through
this discussion, you will find that most metrological principles are familiar. What may be new is how they are integrated
under the umbrella of metrology. The goal is to make good measurements and produce useful and reliable data.
To focus on metrology in forensic chemistry, we will utilize a NUSAP system concept for quantitative data presentation. While not used explicitly in forensic chemistry, its concepts are making it an ideal platform for evaluating the
reliability of results [1–6]. NUSAP stands for Number-Units-Spread-Assessment-Pedigree and contains qualitative
and quantitative criteria associated with a numerical result such as the weight of a powder or blood alcohol concentration. The NUSAP system has been used for policy decisions, such as environmental modeling and risk analysis, all
areas that, like forensic science, create data upon which critical decisions depend.
Consider a net weight of a white powder reported as follows:
77.56 ± 0.31 g at the 95% confidence level
As shown in Figure 1.1, this expression can be broken down into individual components. The measurand is the quantity being measured or determined, here the weight of a powder. The number (N) is 77.56; the units (U) are grams
(g), and the spread (S) is ± 0.31 g. These are the quanvtitative elements of the reported value. The spread (or estimated

uncertainty) of the result could have been obtained in several ways; many will be discussed later in this chapter and
revisited in Chapter 2. The Student’s t-value was used here to obtain a confidence interval, a common approach, but
hardly the only one. This descriptor (95% confidence interval, or CI) is the assessment (A) of the spread.
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3


4    Forensic Chemistry

Figure 1.1  The NUSAP approach to characterizing a measured value.

The N and S are quantitative values, and U is a descriptor, but even this expression is incomplete without one additional and critical factor: the pedigree (P). The pedigree of a reported result refers to the history or precedent used
to gather the data; it encompasses everything done to stand behind that data’s reliability. Pedigree includes quality
assurance and quality control (QA/QC, Chapter 2) and many other factors. Additional elements include traceability
of weights and standards, laboratory protocols and methods, analyst training, laboratory accreditation, and analyst
certification, all of which support the reported value’s reliability.
An essential element of NUSAP is an estimate of uncertainty. Uncertainty is part of any measurement and is the
spread or variation of the results. Because this spread has an assessment and a pedigree associated with it, stating the
uncertainty imparts greater credibility and trust in a result, not less. Uncertainty is related to ensuring the reliability
of the data, one of our primary goals. Forensic reports may not include all the components incorporated in a NUSAP
approach, but this information and data should be available. Uncertainty must be known and producible should it be
needed by the courts, law enforcement, or other data users.
Before we delve too deeply into the topic of uncertainty, two points must be emphasized. First, in this book’s context,
uncertainty is defined as the expected spread or dispersion associated with a measured result. There are many ways to
characterize this range, and we examine several in this portion of the text. Uncertainty in this context does not imply
doubt or lack of trust in the measured result. Just the opposite is true. Reporting a reliable and defensible uncertainty
adds to the validity, reliability, and utility of the data. The second point is to distinguish between uncertainty and
error. In our context, error is defined as the difference between an individual measured result and the true value (i.e.,
the accuracy). Error and uncertainty are not synonymous and should not be treated the same, although both are

important to making and reporting valid and reliable results. In this chapter, we will examine a simplified approach
to calculating uncertainty. Later, we will integrate additional information to generate more realistic and defensible
estimates of uncertainty. Finally, keep in mind that we estimate uncertainty; it can never be known exactly.

1.2 SIGNIFICANT FIGURES, ROUNDING, AND UNCERTAINTY
In math and science courses, you have been introduced to significant figures and practiced rounding based on
significant figures using worksheets and problem sets. While the practice is valuable, it can make significant figures
seem artificial and more of a mathematical construct than a metrological one. Nothing could be farther from the
truth. Significant figures arise from the instruments used to measure quantities. Many instruments and devices can
contribute to the determination of significant figures, but in the end, measurement devices and our reading of them
dictate significant figures.
Why is this concept so important? Because forensic data has consequences. Consider a blood alcohol concentration.
A blood alcohol level of 0.08% is the typical cutoff for intoxication. How would a value of 0.0815 be interpreted? What
about 0.07999? 0.0751? Should these values be rounded off or truncated? If they are rounded, to how many digits?
Instrumentation and devices used to obtain the data dictate how to round numerical values. In this artificial but telling example, incorrect rounding could mean the difference between no charges, the loss of a driving license, legal


Making Good Measurements   5

Figure 1.2  Bathroom scale readings and significant figures. Significant figures are every figure (digit) that we are sure of plus one
so both weights have 4 significant figures. Three are certain and the fourth is an estimate. Even the last digit from the digital scale
is an estimate.

action, or allowing a dangerous person to keep driving. Significant figures become tangible in analytical chemistry –
they are real and they matter. The rules of how significant figures are managed in calculations are covered in many
introductory classes, so we will focus on the highlights. You should review these rules to get the most out of this
section. The rules and practices of significant figures and rounding must be applied properly to ensure that the data
presented are not misleading, either because there is too much precision implied by including extra unreliable digits
or too little by eliminating valid ones.
The number of significant digits is defined as the number of digits that are certain, plus one. The last digit is uncertain

(Figure 1.2), meaning that it is a reasonable estimate. Consider the top example of an analog scale in the figure. One
person might interpret the value as 125.4 and another as 125.5, but the value is definitely greater than 125 pounds and
definitely less than 126. In the lower frame, the digital scale provides the last digit, but it is still an uncertain digit.
Just because it is digital, it is not automatically “better.” The electronics are making the rounding decision instead of
the person on the scale. The same situation arises when you use rulers or other devices with calibrated marks. Digital
readouts of many instruments may cloud the issue a bit, but lacking a specific and justifiable reason, assume that the
last decimal on a digital readout is uncertain.
Recall that zeros have special rules and may require a contextual interpretation. As a starting point, convert the
number to scientific notation. If this operation removes the zeros, then they were placeholders representing a multiplication or division by 10. For example, suppose an instrument produces a result of 0.001023 that can be expressed
as 1.023 × 10−3. The leading zeros are not significant, but the embedded zero is. The number has four significant digits.
Trailing zeros can be troublesome. Ideally, if a zero is meant to be significant, it is listed, and conversely, if a zero was
omitted, it was not significant. Thus, a value of 1.2300 g for a weight means that the balance displayed two trailing
zeros. It would be incorrect to record a balance reading of 1.23 as 1.2300. The balance does not “know” what comes
after the three, so neither do you. Recording that weight as 1.2300 would conjure up numbers that were useless at
best and deceptive at worst. If this weight were embedded in a series of calculations, the error would propagate, with


6    Forensic Chemistry

potentially disastrous consequences. “Zero” does not imply “inconsequential,” nor does it imply “nothing.” In recording a weight of 1.23 g, no one would arbitrarily write 1.236, so why should writing 1.230 be any less wrong?
Another ambiguous situation is associated with numbers with no decimals indicated. For example, how many significant figures are in 78? As with zeros, context is needed. If we are counting the number of students in a room, this
is a whole, exact number. This number itself would not factor into significant figure determinations. The same is true
of values like metric conversions. Each kilogram is comprised of 1,000 g. It is not 1000.2 rounded down; 1000 is an
exact number. If used in a calculation, you would assume an infinite number of significant figures; like 78 above, the
number of digits plays no role in rounding considerations. You may see notations such as 327 with a decimal point
placed at the end of the number (i.e., 327.). This is done purposely to tell you that this number has three significant
digits; it is not meant to represent a whole number or exact conversion factor.
While metric conversions are based on exact numbers, not all conversions are. For example, in upcoming chapters,
we will routinely convert body weights in pounds to kilograms and vice versa. The conversion factor for that calculation is 1 pound = 0.45359237 kg. It is up to you to decide how many significant figures are required for the calculation.
When in doubt, keep them all and round at the end, but work on developing judgment skills that allow you to select

the appropriate number. The more digits kept, the more likely a transposition error. If you really do not need eight
digits, do not use eight. Keeping extra digits does not make a conversion any “better” or “more exact.” How do you
know how many is enough? In cases where you have a choice, never allow the number of significant figures in a conversion factor to control the rounding of the result.
In combining numeric operations, round at the end of the calculation. The only time that rounding intermediate
values may be appropriate is with addition and subtraction operations, although caution is advised. If you must
round an addition/subtraction, rounded to the same number of significant digits as there are in the number with the
fewest digits, with one extra digit included to avoid rounding error. For example, assume that a calculation requires
the formula weight of PbCl2:
Pb = 207.2


g
g
; Cl = 35.4527
s
mol
mol

g
207.2 + 2 ( 35.4527 ) = 278.1054 = 278.1
mol



The formula weight of lead has one decimal which dictates where rounding occurs.
Figure 1.3 presents another example of rounding involving calculations. Here we are calculating mileage in miles per
gallon (mpg). The same concepts hold for calculating kilometers per liter (km/L). Two instruments are used, and we

Figure 1.3  Rounding in multiplication and division. Both values have four significant figures, so the calculated result is rounded
to four.