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To be a good medical writer, you need to know something 

about mathematics. Mathematics is the art of number, and 

numbers originated from words that were coined for the pur-

pose of counting. However, some things can be counted, and 

some things cannot.

Count and Noncount Nouns
Discrete (as opposed to discreet!) means separate and distinct 

from other things. Objects that are discrete can be counted. For 

example, you might count the number of apples in a basket, 

but you can never count the number of gasoline in a tank. For 

this reason, apple is a count noun, but gasoline is a noncount 

noun. So you can ask, “How many apples are in the basket?” 

but it would be ungrammatical to ask, “How many gasolines 

are left in the tank?” Instead, you might ask, “How much gaso-

line is left in the tank?”

 Many is used with count nouns; much is used with non-

count nouns. Some quantifiers (eg, all, any, enough, most, 

plenty of, some, and no) can be used with count or noncount 

nouns. However, there are some quantifiers that are used only 

with count nouns (eg, every, many, a few) and others that are 

used only with noncount nouns (eg, much, less, a little).

 If we want to talk about more than 1 of something in 

English, we use the plural form of the noun. The plural form 

is usually made by adding s or es to the end of the noun. 

However, there are many exceptions (see Table on next page). 

These include some words of Anglo-Saxon origin, such as 

child/children, or woman/women, ox/oxen, goose/geese. Note 

that many of the animal nouns that came from Anglo-Saxon 

are the same in singular and plural: fish, sheep, moose. Many 

words of Greek or Latin origin that are important in medicine 

have irregular plural forms: bacterium/bacteria, corpus/

corpora, genus/genera, medium/media, species/species,  

stigma/stigmata.

 For some nouns with irregular plurals and some non-

count nouns, a regular plural form has become commonplace 

or is used in specific circumstances. For example, water is a 

noncount noun. However, the word waters is used to refer to 

a watery geographical area (eg, the navigable waters of the 

United States) or in some poetic contexts. Amniotic fluid, 

which surrounds the fetus in the womb, is also sometimes 

called waters.

Collective Nouns
A collective noun is a noun that refers to a group (set) of per-

sons or things. For example, a swarm refers to a group of 

insects, and a choir refers to a group of singers. This raises 

problems of agreement with pronouns and verbs. Should you 

refer to the collective as “it” or “them”? Should you use the 

singular or plural form of the verb to refer to the collective’s 

actions? The answer depends on whether the individual mem-

bers or the group is being emphasized:

• The emergency department staff are trained in the latest 

resuscitation techniques (emphasizing individuals).

• The hospital’s emergency department staff is the best in 

the city (emphasizing the group).

 Note that British people are more likely than Americans to 

use plural pronouns and verbs for collectives, such as  

businesses:

• Bloomingdale’s is having a sale on swimsuits (United States).

• Fenwick are having a sale on swimming costumes (Britain).

Units of Measure
Many things that cannot be counted can nevertheless be mea-

sured. To measure them, we need to find some unit of mea-

sure. For example, we can say “1 liter of water” or “2 bushels of 

wheat.” Please notice the grammatical structure: the number 

Counting and Measuring
Laurie Endicott Thomas, MA, ELS / Madison, NJ



122 AMWA Journal / V36 N3 / 2021 / amwa.org 

Singular Plural

addendum addenda, also addendums

aircraft aircraft

alumna alumnae

alumnus alumni

analysis analyses

antenna antennae, also antennas

antithesis antitheses

apex apices, also apexes

appendix appendices, also appendixes

axis axes

bacillus bacilli

bacterium bacteria

basis bases

beau beaux, also beaus

bison bison

bureau bureaus, also bureau

cactus cacti, also cactus or cactuses

château châteaux, also châteaus

child children

codex codices, also codexes

concerto concerti, also concertos

corpus corpora

crisis crises

criterion criteria, also criterions

curriculum curricula, also curriculums

datum data

deer deer 

diagnosis diagnoses

die dice, also dies

dwarf dwarves, also dwarfs

ellipsis ellipses

erratum errata

faux pas faux pas

fez fezzes, also fezes

fish fish, also fishesa

focus foci, also focuses

foot feet, sometimes foot

formula formulae, also formulas

fungus fungi, also funguses

genus genera, also genuses

goose geese

graffito graffiti

grouse grouse, also grouses 

half halves

hoof hooves, also hoofs 

hypothesis hypotheses

index indices, also indexes

lacuna lacunae

larva larvae

leaf leaves

libretto libretti, also librettos

loaf loaves

locus loci

louse lice

man men

matrix matrices, also matrixes 

medium media, also mediums 

memorandum memoranda, also memorandums

minutia minutiae

moose moose

mouse mice

nebula nebulae, also nebulas

nucleus nuclei

oasis oases

octopus octopuses or octopodes

offspring offspring

opus opera

ovum ova

ox oxen, also ox

parenthesis parentheses

phenomenon phenomena

phylum phyla

quiz quizzes

radius radii

referendum referenda, also referendums

salmon salmon

scarf scarves

schema schemata, also schemas

self selves

series series

sheep sheep

shrimp shrimp, also shrimpsa

species species

stigma stigmata

stimulus stimuli

stratum strata

swine swine

syllabus syllabi, also syllabuses

symposium symposia, also symposiums

synopsis synopses

tableau tableaux, also tableaus

thesis theses

thief thieves

tooth teeth

trout trout, also troutsa

tuna tuna, also tunasa

vertebra vertebrae, also vertebras

vertex vertices, also vertexes

vita vitae

vortex vortices, also vortexes

wharf wharves, also wharfs

wife wives

wolf wolves

woman women

Singular Plural

Table. Irregular English Plurals

aThe former is typically used to refer to more than 1 individual of the same species, and the  latter is typically used to refer to more than 1 species.



      AMWA Journal / V36 N3 / 2021 / amwa.org    123

is an adjective modifying the unit of measure. The unit of mea-

sure is a noun. The material being measured is now the object 

of a prepositional phrase (“of water”). If you are talking about 

some noncount noun that is being measured in this way, it will 

be treated as if it were a singular: 20 kilometers is (not are) a 

long walk.

 A unit of measure is arbitrarily defined; thus, the number 

associated with a measurement is meaningless unless the unit 

of measure has been defined, so you must carefully specify 

units of measure. Units of measure typically relate to some nat-

ural phenomenon. For example, the inch was originally based 

on the width of a man’s thumb, and the foot was based on the 

length of a man’s foot. The main basis of the International 

System of Units (SI, for Système International [d’unités]) is the 

meter. The SI grew out of the metric system that was developed 

in Revolutionary France. The meter was supposedly based on 

1/10,000 of the distance from the North Pole to the Equator. 

Other units of measure in the SI were derived from the meter. 

A centimeter is 1/100th of a meter. A liter is 1,000 cubic cen-

timeters, and a kilogram originally represented the mass of a 

liter of water. A newton is the amount of force to make a 1-kg 

object accelerate 1 meter per second per second. Thus, mea-

surements of force involve units of time as well as units of mass 

and distance.

 The SI also includes many units that are important in phys-

ics and chemistry. A coulomb (C) is a measure of electrical 

charge, and an ampere (A) is a measure of electrical current. A 

candela (cd) is a measure of luminous intensity. A mole (mol) 

is a measure of the amount of a substance. A mole is defined 

as 6.02214076 × 1023 particles (eg, atoms or molecules). The 

number of particles in a mole is called Avogadro’s number.

 Our measurements of time were originally derived from 

the duration of a day. Each day is divided into 24 hours, and 

each hour into 60 minutes, each minute into 60 seconds. 

The 60-minute hour and 60-second minute are legacies of 

the ancient Mesopotamians, who used the number 60 as the 

basis of their number system. (The number 60 is the small-

est number that can be divided evenly by every whole number 

from 1 to 6.) The ancients also divided a circle into 360°—partly 

because 360 can be evenly divided by so many different num-

bers and partly because 360 is close to the number of days in 

the year. (The lunar calendar has 355 days, and the solar cal-

endar has 365 days). Thus, the sun would advance roughly 1° 

along the ecliptic (its circular path relative to the background 

of stars) every day.

Whole and Real Numbers
When we count objects, the result will be an integer. But when 

we measure the amount of something, as opposed to count-

ing the number of items, the result would theoretically be a 

real number, along with a unit of measure. A real number is a 

number that can be expressed as some point along a number 

line. To express a measurement, however, we will end up using 

a rational number, as we will report only a limited number of 

digits after the decimal point. A rational number is one that 

can be expressed as a quotient or fraction of 2 integers. Its  

decimal expansion, if it has one, will either terminate or end  

up repeating itself endlessly. For example, ¾ = 0.75 and  

¹/³ = 0.33333…. (sometimes written 0.3, with the overbar repre-

senting the repeating decimal expansion). In contrast, irratio-

nal numbers have a decimal expansion that continues forever 

without repeating. Examples include p (the ratio of the circum-

ference of a circle to its diameter), e (Euler’s number, which is 

useful for calculating compound interest), and the square  

root of 2.

 Using different units (eg, miles vs kilometers) will yield a 

different number, so you have to include the units with the 

number. Which unit of measure should you use? In scientific 

writing, you should use the SI (meters, kilometers, kilograms, 

etc). But if you are writing for consumers in the United States, 

you should probably use the units that are familiar to consum-

ers (feet and inches, miles, pounds and ounces, etc).

Accuracy, Precision, and Uncertainty
Accuracy refers to how well a measurement agrees with the 

truth. In contrast, precision refers to the agreement among 

repeated measurements (made under the same conditions). 

Thus, a measurement that is accurate may be imprecise, and a 

measurement that is precise may be inaccurate. When choos-

ing between methods of measurement, you often have to make 

a tradeoff between precision and accuracy. For example, a digi-

tal clock displays a precise, rational number, but that reading 

does not represent the true time. In contrast, an analog clock 

expresses time as a real number that cannot be read precisely.

 Both inaccuracy and imprecision contribute to uncer-

tainty. All measurements, and all quantities calculated from 

measurements, will have some degree of uncertainty. The 

degree of uncertainty can be expressed in various ways. One 

is by showing only a limited number of significant digits. For 

example, a reported value of 3.5 implies that the actual value 

is probably somewhere between 3.45 and 3.55. In contrast, a 

reported value of 3.50 implies that the actual value is prob-

ably somewhere between 3.495 and 3.505—a much narrower 

range. You can also express the uncertainty in units of measure 

or as a percentage of the total value: 25.2 mL ± 0.05 mL can be 

expressed as 2.52 mL ± 0.2%.



124 AMWA Journal / V36 N3 / 2021 / amwa.org 

 Even when we are dealing with counts, such as the number 

of people who live in a city, we sometimes have to deal with 

uncertainty. As a result, we may have to settle for an approxi-

mate number, such as when we say that the population of New 

York City was 8.40 million in 2018. Nor should we report too 

many digits after a decimal point: we shouldn’t report a value as 

5.38761 when the precision of the value really only lets us say 5.4.

Fractions and Percentages
A fraction is made by division. The top number (numerator) is 

divided by the bottom number (denominator). A percentage is 

a fraction whose denominator is 100. Whenever you encoun-

ter a percentage or any other fraction, try to figure out what 

the numerator and denominator represent. For example, the 

forced expiratory volume in 1 second (FEV1) is the amount of 

air that a patient can exhale in 1 second and is measured in 

liters. This value can then be divided by the full forced vital 

capacity (FVC), which is the total amount of air that the person 

can exhale after taking the biggest possible breath, to yield the  

Tiffeneau-Pinelli index (FEV1/FVC), which is a unitless rational 

number. The FEV1 and FVC can also be expressed as a percent-

age of the values that are predicted, given the patient’s sex, age, 

height, and race.

 When talking about values that are already expressed in 

percentages, be cautious about using percentages to express 

changes. For example, if a value increased from 10% to 20%, 

that’s an increase of 10 percentage points, not 10% (it’s a 100% 

increase; see Percentage Increase and Decrease).

Negative Numbers and Vectors
Addition is the arithmetic operation that originally represented 

adding objects to a collection. Its opposite is subtraction, 

which originally represented the removal of objects from a col-

lection. If you have 5 apples in a basket, you cannot remove 

more than 5 apples from that basket. But if you have $100 in 

your checking account and write a check for $200, you will end 

up with a balance of −$100 in your account. You would have 

to deposit $100 in the account to bring the balance up to 0. 

Accountants sometimes use parentheses instead of a minus 

sign to indicate negative numbers.

 Addition and subtraction are often represented by right-

ward or leftward movement, respectively, on a number line. 

Thus, addition and subtraction involve not just quantity but 

direction. In mathematics, a geometrical object that has a 

direction as well as a magnitude is called a vector. A line is 

one-dimensional, so there are only 2 directions. In contrast, a 

map is two-dimensional, which allows for an infinite number 

of directions. If I walk 1 block north, then 1 block west, then 1 

block south, then 1 block east, I will have walked a distance of 

4 blocks, but I will end up back where I started. Human beings 

can easily think in terms of 4 dimensions: the 3 dimensions of 

Euclidean geometry plus time. However, mathematicians often 

deal with problems that involve more than 4 dimensions. This 

allows them to develop a mathematical model of relationships 

among many variables at the same time.

Exponents and Logarithms
Exponentiation is when you multiply a base number (b) by 

itself n number of times (b n). For example, 23 = 2 × 2 × 2 = 8. 

The n is called an exponent, and we often say that b has been 

raised to the nth power. If n = 2, we say that the base is squared. 

If n = 3, we say that the base is cubed. Medical communica-

tors often deal with powers of 10: 10 = 101, 100 = 102, 1,000= 103, 

10,000 = 104, and so on. However, any real number could serve 

as the base or the exponent.

 The use of exponents can turn a multiplication problem into 

an addition problem: if 2 exponential expressions have the same 

base, you can multiply the 2 by adding their exponents: 102 × 103 

= 105. To divide, you subtract the exponents: 105 ÷ 103 = 102. Any 

nonzero number divided by itself is 1; therefore, b 0 = 1. You can 

also have negative exponents: b -n = 1/b n. You can also raise neg-

ative numbers to any power. Note, however, that if you raise a 

negative number to an even power (eg, −1 × −1), the product will 

be a positive number. If you raise it to an odd power, the result 

will be a negative number (eg, −1 × −1 × −1 = −1).

 In medical writing, you will often see powers of 10, espe-

cially in scientific notation: 5.23 × 105 = 523,000, but 5.23 × 10−5 

= 0.0000523. Sometimes E notation is used to express powers 

of 10. 5.23E5 means 5.23 × 105, and 5.23E−5 means 5.23 × 10−5.

 A logarithm is the inverse function of exponentiation. If 

b n = x, then n = logb(x). Because 23 = 8, log2(8) = 3. Because 

exponents can be negative, you can have negative loga-

rithms, which represent the inverse of a number. Because ½ 

is the inverse of 2, the log2(½) = −1. Likewise, the log10(¹⁄10) = −1 

(Figure on next page).

 Some units of measure are based on a logarithmic scale. 

For example, pH is based on the negative of the base-10  

logarithm of the activity of the H+ ion (as measured in moles 

per liter).

pH= –log10 (aH +) = log10  

 A solution of pure water has hydrogen activity of 1 × 10−7 

mol/L. The reciprocal of that is 1 ×107, or 107; log10(107) = 7. So 

the pH of pure water is 7. Water with a pH of 6 would have a 

hydrogen activity of 1 ×10−6 mol/L, which is 10 times as many 

hydrogen ions as in pure water!

1
aH +( )



      AMWA Journal / V36 N3 / 2021 / amwa.org    125

 

Base-10 logarithms are used so often that they are often just 

written as log(x). The natural logarithm, abbreviated  

ln(x), has Euler’s number (e) as its base. Euler’s number is an 

irrational number that is useful in many different areas of 

mathematics.

 Medical writers should be aware that viral load is often 

expressed in base-10 logarithms. I once edited a news article 

that described a patient as having a viral load of 5 copies/mL. 

That value was dubious: a value that low had to be below the 

limit of detection of any available assay. When I looked at the 

source material, I found out that the patient’s reported viral 

load was actually 5 log10 copies/mL, which meant 100,000 

copies/mL. Big difference!

Stevens’ Taxonomy of Measurement
Medical writers must be aware that numbers do not always 

represent counts, or some point along a number line, or 

a vector. To explain this problem, Stanley Smith Stevens 

explained that there are 4 types of measurement scale.1

• Nominal— A nominal scale is used when items or individu-

als are being assigned to groups that do not overlap. Such 

groups may be labeled with numbers: group 1, group 2, 

group 3. However, these numbers are simply being used as 

labels and do not express any sort of quantity.

• Ordinal— An ordinal scale is used when items or individuals 

are being ranked according to how they compare with each 

other in terms of some property. For example, the runners in 

a race will be ranked first, second, third, and so on, accord-

ing to how fast they ran. However, these ordinal numbers 

merely show rank. They do not use units of measure, and 

they do not show absolute quantities or ratios. For exam-

ple, the second-place finisher in a race was faster than the 

fourth-place finisher—but not necessarily twice as fast. The 

Wong-Baker FACES pain rating scale2 is an ordinal scale. So 

are the Likert scales that are used in opinion research  

(eg, 1 = strongly disagree, 2 = disagree, 3 = neither agree  

nor disagree, 4 = agree, 5 = strongly agree).

A logarithm is the inverse function of exponentiation. If bn = x, then n = logb(x). Since 23 = 8, 
log2(8) = 3. Since exponents can be negative, you can have negative logarithms, which 
represent the inverse of a number. Since ½ is the inverse of 2, the log2(½) = −1. Likewise, the 
log10(¹⁄₁₀) = −1 (Figure 1). 

Some units of measure are based on a logarithmic scale. For example, pH is based on the 
negative of the base-10 logarithm of the activity of the H+ ion (as measured in moles per liter).  

𝑝𝑝𝑝𝑝 = 	−𝑙𝑙𝑙𝑙𝑙𝑙!"(𝑎𝑎#!) = 𝑙𝑙𝑙𝑙𝑙𝑙!" ,
1
𝑎𝑎#!

.	 

A solution of pure water has hydrogen activity of 1 × 10−7. The reciprocal of that is 1 ×107, or 
107; log10(107) = 7. So the pH of pure water is 7. Water with a pH of 6 would have a hydrogen 
activity of 1 ×10−6, which is 10 times as many hydrogen ions as in pure water! 
 

 
Figure 1. Logarithms are the inverse function of exponentiation: If bn = x, then n = logb(x). 
Exponentiation allows you to raise any real number (any point along a number line) to any 
real power. Note that x0 always equals 1, and x1 always equals x. For this reason, logb(0) is 
always 1 and logb(1) is always b, regardless of the value of b (i.e., regardless of the base of the 
logarithm). A negative exponent represents the inverse of a number (e.g., 2−1 = ½). Thus, a 
negative logarithm equals the logarithm of the inverse of the value: log2(½) = −1 and −log2(½) 
= 1. Courtesy of Richard F. Lyon via Wikimedia Commons. 

Base-10 logarithms are used so often that they are often just written as log (x). The natural 
logarithm, abbreviated ln (x), has Euler’s number (e) as its base. Euler’s number is an irrational 
number that is useful in many different areas of mathematics.  

Medical writers should be aware that viral load is often expressed in base-10 logarithms. I 
once edited a news article that described a patient as having a viral load of 5 copies/mL. That 
value was dubious: a value that low had to be below the limit of detection of any available 
assay. When I looked at the source material, I found out that the patient’s reported viral load 
was actually 5 log10 copies/mL, which meant 100,000 copies/mL. Big difference!   

Figure. You can raise any real number (b) to any real power 
(y), even negative and fractional powers. The logarithmic 
function is the inverse function of exponentiation: If by = x,  
then y = logb(x). The graph shows the value of logb(x) for  
x>0 and some nonzero values of b. The value of log0(x) is  
undefined; but for b≠0, logb(1)=0 and logb(b)=1. Also, 
logb(x) = −logb(1/x). Thus, the value of logb(0) is undefined 
but approaches −∞ as x approaches 0. The logarithm of a 
negative number is not a real number but involves a complex 
expression. Graph courtesy of Richard F. Lyon via Wikimedia 
Commons.

Percentage Increase and Decrease
The formula for calculating percentage increase and  
decrease is:

Percentage Increase = [(Final Value − Starting Value)/ 
|Starting Value|] × 100

If you weigh 50 kg and gain 100 kg, that’s a 200% increase 
in weight:

[(150 – 50)/50] × 100 = 200%

But if you then lose that 100 kg, that’s only a 67% decrease 
in weight: 

[(50-150)/150] × 100 = −67%

Fold Increase and Decrease

A fold is a ratio between 2 values. The formula for  
calculating fold increase is:

Fold change (for increases) = Final value/Starting 
value. 

If you weigh 50 kg and gain 100 kg, then that’s a 3-fold 
increase in weight:

(150/50) = 3 

A fold decrease is calculated as follows:
Fold change (for decreases) = −(Starting value/ 
Final value).

If you weigh 150 kg and lose 100 kg, then that’s a −3-fold 
change (3-fold decrease) in weight:

− (150/50) = −3

However, some people use the fold increase formula for 
calculating fold decreases. As a result, they would describe 
a change from 150 kg to 50 kg as a 0.33-fold decrease in 
weight. So if you see someone express a fold decrease, 
make sure you know what they really meant!  



126    AMWA Journal / V36 N3 / 2021 / amwa.org        

• Interval— An interval scale not only orders items or indi-

viduals according to some characteristic but also establishes 

equal intervals between the units of measurement. This 

allows you to do some mathematical operations, such as 

calculating averages. However, the 0 point may be meaning-

less. For this reason, the measurements cannot be expressed 

in ratios. For example, in the Celsius or centigrade scale, 0° 

was set to represent the freezing point of water, whereas 100° 

was set to represent the boiling point of water. However, the 

Fahrenheit scale sets 0° at a different point and uses different 

intervals. Water that is at 40 °C (104 °F) is warmer than water 

at 20 °C (68 °F), but it is not twice as warm! So don’t express 

such a change in temperature as a multiple or a percentage.

• Ratio scale— A ratio scale has a meaningful 0 point as well 

as equal intervals. This allows you to calculate ratios. For 

example, you can say that 1 thing weighs twice as much as 

another, or that something costs twice as much as some-

thing else.

Conclusion
So if you are being asked to report on the meaning of the out-

come measures used in a study, you must present the numbers 

accurately and specify the units (if any). You must also think 

about what those numbers really mean! For example, it is an 

established convention that the 0 point on a psychological or 

educational measurement is arbitrary and may be meaningless.

Author declaration and disclosures: The author notes no commercial 
associations that may pose a conflict of interest in relation to this article.

Author contact: www.nottrivialbook.com; lthomas521@verizon.net

References
1. Stevens SS. Measurement, statistics, and the schemapiric view. Like 

the faces of Janus, science looks two ways—toward schematics and 

empirics. Science. 1968;161(3844):849-856.

2. Wong DL, Baker CM. Pain in children: comparison of assessment scales. 

Pediatr Nurs. 1988;14(1):9-17.

A Career in 
Medical Communication:
Steps to Success
Learn about the skills and attributes needed 
to be a successful medical communicator 
and discover opportunities in the field.

www.amwa.org/career_steps

http://www.nottrivialbook.com
mailto:lthomas521@verizon.net
http://www.amwa.org/career_steps



