## Prefer Arabic numerals to Roman numerals

Roman numerals should be used only in certain stylized situations, such as the numbering of preliminary pages of a book or the tables in some journals, blood-clotting factors, or cranial nerves. At the same time, if Roman numerals are part of an established terminology do not change them to Arabic numerals. (For example, continue to speak of a Type II error.)

Arabic numerals are easier to read and interpret than Roman numerals are. Use them to number experimental research groups, organisms, virus types, and volume numbers in bibliographic material (even though Roman numerals may have been used in the original).

group 3, echovirus 30

case 3 in experiment 5

blood-clotting factor VIII

Creative Acupuncture 9: 6-35

See the author's note in the preface (p. xiv).

For units such as weights, percentages, and degrees of temperature, use Arabic numerals. For example, write 3.2 m or 72 °F, regardless of the way other numerical expressions may be treated. Unless a journal specifies otherwise, do not follow written numbers with a figure in parentheses representing the same number ("send three [3] copies to the editor"). However, it is both acceptable and desirable to include parenthetical material that amplifies understanding of other numerical data.

He was given 2 mg of tetracycline on each of three occasions.

A 10% mortality rate is common.

Necrosis occurred in almost 20% (50/247) of the cases.

### The SI metric system for measurements and weights

There actually are several metric systems, including the centimeter-gram-second system and the meter-kilogram-second system. However, these systems are gradually being replaced by a modernized metric system called SI, for Systeme International d'Unites. It provides unambiguous symbols that are standard in all languages (Young and Huth, 1998). The system is constructed upon seven base plus two supplementary units of measurement (Table 7.7).

Most scientific journals use the SI system and also permit some widely used units outside the SI system, such as liter, hour, bar, and angstrom. Most scientific style manuals include a chart to convert measurements from traditional units to their SI equivalents.

All other units for physiochemical quantities are derived from these SI base units, though they may have special names and their own symbols. For example, the widely used liter is non-SI; its equivalent is one cubic decimeter. (Note that in the United States the symbol "L" is generally preferred, because lower case "l" can be confused with 1.) Prefixes join base units to express multiples. Because kilogram, the base unit for mass, already has a prefix, it is an exception. In this case attach the prefix to the unit stem "gram" rather than adding it to kilogram.

174 7 Attending to grammar, numbers, and other mechanics Table 7.7. Fundamental SI units of measurement

Quantity Name Symbol

Base units

Quantity Name Symbol

Base units

length |
meter (metre) |
m |

mass |
kilogram |
kg |

time |
second |
s |

amount of substance |
mole |
mol |

thermodynamic temperature |
kelvin |
K |

electric current |
ampere |
A |

luminous intensity |
candela |
cd |

Supplementary units | ||

plane angle |
radian |
rad |

solid angle |
steradian |
sr |

For quantities much larger or smaller than a given base unit, standard prefixes are used (Table 7.8). The usual practice is to choose the prefix for multiples of 102 or 10 3 so the number accompanying the unit is less than 1000. Only one prefix may be used for most symbols, and a prefix is never used alone. Both the prefix and the unit it modifies are either abbreviated or spelled out.

Incorrect: Add 6 m^g of substrate.

Correct: Add 6 ng of substrate. [or six nanograms]

When using SI, employ exponents for such expressions as 2 m2 (rather than 2 sq. m). Units are created and definitions are modified as measurement technology progresses.

Factor (power of ten) |
SI prefix |
Symbol |

18 |
exa |
E |

15 |
peta |
P |

12 |
tera |
T |

9 |
giga |
G |

6 |
mega |
M |

3 |
kilo |
k |

-3 |
milli |
m |

-6 |
micro |
H |

-9 |
nano |
n |

-12 |
pico |
p |

-15 |
femto |
f |

-18 |
atto |
a |

Very large and very small numbers

Very large or very small numbers can be expressed in different ways. One is to use SI prefixes. Another is to use scientific notation. Check the Instructions to Authors and be consistent throughout the document.

SI prefixes: 8,000,000 N/m2 (force of newtons per square meter) becomes 8 MN/m2 (not 8 N/mm2 because the acceptable prefix should be attached to the numerator)

Scientific notation: 8 x 106 N/m2

Often, a number can be rounded off without losing meaning. For example, 6,234,275 could be expressed as 6.2 million for most practical purposes. If a quantity must be converted to SI units, multiply the quantity by the exact conversion factor, then round it off appropriately. The format for reporting very large round numbers depends somewhat on the journal. In the absence of other specific instructions, substitute a word for part of the number (such as 1.5 million for 1,500,000). Because of usage differences between Europe and the United States, it is better to avoid the words billion, trillion, and quadrillion.

When reporting large but exact numbers, U.S. journals use commas between groups of three digits (695,446) in most figures of 1,000 or more. (Exceptions include page numbers, binary digits, serial numbers, degrees of temperature, degrees of freedom, and numbers to the right of a decimal point.) For an international audience, do not break up numbers above 999 into groups of three digits with commas. In some countries, a comma indicates a decimal point. Instead, international journals often leave spaces (695 446).

The number of places to which a large decimal value is carried reflects the precision with which the quantity was measured. Omit statistically non-significant decimal places in tabular data. One useful rule of thumb is to report summary statistics to two digits more than are in the raw data. For example, if scores on a test are whole numbers, report descriptive statistics to two decimal places.

Similar entries in a table row or column should be measured to the same level of accuracy, and the number of significant digits must be commensurate with the precision of your experimental method. The best level of precision for numerical data will vary, but rounded-off values often display patterns and exceptions more clearly than precise values.

### Percentages

Three similar-sounding words confuse this subject. The term percent (sometimes written as two words,percent) means "in, to, or for every hundred"; the symbol % can take its place. Always place a number before the symbol. Percentage means "a number or amount stated in a percent." Percentile is a statistical term for the value in a distribution of frequencies divided into 100 equal groups.

Except at the beginning of a sentence, use the symbol % and Arabic numbers for percentages. Repeat the symbol for each number in a series or range, including zeroes.

Group |
n |
Mating success (%) |

Experienced |
55 |
50% |

Naive, drug-treated |
5 |
60% |

Experienced, drug-treated |
5 |
80% |

Naive controls |
25 |
41% |

These values were compared with the percentages for 1982.

Ten percent of our students scored at the 99th percentile.

The incidence of mononucleosis ranged from 0% to 24%.

The bacteria were found in 15%, 28%, and 0% of the animals in groups 1, 2, and 3, respectively.

For purposes of comparison, percentages are often much more useful than an array of raw data. However, handling percentages properly can be tricky. One absolute requirement: whenever percentages (or other proportional figures) are employed, the finite number (n) from which the percentages are derived must be given somewhere. Often these numbers are presented in a separate column in the table.

Some authorities also recommend that the text include the actual number of subjects for each percentage if the cited series includes fewer than 100 subjects. They also recommend that you use decimals in percentages in series only when the percentages are based on more than 1,000 subjects.

Pulmonary disease was present in 50% (16) of the dogs,

OR ... in 16 (50%) of the dogs, OR ... in 50% (16/32) of the dogs.

Whenever there might be a possibility of misunderstanding, state the basis for the percentages. For example, in reporting certain analyses, it may be essential to specify whether moisture-free ("dry") weight, fresh ("wet") weight, or volume was used.

Journals differ in what denominator magnitude (value of n) they will accept as adequate basis for a percentage. Percentages given for compared fractions with small denominators are likely to imply statistically significant differences when none in fact exist. In the example in Table 7.9, the percentages of drug-treated naive animals and drug-treated experienced animals look very different (60% vs. 80%), but in fact because of the small sample sizes, the real difference was only due to the differing behavior of a single animal.

Some clinical journals allow percentages only for fractions with denominators greater than 50. Thus, percentages would be given for the reader's convenience for 31/75 (41%) but not for 12/25. When some fractions would appear with percentages and others without them, it might be stylistically better to omit the percentages entirely. If differences in compared fractions are assessed statistically, the assessment must be based on the absolute numbers, not the percentages.

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