﻿ ﻿Forms of Numbers - Numbers and Percentages

# Forms of NumbersNumbers and Percentages

18.7.1 Decimals.

The decimal form should be used when a fraction is given with an abbreviated unit of measure (eg, 0.5 g, 2.7 mm) to reflect the precision of the measurement (eg, 38.0 kg should not be rounded to 38 kg if the scale was accurate to tenths of a kilogram) (see 17.4.2, Decimal Format).

The patient was receiving gentamicin sulfate, 3.5 mg/kg, every 8 hours. Her serum gentamicin level reached a peak of 5.8 μg/mL and a trough of 0.7 μg/mL after the third dose.

Place a zero before the decimal point in numbers less than 1, except when expressing the 3 values related to probability: P, α, and β. These values cannot equal 1, except when rounding (see 19.5, Glossary of Statistical Terms). Because they appear frequently, eliminating the zero can save substantial space in tables and text. (Although other statistical values also may never equal 1, their use is less frequent, and to simplify usage, the zero before the decimal point is included.)

P = .16

1 − β = .80

Our predetermined α level was .05.

But: κ = 0.87

Note, however, that α and β may sometimes be used to indicate other statistics, and in some of these cases, their values may be 1 or greater.

Cronbach α = 0.78

standardized β coefficient = 2.34

By convention, a zero is not used in front of the decimal point of the measure of the bore of a firearm.

.45-caliber semiautomatic handgun

Odds ratios, likelihood ratios, and relative risks are reported to the hundredth place unless the point estimate is very small.

In unadjusted Cox proportional hazards regression, bariatric surgery was associated with reduced mortality (hazard ratio, 0.64; 95% CI, 0.51-0.80).

18.7.2 Percentages.

The term percent derives from the Latin per centum, meaning by the hundred or in, to, or for every hundred. The term percent and the symbol % should be used with specific numbers. Percentage is a more general term for any number or amount that can be stated as a percent. Percentile is defined as the value on a scale of 100 that indicates the percentage of the distribution that is equal to or below it.

Ten percent of the work remained to be done.

Heart disease was present in a small percentage of the participants. (But: Five percent of the participants had heart disease.)

Her body mass index placed her in the 95th percentile of the study group.

Unless otherwise indicated, data in a table are expressed as number (percentage). If it is a table footnote, space is often saved by showing the data as “No. (%).”

Use arabic numerals and the symbol % for specific percentages. The symbol is set closed up to the numeral and is repeated with each number in a series or range of percentages. Include the symbol % with a percentage of zero.

A 5% incidence (95% CI, 1%-9%) was reported.

The prevalence in the populations studied varied from 0% to 20%.

At the beginning of a sentence, spell out both the number and the word percent, even if the percentage is part of a series or range. Often it is preferable to reword the sentence so that a comparison between percentages is more readily apparent.

 Acceptable: Twenty percent to 30% of patients reported respiratory symptoms. Better: The percentage of patients who reported respiratory symptoms ranged from 20% to 30%. Or: Between 20% and 30% of the patients reported respiratory symptoms.

When referring to a percentage derived from a study sample, include with the percentage the numbers from which the percentage is derived. This is particularly important when the sample size is less than 100 (see 19.4, Significant Digits and Rounding Numbers). To give primacy to the original data, it is preferable to place the percentage in parentheses.

Of the 26 adverse events, 19 (73%) occurred in infants.

Any discrepancy in the sum of percentages in a tabulation (eg, because of rounding numbers, missing values, or multiple procedures) should be explained.

The terms percent change, percent increase, and percent decrease are often used in place of percentage of change. Although these less formal terms are acceptable, their usage must be precise. They generally are computed as the difference between an index value and either an earlier or later value divided by the index value. Although a percent increase may exceed 100%, a percent decrease generally cannot. A percent decrease can also be expressed as a negative percent increase.

These terms must be differentiated from percentage point change, increase, or decrease, which are obtained by subtracting one percentage value from another. For example, a change in rate from 20% to 30% can be referred to either as an increase of 10 percentage points, as in “the intervention group improved 10 percentage points,” or as a 50% increase (percent change), as in “the intervention group showed a 50% improvement” ([30% − 20%]/20%). The 2 terms are not interchangeable. Because the percent change does not indicate the actual beginning or ending values or the magnitude of the change, the actual values should be provided whenever possible.

18.7.3 Reporting Proportions and Percentages.

Whenever possible, proportions and percentages should be accompanied by the actual numerator (n) and denominator (d) from which they were derived. In text, the numerator and denominator should be expressed as “n of d” not by the virgule construction “n/d,” which could imply that the numbers were computed in an arithmetic operation.

Death occurred in 6 of 200 patients.

Not: Death occurred in 6/200 patients.

For clarity, when a numerator and denominator are accompanied by a resulting proportion or percentage, the proportion or percentage should not intervene between the numerator and denominator.

Death occurred in 6 of 200 patients (3%).

Death occurred in 3% (6 of 200) of patients.

Of the 200 patients, death occurred in 6 (3%).

Of the 200 patients, 6 (3%) died.

Not: Death occurred in 6 (3%) of 200 patients.

The denominator may be omitted if it is clear from the context.

Death occurred in 10 patients (10%).

In expressing a series of proportions or percentages drawn from the same sample, the denominator need be provided only once.

Of the 200 patients, 6 (3%) died, 18 (9%) experienced an adverse event, and 22 (11%) were lost to follow-up.

18.7.4 Reporting Rates and Ratios.

Use the virgule construction for rates when placed in parentheses (eg, 1/2) but never in running text. A colon is used for ratios (eg, 1:2). Rates should use the decimal format when the denominator is understood to be 100; otherwise, the denominator should be specified.

Of all individuals exposed, children were affected at a rate of 0.05.

The infant mortality rate was 3 per 10 000 live births.

Not: The infant mortality rate was 3/10 000 live births.

18.7.5 Roman Numerals.

Use roman numerals with proper names (eg, Henry Ford III). Note that no comma is used before the numeral. However, arabic numerals should be used as designators in all other cases (eg, round 2, Table 4, year 5; see 10.4, Designators) unless roman numerals are part of formally established nomenclature (see 14.0, Nomenclature).

 Step I diet Schedule II drug level I trauma center Axis I diagnosis NYHA class II But: type 2 diabetes, phase 3 study

Use roman numerals for cancer stages and arabic numerals for cancer grades (see 14.2, Cancer). In pedigree charts, use roman numerals to indicate generations and arabic numerals to indicate families or individual family members (see 4.2.2.4, Pedigrees). Roman numerals are also used for clotting factor and cranial nerve names. Roman numerals also may be used in outline format (see 4.1, Tables).

In bibliographic material (eg, references or book reviews), do not use roman numerals to indicate volume number, even though roman numerals may have been used in the original. However, if roman numerals were used in the original title or in an outline, refer to the title or outline as it was published, with roman numerals. Retain lowercase roman numerals that refer to pages in a foreword, preface, or introduction. Roman numerals may also be used to number supplements to journals so that roman numerals appear adjacent to page numbers in references to the work. In this case, the roman numerals should be retained.

For the use of roman numerals in biblical and classical references, follow the most recent edition of the Chicago Manual of Style (see 3.0, References).

The following list indicates the roman equivalents for arabic numerals. In general, roman numerals to the right of the greatest numeral are added to that numeral, and numerals to the left are subtracted. A horizontal bar over a roman numeral multiplies its value by 1000.

 1 I 2 II 3 III 4 IV 5 V 6 VI 7 VII 8 VIII 9 IX 10 X 11 XI 12 XII 13 XIII 14 XIV 15 XV 16 XVI 17 XVII 18 XVIII 19 XIX 20 XX 30 XXX 40 XL 50 L 60 LX 70 LXX 80 LXXX 90 XC 100 C 200 CC 300 CCC 400 CD 500 D 600 DC 700 DCC 800 DCCC 900 CM 1000 M 5000 V_

Principal Author: Edward H. Livingston, MD

Acknowledgment

I thank Stephen J. Lurie, MD, PhD, and Margaret A Winker, MD, who wrote this chapter in the 10th edition of the AMA Manual of Style, on which this chapter is based. I also thank the following for their comments: Diane Cannon, formerly of the JAMA Network; Lila Haile, BA, JAMA, now with the Medical Council of Canada; Trevor Lane, MA, DPhil, Edanz Group, Fukuoka, Japan; and Ana Marušić, MD, PhD, Journal of Global Health and University of Split School of Medicine, Croatia.

References

1.Taylor BN, Thompson A. The International System of Units (SI). NIST special publication 330. 2008. Accessed December 6, 2018. https://www.nist.gov/sites/default/files/documents/2016/12/07/sp330.pdf

2.Billion bites the dust. Nature. 1992;358(6381):2. doi:10.1038/358002b0