Subject Index - Data and Measurement

abbreviations and acronyms

An abbreviation is a shortened form of a word used in place of the full word (e.g., Inc.). An acronym is a word formed from the first letters of each of the words in a phrase or name (e.g., NREL or DOE). Abbreviations and acronyms are treated similarly in NREL publications.

Using Abbreviations and Acronyms Sparingly
Avoid using a given acronym unless you use it extensively in a publication. In a short report, do not use an acronym for a phrase you use five or fewer times. In a long report, do not use an acronym for a phrase you use fewer than 10 times. In a webpage, do not use an acronym for a phrase you use fewer than three times.
Some two-letter abbreviations and acronyms are acceptable (e.g., AC and DC, or MW). Avoid other two-letter acronyms that are less universally used (e.g., EE and RE).
If you use many acronyms in a report, add a list of acronyms at the beginning of the report. For an example, see this sample report.
Spelling out Acronyms
In general, each time you use an acronym for the first time in the body of a report or on a given webpage, spell it out and put the acronym in parentheses after the full name. However, you do not need to spell out most common abbreviations and acronyms (e.g., AC, DC, cm, m, Hz, kW, MW, GW, and rpm) in most technical reports.
Abbreviating Measurement Units
Spell out a technical abbreviation in full in text when you use it without numerals. For example, write "a few centimeters" rather than "a few cm."
Abbreviate units of measurement when they are used with a numeral or numeric value (e.g., 900 W/m², 43 cm, or 60 Hz). With a few exceptions (such as %, °, $, and ¢), use a space to separate them from numerals.
Abbreviating Plurals
Use a small s (no apostrophe) for plurals of most abbreviations. For plurals of units of measurement, omit the s (e.g., 15 cm, 6 m, 5 million Btu, 75 dB, 40 W).
Abbreviating Equations and References
You can abbreviate "equation" and "reference" when you use them with numbers, but spell them out at the beginning of a sentence.
See Eq. 1-1, Eq. 2-7, and Ref. 10.
Equation 2-1 shows the relation.
Abbreviating in Journals
For a journal article, consult the publisher's or professional society's guidelines for abbreviations, if they are available. For abbreviations of journal titles, please see the Woodward Library website.

British thermal units

The abbreviation for "British thermal unit" is Btu. "Btu" is used for both singular and plural cases.

criterion, datum, memorandum, phenomenon, and their plurals

"Criterion" is a singular noun (one criterion), and "criteria" is the plural (two or more criteria). "Data" is the plural of "datum." The plural of "memorandum" can be either "memoranda" or "memorandums." "Phenomenon" is singular, and "phenomena" is plural.

data in tables

Place a zero to the left of the decimal in any number less than 1 in text and tables (e.g., 0.5, 0.039). Align columns of data vertically on the decimals. When the units of measurement for the data are different, alignment is not necessary (but be sure to specify the units).

dataset

“Dataset” is spelled as one word.

degree symbol

Do not include a space before or after the degree symbol.

36°C
85°F

Repeat the degree symbol in ranges.

32°C–36°C (temperature)
60°–90° (angles)

Express kelvins as K rather than as °K; leave a space before the K.

85 K

dollars

Express thousands of dollars using a comma.

$5,000

Express millions and billions of dollars this way.

$3 million
$1.2 billion

Do not use a hyphen to join a number and words such as “million” or “billion,” even when used as a unit modifier.

$4 million prize
$200 billion budget

In technical reports and papers, use a dollar sign to express costs less than $1.

$0.25
$0.06 per kilowatt-hour

equations

Make sure that all the terms in your equations are defined and used consistently both in the text and in subsequent equations, figures, and tables.

The conductive heat flow equation is:

dQ/dt = AKdT/dx

where
dQ/dt = the time rate of heat transfer
A = the area of an end contact
K = the thermal conductivity
dT/dx = the thermal gradient.

fractions

Use words instead of numerals for simple fractions in text.

a third of the way
one-fifth its actual size
three-fourths of the participants

Write out complex fractions with numerals separated by a solidus.

1/64
23/32
5-1/2 days afterward
2-1/2 times greater

Display complex, built-up fractions by centering them vertically between two parts of a paragraph.

Example of an equation centered and placed vertically between two parts of a paragraph.

Place a zero to the left of the decimal in fractions less than 1.

0.125
0.006

kilowatt (kW)

kilowatt-hour (kWh)

mathematical symbols

Leave a space on either side of mathematical symbols used as operation signs.

T_in - T_amb

°C × 1.8

The solidus (a/b) or division sign is an exception. Do not leave a space between numerals and the symbols for degrees, dollars, and percent (32°, $100, 17%). (However, leave a space between numerals and symbols of measurement such as cm and Å.) Do not leave a space between symbols such as >, <, and ≥ and the numeral unless they are the operation signs in an equation.

megawatt (MW)

megawatt-hour (MWh)

metric conversions

For quick online conversions of English units of measurement to metric units, see the Digital Dutch WWW Unit Converter website or IFP Reference Conversions on the French Property website.

multiplication symbols

Be as consistent as possible in using multiplication symbols in your paper or report. As appropriate, choose one symbol (× or ·), or omit the symbol and use proximity or parentheses: ab, (ab) (cd), etc.

non-SI (English) units of measurement

Use non-SI (Systeme International d'Unites) or nonmetric units of measurement (English or Imperial units) instead of metric units only when they are the industry standard. Otherwise, state metric units first, followed by English equivalents in parentheses.

38.1 m (125 ft)

numbers

1. Units of Measurement and Mathematical Expressions

Use numerals with units of measurement and time.

2-1/2 hours	87 years
4.5 months	6 liters
36 cm	25 kW

With units of time, you can spell out numbers less than 10 if you do so consistently (this applies mainly to outreach products rather than technical reports and papers).

five-year plan
two-hour test
three-week turnaround

Use numerals to imply arithmetical values or manipulation.

a factor of 3
multiplied by 2
a ratio of 4:5
values of 1 and 48

Express measurement errors as:

6.0 nm ± 0.2 nm.

Leave a space between the number and the unit of measurement (0.2 nm) and put spaces around the operation sign. When the measurement error appears by itself, omit the space between the sign and the number.

The measurement error is ±0.2 nm.

2. Aligning Numbers

Align numbers that share a common unit of measurement on the decimals in columns of tables. Put a zero before the decimal in numbers smaller than one.

0.800
2.450
187.362

If all the numbers in a column do not share the same unit of measurement, you may center the numbers in the column and specify the unit of measurement.

3. Fractions and Decimals

You can spell out and hyphenate simple fractions (this is preferred in text) or express them, like more complex fractions, in numerals with a solidus.

one-fifth or 1/5
1/64 (but not 1/64th)

Use a hyphen to separate the integral and fractional parts of a mixed number, or convert the fraction to a decimal.

2-1/2 cm in diameter
2.5-cm-diameter solar cell

For numbers of 1 million or more, use the numeral (and a decimal, if necessary) and the words million, billion, etc.

1.1 million households
3.5 billion people
$2.5 million in funding

4. Precision and Numbers

Measurement uncertainty analysis calls for precision in measurements to a significant digit to the right of a decimal point, such as two or three digits (hundredths or thousandths). If you're not absolutely sure, check with an expert before changing the number of digits to the right of the decimal, or rounding the numbers. See also standard errors.

5. Punctuating Numbers

Use a comma to separate groups of three digits in numbers.

5,182
113,728
2,225,000

6. Ranges of Numbers

To show ranges, use an en dash (which is a little shorter than an em or long dash) with no spaces. Alternatively, if you write out a range, make sure you use the word "to" when you use "of" or "from" before the range. To express a range between some number and another number, always use the word "and" (not "to") with the word "between."

15%–25%
from 32°C to 40°C
6–12 cm
from 66 to 80 V
10–20 m²
between 8 and 12 m (not "between 8 to 12 m")
$3 million–$4 million

Note that some symbols, such as ° and %, are repeated in a range.

7. Scientific Notation

Express multiples of SI (metric) units in powers of 10 with the appropriate prefixes and technical abbreviations.

mm (millimeters, 10^-3 m)
MJ (megajoules, 10⁶ J)

Use standard scientific notation to express very small and very large numbers.

2.5 × 10^-3
3.56 × 10⁶

Avoid using M to mean "thousands" and MM to mean "millions"; use a capital M for "mega," or millions, as in MW for "megawatts."

8. Spelling out Numbers

Except with units of measurement and time (in technical reports), spell out numbers less than 10.

eight experimental runs
three species of yeast

Spell out all numbers at the beginning of a sentence.

Fifteen trials later, the results were the same.
Thirty-five participants attended the seminar.

In general, spell out numbers at the beginning of a bulleted item, but use best judgment depending on the context (e.g., a list of sentence fragments using numbers with many digits).

The electrical safety point of contact recorded the following during their field walk:

Seven staff occupied the laboratory while performing electrical work.
Twenty-five staff observed from a nearby corridor.

The photovoltaic cost benchmark data encompass:

30 states
1.6 million individual PV systems
81% of all U.S. residential and nonresidential systems.

When a sentence contains one or more numbers greater than nine that are related to a smaller number, use numerals for all of them.

The results were the same in 3, 12, and 18 trials.
The contractor tested 8 devices in May, 12 in June, and 9 in July.

Spell out the first of two adjacent numbers unless the first one requires three or more words.

ten 5-kW arrays
thirty-two 4-cm² devices
135 16-cm collectors

percent, %, and percentage

Use the symbol % with numerals; use the word "percent" when you spell out numbers at the beginning of a sentence. To determine whether "percent" or % is singular or plural, look at the noun following it. If the next noun is a plural, use a plural verb; if it's singular, use a singular verb.

The maximum glucose yield was 60%.
Six percent of the pipes were rusty.
More than 10% of that amount was allocated to planning.

When there is no number, use the word "percentage," unless people in your field use a different terminology, such as "percent difference."

This table shows the percentages of government buildings having solar roofs, by state.

pressure

Use the standard SI unit for pressure or stress, which is the pascal (Pa) or the bar. Non-SI units include psi (pounds per square inch), millimeters of mercury, torr, and atmospheres, and they are still in relatively widespread use.

ratios

In general, use a colon to indicate a ratio.

We prepared a 3:1 dilution.

However, some industries (such as the American automotive industry) use a solidus to express a ratio.

The engine is designed to have an optimum air/fuel ratio.

scientific notation

Standard scientific notation represents a number as a factor multiplied by a power of 10; 3,560,000 is expressed as 3.56 × 10⁶. This is useful for very large and very small numbers, especially in non-SI units. You can also use certain standard prefixes, many of which are listed here with their abbreviations.

10²⁴	yotta	Y
10²¹	zetta	Z
10¹⁸	exa	E
10¹⁵	peta	P
10¹²	tera	T
10⁹	giga	G
10⁶	mega	M
10³	kilo	k
10²	hecto	h
10¹	deka	da
10^-1	deci	d
10^-2	centi	c
10^-3	milli	m
10^-6	micro	µ
10^-9	nano	n
10^-12	pico	p
10^-15	femto	f
10^-18	atto	a
10^-21	zepto	z
10^-24	yocto	y

We recommend choosing a prefix that permits the numerical value to fall between 0.1 and 1,000 (62 kW rather than 62,000 W).

SI (metric) system

NREL follows national policies and those of scientific societies by using the SI (Systeme International d'Unites, International System of Units) or metric system in expressing technical measurements. English units may follow metric ones or may be used alone in special cases, when that is appropriate for a publication's audience. See also the National Institute of Standards and Technology.

slash (solidus)

The solidus (or slash, slant, shilling mark, or virgule) is a versatile symbol that has mathematical as well as textual functions.

1. Using a Solidus in Fractions

Use a solidus to express a quotient in text when you do not need to use a displayed equation.

These structures yield photoluminescence lifetimes that are related to bulk
lifetime by the expression 1/t = 1/t_B + 2 S/D.

Use a solidus in superscript and subscript fractions.

x^1/2

2. Using a Solidus in Text

In text, use a solidus to indicate some junctions, interfaces, and components.

gas-liquid interface
1-butyl acetate/acetic acid/water (3:1:1)

With abbreviated units of measurement, the solidus stands for "per."

2 g/cm²
355 W/m²

But spell out "per" when you spell out the units of measurement.

several cubic meters per second
a few cents per kilowatt-hour

standard errors

Express standard measurement errors as shown below.

6.0 nm ± 0.2 nm

statistical terms

When referring to statistical or graphical terms, use a hyphen but no italics. Also, do not use capital letters.

p-value
t-test
y-axis

technical abbreviations

Unless your profession, technical field, or scientific discipline specifies something different, use the abbreviations in NREL's list of technical abbreviations or the National Institute of Science and Technology's Guide.

temperature

Use a degree symbol (°) with temperatures expressed in the Celsius and Fahrenheit scales but not with kelvins (just use K). Don't leave a space between the number and the letter for °C and °F, but leave a space between the number and K.

72°F
0 K

units of measurement

Use numerals with units of measurement and time in technical papers and reports, even when the number is less than 10. In some outreach publications, you may spell out numbers less than 10, especially with units of time.

Except with $, °, and %, leave a space between the numeral and the unit. Include a hyphen between a numeral and an abbreviated unit when the value is used as an adjective.

Do not include a period after a unit symbol except at the end of a sentence. The exception to this rule is inches (which are abbreviated “in.”).

2 kW	7 cm²	16.8%
3 m	8-hour days	300 Btu
5 years	$2 billion	45°
4 in.	a 15-MW turbine	65°C

Avoid nonstandard abbreviations such as sec or cc, and instead use standard abbreviations such as s and cm³. Unless your profession, technical field, or scientific discipline specifies something different, use the abbreviations in NREL's list of technical abbreviations or the National Institute of Standards and Technology (NIST) guide.

Use a center dot to indicate multiplication of units (such as N∙m for Newton-meters), and use a slash or negative exponent to indicate division. For example, 344 meters per second can be written as 344 m·s⁻¹ or 344 m/s.

Format variables in italic type and units in roman type:

Correct: t = 3 s, where t is time and s is seconds
Incorrect: t = 3 s, where t is time and s is seconds

Do not mix information with unit symbols or names:

Correct: the water content is 20 mL/kg
Incorrect: 20 mL of water/kg

Avoid mixing symbols and names; for example, use kg/m instead of kilogram/m.

When expressing a range, repeat the unit symbol if it is closed-up with the numeral ($, °, %):

10%–20%
100°C–105°C
60°–90° (example of angular measurements)
$40–$60/MWh

Refer to the NIST style conventions checklist for additional style tips and examples.

watt

zero

For numbers less than one, place a zero before the decimal.

0.5
0.125
0.00125