# 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

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