# What's the correct way to write 3 x 10^6 (three million)?

I am reviewing some research reports and found myself diving into the black hole of technical writing style.

My question is what is the best way to write numbers in millions? I am not writing a novel or story; I working on technical/scientific/academic reports.

1. Three millions
2. 3 x 106
3. 3 X 106

Should I use multiply symbol instead of letter "X"?

• Why your assuming that three million (singular, by the way) is wrong? Or are you asking how to express it as a numeral if 3,000,000 is too long? (Incidentally, I made a minor tweak to the title of your question that should help clarify it.) – Jason Bassford Supports Monica Feb 21 at 15:05
• Hi Jason. Thank you for the clarification. The author of the report used 3 x 10^6. I prefer three millions but I don't want to make changes if they are not necessary. Also the author used lowercase letter "x" as multiply symbol without space around it. I am wondering if I should just change it to three million or use multiplication symbol with space around it? – Twisted Meadow Feb 21 at 15:10
• Where will you submit what you write? What software will you use to write it? I'd err on making it as "right" as possible, e.g. if you can use LaTeX or MathJax type 3\times 10^{6}. – J.G. Feb 21 at 15:15
• This is something that can also be dependent on a particular style guide, as well as determined by the context of the other types of notation used—meaning that you want to maintain consistency. There will be several different acceptable answers in general. The one to use in a specific case is up to style and the particular audience or publication. I don't know enough about mathematical publishing, however, to give a more detailed answer. – Jason Bassford Supports Monica Feb 21 at 15:18
• It would be nice to have the context in which this is appearing. Is it in a data table? Is it being used in the text? If the latter, what is the sentence it's being used in? – eyeballfrog Feb 21 at 19:17

When you select one way of number notation, stick to it.

"Three million" is appropriate in a text where readability is more important than precision, like "The intensity was three million times stronger than the reference". Whenever the number that you use needs to be referenced of copypasted, use a numeric form.

Scientific notation is a de-facto standard for scientific papers. Multiplication symbol ( × ) is used, so the number would be written as 3 × 106. To reflect the level of precision you may opt to write 3.0 × 106 or 3.00 × 106

The letter x can be used as a "cheap substitute" for the multiplication symbol.

You can also follow ISO 31-0 and write it as "3 000 000" (note it is using the spaces as group separators). This will convey the idea that this number is precise rather than approximate.

• If you're using an 'x' for the multiplication symbol, it's more common to use a lower case 'x'. – Arcanist Lupus Feb 22 at 3:01

"Three million" and "3 x 106" potentially mean different things. Since the original author wrote "3 x 106", my bias would be to leave it (other than changing the lower case x to a multiplication sign) unless you are confident that you aren't changing the meaning.

In standard scientific writing, "3 x 106" often means that there was a measurement with only a single significant digit of precision. In other words, the implied error bars on this measurement are ± 5 x 105 which means that the measurement was quite imprecise. A reported value of "3.00 x 106" would indicate a measurement with three significant digits of precision in which case the implied error bars would be ± 5 x 103. Writing the text "three million" or the number "3 000 000" potentially discards that nuance. On the other hand, the text "three million" or the number "3 000 000" tends to imply an intentionally approximate value rather than the result of a particular measurement. If I say that "the gas was three million times as hot at the end of the experiment", it is clear that I am giving a rough number for context rather than a precisely measured value that should be used in calculations.

Assuming that the different variations do not change what is being communicated, what numbers need to be compared with each other. If the three million value is compared elsewhere with measurements of one hundred thousand and of one billion, writing the numbers in words is problematic because readers tend to focus on the leading parts (3, 100, and 1) rather than the million, thousand, and billion. It can be easy for a reader to miss the fact that three million is 3 times more than one hundred thousand and three one-thousandths of one billion. "One billion" often feels smaller than "three million" or "one hundred thousand". On the other hand, when you use scientific notation, it is much easier to appreciate the difference in scale between 3 x 106, 1 x 105, and 1 x 109.

Beyond that, your style guide may provide some rules about how to present various types of numbers.
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