Three rules that produce most of the errors
The first is the space above. It is easy to check by search and impossible to check by reading.
The second is mixing symbols with spelled-out names. The guide is clear that values should be expressed using the symbols for the units rather than the spelled-out names, and that the two are not interchangeable within an expression.1 A document that writes 5 kg in one paragraph and five kilograms in the next has made a decision twice.
The third is the treatment of the numbers themselves, which no international standard settles because it is a house question. The GPO Style Manual uses a figure for a single number of 10 or more, with 50 ballots and 24 horses as its examples.2 Where two or more numbers appear in a sentence and one of them is 10 or larger, figures are used for each.2 Another manual will say something else, and both are correct within their own house.
The errors that survive every read
Four categories, and none of them is caught by reading the sentence.
A transposed digit is the first, and it is the one that reaches print most often. Nothing in a spell checker knows which number was intended, and 1,750 written as 1,570 is invisible to every automated pass and to most human ones.
A figure that disagrees with itself across the document is the second. A number in an abstract, a number in a table, and a number in a discussion should agree, and on a paper with several authors they often do not. Editors Canada's copy editing standards cover exactly this, including checking calculations and incorrect imperial or metric conversions.3
A unit that changed without the number changing is the third. That is what a botched conversion looks like on the page, and it survives every read that is not looking for it.
A percentage that is a percentage of something unstated is the fourth. It reads perfectly and cannot be checked by anyone, including the author, six months later.
Where the destination sets the convention
Journals publish their requirements, and they are specific. The International Committee of Medical Journal Editors asks that measurements of length, height, weight, and volume be reported in metric units, and that temperatures be given in degrees Celsius.4 It also asks for standard abbreviations only, notes that nonstandard ones confuse readers, and advises against abbreviations in the title.4
Where a destination has published a rule, it outranks the house preference and the author's habit. Where none exists, the document has to choose one and hold it, which is a style sheet question rather than a correctness question.
The pass that finds them
Numbers cannot be proofread by reading, because the eye supplies what it expects. They are found by extraction instead, which is a different operation with a different rhythm.
Every figure in the document is listed with its location. Figures that appear more than once are grouped so the copies can be compared. Every unit is listed the same way, so that a document using both kg and kilograms shows it in one column. Every percentage is checked for a stated denominator.
That is a mechanical pass, it is dull, and it finds things a careful reading never will. It is also the pass most often skipped under a deadline, which is why the errors it finds are the errors that reach print.
An editor does not decide whether a figure is correct, whether a conversion was appropriate, or whether a measurement means what the author says it means. Those belong to the author and their own reviewers. What an editor supplies is the list of places where the document disagrees with itself.
Everything a client sends is treated in confidence, including data, drafts, and correspondence. We work on technical documents and journal articles to whichever convention the destination publishes.