Mind the gap

Imagine you are skim-reading a report and your eye lands on the number 15,469. How many is that? Now imagine you are reading the same report, published elsewhere, and the number appears as 15.469. How many is that? What if the number was written as 15 469 or 15469? Did any of these take you longer to understand / make sense of than the others?

If you learned your number conventions in the UK, you probably answered the first instantly, hesitated over the second, and found the last one the slowest – even though it is the only version with no ambiguity in it at all. In Berlin, for example, 15.469 is fifteen thousand four hundred and sixty-nine but in Birmingham it’s just under fifteen and a half: the same representation means a different number to different people. Meanwhile 15469 is the same number everywhere on earth, but nobody wants to read it!

Our team recently spent a morning discussing this, by email, as we are based in different locations. What follows are some of the considerations that came up in our conversation.

It began with a ‘simple’ question. Lynn, our copyeditor, shared a poll with the team:

“APA 7 style and non-technical UK style separate thousands with commas, e.g. 15,469 and 3,207. UK 'technical' style, which includes mathematics, permits thin spaces instead, e.g. 15 469 and 3 207. Which would you prefer?”

Two options. One click. But definitely not a straightforward answer! The email thread that grew around it took in six people, two hemispheres, a live experiment with a screen reader, a diversion about whether the digit 1 is too easily confused with a lower-case l, and eventually a suggestion that someone ought to write a blog about it – et voilà!

What made the thread interesting was not that people disagreed. It was that everyone was ‘right’, but about different things.

The international argument

Rachad made the case for the space: it is what most readers internationally will be familiar with, and what most academic journals and scientific bodies adopt. He is correct. The SI Brochure, maintained by the Bureau International des Poids et Mesures, is explicit that digits in long numbers may be divided into groups of three by a space, and that neither dots nor commas are ever inserted into those gaps (Bureau International des Poids et Mesures, 2026). The comma-as-thousands-separator is a regional habit that a large part of the world does not share. His summary was the neatest line in the thread: space is better, comma is easier.

The accessibility argument

Ray got there by a different route. His first instinct was the comma; then he reflected that some countries use a full stop, so perhaps the space avoids the problem; then he thought about screen readers, and went straight back to the comma. He was right to worry. A space of any kind, ordinary, non-breaking, or thin, is read by most screen readers as a boundary between two separate numbers, so 1 475 is announced as 'one, four hundred and seventy-five' (Irgens, 2020). The number is not just awkward: it’s plain wrong.

The legibility argument

I went down quite the research rabbit hole and came back with the point that past a certain length, something is needed. This is not really a typographic preference; it is a fact about working memory. Grouping digits is a textbook case of 'chunking', first described by Miller (1956) and substantially revised by Cowan (2001), whose estimate of our capacity – around four items, not seven – is why phone numbers, bank card numbers and sort codes are all printed in blocks. An unbroken string of six digits asks the reader to hold six things in mind at once. Two groups of three asks them to hold two.

Three arguments, all evidence-based, but pointing in two different directions.

The experiment that complicated things

Then Nadia did something hugely pragmatic: she stopped arguing and tested it.

She opened the LaTeX-generated PDF in Adobe and used the built-in read aloud function to ‘speak’ 1 234 and 1,234. Both were read incorrectly. Only when she typed 1234 was the number read out correctly. She tried again with five digits: 12 345, 12,345 and 12345. Again, only the unseparated version ‘worked’.

This was worth sitting with for a while, because it broke the implicit A or B choice that the thread had assumed. We had been weighing space (bad for screen readers) against commas (fine for screen readers). It turns out that in at least some contexts the comma is not fine either – a screen reader may take it as a list boundary and announce 'twelve, three hundred and forty-five', so whichever separator we choose, the number is being spoken incorrectly to some of our audience.

Ray had already identified the standard remedy: an aria-label, which works rather like alt text for images, letting you supply a spoken version – aria-label="one thousand four hundred and seventy-five" – that differs from the printed one (W3C, 2026). Nadia’s view was that we cannot avoid using aria-labels whichever choice we make, and that we could easily make a consistent habit of using them in this context.

She is right, though I would add a caution that surfaced when I went looking afterwards: accessibility practitioners are wary of using aria-labels to override pronunciation, because it also overrides the user's own screen reader settings, and because braille display users receive the label as literal text (Onsman, 2023). There is a third path that Wikipedia uses: keep the digits unbroken in the underlying data and create the visual gaps with CSS (Cascading Style Sheets) margins, so that sighted readers see 15 469, screen readers receive 15469, and anyone copying the number gets something a spreadsheet will accept. It costs more to build, but it may be the only option that serves everyone at once.

And there is a further question that would not have been asked five years ago, which Ellen raised: What does a space do to machine interpretation? When our content is increasingly parsed by systems we do not control, a separator is no longer only a message to a human audience.

Where we landed, provisionally

The thread converged somewhere none of the poll options had offered.

Nadia recalled that some textbooks used no separator for four-digit numbers and introduced the use of one only from five digits upwards. Lynn, who had already noted that from a legibility standpoint the unseparated form works up to about four figures and no further, was happy with that, and everyone else agreed.

Which is, satisfyingly, exactly what the SI Brochure says: when there are only four digits, it is customary not to use a space to isolate a single digit (Bureau International des Poids et Mesures, 2026). We had reasoned our way, by committee, to an existing international convention. There is a lesson in that somewhere!

That leaves the five-digits-and-up case genuinely open. The poll's majority was for commas; the discussion has since made the case for spaces plus aria-labels look stronger than it did at nine in the morning.

Why this was not a waste of a morning

It would be easy to read the thread as a group of professionals spending three hours on a comma. I want to argue the opposite.

A style guide is often mistaken for a rulebook: a list of preferences adhered to by a copyeditor. It is better understood as a record of decisions a team has already made about its audience, so that nobody has to make them again from scratch. Every entry encodes an answer to the question 'Who is accessing this, and what will help them?' That question has no context-free answer, which is why the guide exists.

What our thread exposed is how many distinct audiences are hiding inside one small typographic choice. There is the person in another country, for whom the comma is a decimal point. The person using a screen reader, for whom the space is a full stop. The person with limited working memory, for whom the unseparated string is a wall. The developer – John, in our case – for whom the numbers appear not in edited prose but in the interface of the Cambridge Mathematics Framework, generated by code that has to be told how to format them. And now the machine reader, for which Generative Engine Optimisation guides (GEO guides) are in development, but don’t yet offer this level of detail.

Conventions are invisible right up until the moment someone asks you to justify one. Then you discover that the answer involves cognitive psychology, international standards bodies, assistive technology, and a poll.

Further considerations

An audience the thread did not mention, because it sits outside our own house style, is the Year 6 learner in a UK school. Since 2016 the Standards and Testing Agency has used the comma as the thousands separator in Key Stage 2 mathematics assessments, and its marking principles rely on which symbol a learner uses; a comma is credited even when misplaced, provided the digits stay in order, while another symbol, a decimal point or apostrophe used incorrectly, loses the mark (Standards and Testing Agency, 2025). What the rule never names is the space, the very form the SI Brochure prescribes, because a space is not a symbol but the absence of one. Far from being marked wrong, it slips through the categories altogether: accepted, if at all, under the catch-all that any unambiguous answer will do, but expressly allowed in the modified-print papers (Standards and Testing Agency, 2024). Which is another anomaly, since braille helpfully has different notations for commas, full stops and decimal points but never usually uses spaces in its representation of numbers (Braille Authority of the United Kingdom, 2004 / 2006).

There is a mathematical point here too, and it is the one I keep returning to. The separator is not decoration. In 15 469 the gap marks the boundary between the number of thousands and the number of ones (each containing hundreds, tens and ones within them) – it is a visible trace of the base-ten grouping structure that we spend years, in the UK, teaching children to see. When we set a house style for it, we are making a claim, however quietly, about how the structure of number should look on a page. Ray's stray finding about the digits 0 and 1 being mistaken for capital ‘O’ and lowercase ‘l’ makes the same point from the other end: notation carries meaning, and the choice of glyph is never neutral.

Over to you

Two things to try:

Look at the last document you wrote and find the largest number in it. How is it separated? Did you choose that, or did the software? What would a screen reader make of it?
This might be of more interest if you teach: how do your learners read 15 469? Have they ever been told what the gap is for – that it marks the boundary (in this case) of the number of thousands, rather than a pause, as a gap between words would signify? Or is it something they have been left to infer, perhaps wrongly?

We would love to hear how your own team resolved this, or whether you have simply never had the discussion. If it is the latter, I recommend it. Set aside a morning.

Reference

Join the conversation: You can message us @CambridgeMaths or comment below.