Nicholas Bodley wrote:

> Europe would show [decimal 1/4] as [0,25] ; the USA, as [0.25].

This is not exact. English-speaking European countries use the dot as well.
These presentation conventions are more linked to the language than to the
geographical location.

Moreover, the symbol used for separating the decimal part of the number is
often dependent on what is being counted. The generic dot (or comma) it is
often substituted with a symbol for the relevant unit of measure (e.g., "m"
for "meter" or "$" for "dollar").

> I understand that India subdivided large integers into groups
> of four, but I think we've discussed that briefly, already.

While the decimal separator has a mathematical significance (it establishes
the "scale" of the number), the so-called "grouping separator" only has the
linguistic purpose of making it easier to translate of written number into
linguistic units, so it is even more strictly connected to language.

Most Western languages group digits in group of *three* because their basic
lexemes to express numbers represent powers of 10 where the power is a
multiple of *three*: "thousand" = 1000 = 10^3; "million" = 1000000 = 10^6;
"billion" = 1000000000 = 10^9, etc.

E.g., Americans write 12345678901 as "12,345,678,901" because, in American
English, the number corresponds to this phrase:

"Twelve (12) billions
three hundred forty-five (345) millions
six hundred seventy-eight (678) thousand
nine hundred and one (901)"

Languages using different lexemes use correspondingly different groupings.
E.g., Indian languages (including Indian English) use:
"thousand" = 1,000 = 10^3; "lakh" = 10000000 = 10^7; "crore" = 10000000000 =
10^10, etc.

Consequently, Indians write 12345678901 as "1234,5678,901" because, in
Indian English, the number corresponds to this phrase:

"One thousands two hundreds thirty-four (1234) crores
five thousands six hundreds seventy-eight (5678) lakhs
nine hundreds and one (901)"

> Topic for another time: Mathematical notation is often akin to slang!

Numbers written grouping digits are hardly mathematical notation: they are a
just a sort shorthand for a particular kind of phrases that it would be too
fatiguing to spell out in letters.

_ Marco