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March 10

Rounding numbers up instead of down

English, and as far as I know, most other languages, round numbers strictly down. For example, we call 99 "ninety-nine", not "one hundred less one". We do this even for numbers for which it really makes no sense to round down, such as a price of $19995 (spoken as "nineteen nine ninety-five", not "twenty thousand less five"). I am aware that some languages such as Latin and (if I remember correctly) Hindi round up 19, 29, 39, etc. But do any languages extend this to other numbers?

To be more specific: do speakers of literally all languages with a decimal numeral system treat the number 378 as 300 with a surplus of 78, rather than as 400 with a deficit of 22 ? 2601:18A:C500:7170:C3D2:B296:9A92:B82D (talk) 02:31, 10 March 2023 (UTC)[reply]

Latin employed subtractive composition at least in the number names duodeviginti 18, undeviginti 19, duodetriginta 28, undetriginta 29, duodequadraginta 38, undequadraginta 39, undequinqaginta 49, undesexaginta 59, undeoctoginta 79, and undenonaginta 89. Probably more languages use subtractive composition in time reckoning ("a quarter to five") than in number names... AnonMoos (talk) 03:45, 10 March 2023 (UTC)[reply]

Germanic languages, including Old English, named "and a half"-numbers by rounding up: e.g. German anderthalb for 1½, dritthalb for 2½, vierthalb for 3½, fünfthalb for 4½; Danish halvanden, halvtredje, halvfjerde, halvfemte, etc. In all (?) Germanic languages, these half-numerals went out of use by 20th century. 2A02:5080:2B0C:9200:7148:6641:6BB1:71F8 (talk) 10:32, 10 March 2023 (UTC)[reply]

Anderthalb is still quite common in German, but I (as a native speaker) wasn't aware of its literal meaning (andert ≈ "other" = "second"). Thanks! --Wrongfilter (talk) 16:10, 10 March 2023 (UTC)[reply]

In Finnish, 8 (kahdeksan) and 9 (yhdeksän) are transparently derived from 2 (kaksi) and 1 (yksi) respectively (even if the origin of the suffix is not clear). But these are an isolated case in the language AFAIK. ColinFine (talk) 14:37, 10 March 2023 (UTC)[reply]

Swedish time has eg halv två (half two) for 1.30. DuncanHill (talk) 14:46, 10 March 2023 (UTC)[reply]

...and "fem i halv två" ('five in half two') for 1.25. --Soman (talk) 15:06, 10 March 2023 (UTC)[reply]

German time is similar, "halb zwei" (half [before] two) is 1:30. MinorProphet (talk) 15:11, 10 March 2023 (UTC)[reply]

It doesn't actually mean "half before two" but "half of the second hour". It can become confusing when people (in the South of Germany) use viertel zwei (1:15) and dreiviertel zwei (1:45), even though it's completely logical. --Wrongfilter (talk) 16:10, 10 March 2023 (UTC)[reply]

Polish used to have a similar system (perhaps a calque from German): półtora (half to two) for 1½, półtrzecia (halft to three) for 2½, półczwarta (half to four) for 3½, etc. With the exception of półtora, these are now almost forgotten and replaced with trzy i pół (three and a half), cztery i pół (four and a half), etc. — Kpalion^(talk) 00:56, 12 March 2023 (UTC)[reply]

półtora presumably incorporates a cognate of vtor– 'second' (rather than dv– 'two'). —Tamfang (talk) 23:54, 14 March 2023 (UTC)[reply]

… while in England, apparently, "half seven" means 7:30. That was a bit puzzling for my American tour party, some of whom were aware of the German form. —Tamfang (talk) 23:53, 14 March 2023 (UTC)[reply]

Here's a reference; as well as Latin and Finnish as mentioned above it talks about Yoruba, and mentions some isolated cases in Ancient Greek, Hebrew and Aramaic. [1] 70.67.193.176 (talk) 18:18, 10 March 2023 (UTC)[reply]

You've gotten some good answers, but just for the sake of it: you're using the word "rounding" in a way that many people would find confusing. As our article on rounding says, "Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation.". In other words, rounding would be the activity that sees 99 and says "one hundred". I don't know what the proper term for what you're asking about is. I like AnonMoos's "subtractive composition", but some quick googling suggests that's not standard either. If someone could supply the correct term, it would be a lot easier to search for. Whatever the term is, it's used in English for some time terms with forms like "10 to 5", where we're subtracting 10 minutes away from 5 o'clock. Matt Deres (talk) 19:37, 13 March 2023 (UTC)[reply]

Yeah, rounding up is turning 95 to 100, rounding down is turning 105 to 100. 99 as it is, is not technically rounded. 惑乱 Wakuran (talk) 02:04, 14 March 2023 (UTC)[reply]

It could be rounded to the nearest integer from

4.63 3 = 99.252847

. --Lambiam 11:05, 14 March 2023 (UTC)[reply]

Matt_Deres -- The paper linked to by 70.67.193.176 above calls the phenomenon "Subtractive composite numerals"... AnonMoos (talk) 20:29, 16 March 2023 (UTC)[reply]