Implicature of the day
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Mouseover title: "They rounded down to 182.8 instead of rounding up to 182.9 because 182.9 might make the statement incorrect."
The cited statement is clearly a violation of the Maxim of Quantity. But I don't think I've ever seen a discussion of the pragmatic inference from over-exact numbers to conversion of units, or even a discussion of the problems for cross-cultural translation — though the issue certainly arises frequently.
For example, should we explain to our European colleagues that the U.S. chain Five Below sells only items priced below €4.31 (as of the current rate of exchange)? Presumably that's a case where exact currency conversion is inappropriate.
Robert Coren said,
May 21, 2026 @ 9:26 am
It might seem similarly strange that "normal" human body temperature is described as 98.6F – inappropriately precise, given that actual healthy body temperatures vary fairly widely both from person to person and from time to time for the same person. This all became clear when I noticed that 98.6F is exactly 37C, and presumably whoever originally determined (or published the determination of) "normal" temperature was using Celsius, and probably said it was "about 37"; the sensible translation of this would have been "about 99F", but that's not what happened.
(Note: the mechanism on my iMac that would have allowed me to insert degree symbols isn't working today, for some reason.)
Jkw said,
May 21, 2026 @ 9:42 am
This comes up in idioms too. In England, people say 7 stone weakling. In America, it is 98 pound weakling. A strange conversion that could have been rounded. I don't think either idiom is in common usage anymore.
I do find it funny that a British ton (2240 lbs) is almost the same as a metric ton (1000kg), but an American ton (2000 lbs) is about 10% lighter. I'm not sure when an American ton was reduced from 20 hundredweight to 2000 lbs. I'm sure this has caused problems at times. Similarly to the question of what number is one billion, though I think the American billion has won out.
Ken said,
May 21, 2026 @ 9:58 am
The explainxkcd for this one has an example of false precision which may interest (or irritate) linguists: "now with more than 28.4% more water."
Don Monroe said,
May 21, 2026 @ 10:06 am
I've done this reverse engineering many times over my decades. The most recent example is the arbitrary definition of where outer space starts, at an altitude of 62 miles. Of course it is 100 km.
J.W. Brewer said,
May 21, 2026 @ 10:24 am
FWIW I think "98-pound weakling" is charming precisely because it's not a very round number, and you can be charmed by that w/o realizing that it = 7 stone. But if the adopted expression had originally been 45-kg weakling, it would be odd to adopt it as 99.2-pound weakling or 99-pound-three-ounce weakling.
As to 98.6 degrees F, it's only overprecise if you understand the amount of normal variation. Wikipedia advises that the melting point of copper is 1984.32 F, and the last two digits aren't an artifact of translation because that's given as the equivalent to 1357.77 K or 1084.62 C. Someone is convinced that offering that much precision is not Griceanly inappropriate in that context.
Jonathan Smith said,
May 21, 2026 @ 10:49 am
Happened during covid with signs etc. instructing you to maintain a distance of 6 ft / 1.83 meters.
Julian Hook said,
May 21, 2026 @ 11:41 am
Related to the matter of 98.6 degrees F, I've noticed that my thermometer often reports that my temperature is 97.7, 97.9. 98.1, 98.2, 98.4, or 98.6, but it never reports a temperature of 97.8, 98.0, 98.3, or 98.5. I assume the explanation is that temperatures are internally recorded in Celsius to the nearest 0.1 degree, and then converted to Fahrenheit and rounded off again (so 36.5 C becomes 97.7 F, 36.6 C becomes 97.9 F, and so on).
Also, driving through western Pennsylvania a few years ago, I encountered a sign that read "Bridge 3168 feet ahead." It struck me as so odd that I stopped and took a picture of it. Only later did I realize that 3168 feet is exactly 0.6 miles. (But I never figured out why someone thought it was important to alert drivers to a bridge that far ahead.)
Athel Cornish-Bowden said,
May 21, 2026 @ 12:00 pm
Around the time the UK was making a half-hearted transition to the metric system, a government pamphlet was said to have included a recommendation to move something 2.54 or 5.08 cm ("an inch or two"). I didn't actually see the pamphlet, so this may just be an example someone invented.
Brett said,
May 21, 2026 @ 1:28 pm
One interesting thing about body temperatures is that the average measured value that the standard quoted number was based on actually came out to be 98.4 °F. However, while, given the large quantity of data, the number was that precise as a mean, the last decimal digit was not useful information practically. Variation from person to person, and over time for a single individual, is quite a bit greater than a tenth of a degree. So the number was rounded, in metric, to 37 °C. However, when this was converted to Fahrenheit, it gave 98.6, which is sometimes then rounded up to 99—even though the actual measured average ought to be rounded down to 98 °F.
J.W. Brewer said,
May 21, 2026 @ 1:33 pm
Re Julian Hook's bridge-sign example, thinking in terms of decimal subdivisions of a mile is already suspiciously quasi-metric. It would have been better for the sign to have flagged the approaching bridge at 3300 feet, i.e. five furlongs.
Victor Mair said,
May 21, 2026 @ 1:58 pm
I've always been charmed by the fact that my average body temperature has been 96.8 F for as long as I can remember. All my vital signs are slower / lower than those of most people.
Doug said,
May 21, 2026 @ 2:00 pm
Jkw said, "I'm not sure when an American ton was reduced from 20 hundredweight to 2000 lbs. "
Maybe we left the ton unchanged at 20 hundredweight, but redefined "hundredweight" to be 100 pounds instead of 112 pounds.
David Morris said,
May 21, 2026 @ 3:24 pm
In Australia, the COVID distance was 1.5 m.
Mike Grubb said,
May 21, 2026 @ 3:34 pm
Apropos of Jkw's & Doug's respective posts: Wikipedia's entry "hundredweight" states:
"The short hundredweight or cental of 100 pounds (45.36 kg) is defined in the United States customary system. The long or imperial hundredweight of 8 stone or 112 pounds (50.80 kg) is defined in the British imperial system.
Under both conventions, there are 20 hundredweight in a ton, producing a 'short ton' of 2,000 pounds (907.2 kg) and a 'long ton' of 2,240 pounds (1,016 kg)."
J.W. Brewer said,
May 21, 2026 @ 5:31 pm
Paul Deighan's _A Complete Treatise on Arithmetic, Rational and Practical_, published in 1804 in Dublin, distinguishes between the "short cwt." of 112 lb. and the "long cwt." of 120 lb., although cwt. w/o further specification seems to be the "short[er]" one. Maybe the 100 lb. one wasn't common in Ireland back then? But I expect the story with hundredweight (maybe less used in the U.S. anyways, not least because we weren't as prone to use the "stone" that the 112 lb. version presupposed) is similar to that of gallon – lots of differently sized definitions were traditionally in use in England in different contexts, and eventually there was a drive for standardization but the U.S. and U.K. picked a different option out of the range of prior options to use as the standard.
Chester Draws said,
May 21, 2026 @ 5:56 pm
The example of this that really infuriates me is when New Zealand newsreaders say things like "Yesterday's storm in the US is estimated to have cost 35.3 million dollars in damage".
Someone has plucked a number out of the blue, in this case US$20 million, usually with no real calculations involved and absolutely not intended to be anything other than that. Then the reporters have treated that as if it had some actual merit and applied the exchange rate exactly to it.
JPL said,
May 21, 2026 @ 7:35 pm
It brings up the old problem of referential identity in propositional attitude constructions. Presumably the reverse-engineering speaker knows the bay in places is more than 100 fathoms deep; but the woman next to the guy whose thought was externalized and has realized the equivalence doesn't (let's stipulate) know that. In spite of her understanding what the speaker said, it would not be true to say that she now knows that the bay in places is more than 100 fathoms deep, even though the distance measured by both terms is exactly the same. The expressions are referentially identical, but in this case if you substitute the one expression for the other, the sentence becomes false. (h/t Frege)
F said,
May 21, 2026 @ 10:44 pm
My favorite inappropriate unit conversion is when the rapper 50 Cent was converted to RM1.50 (Malaysian ringgit).
As for human body temperature, I learned as a kid that it's 36.6 Celsius. Though my parents measured it under the arm, so it's a bit lower in any case than the oral temperature typically measured in the US.
Peter Cyrus said,
May 21, 2026 @ 10:53 pm
Conversions need to respect the number of significant figures, and that idea has to be more widely taught.
Graeme Hirst said,
May 22, 2026 @ 1:11 am
And then there's over-zealous rounding without unit conversion: What is up with UK bridge signs? (from Stand-up Maths) https://youtu.be/kH_bSvf7EVA?si=zsMzegySuyYRa3sQ
Andreas Johansson said,
May 22, 2026 @ 2:59 am
A "favorite" example of this was a newspaper piece about indoor temperatures that would repeatedly say things like "approximately 21.1ºC" (i.e., approximately 70ºF).
This does raise something of a legitimate question, though; it's not obvious whether 70ºF has one or two significant digits. (In this case likely two; you're likely to care whether your living room is 65ºF or 75ºF.)
David Marjanović said,
May 22, 2026 @ 5:27 am
It gets worse. 37 °C is rounded up from the abovementioned real value of 36.6 °C – which you get if you measure the old-fashioned way, i.e. in an orifice. My healthy armpit temperature is only 35.9 °C; when I "have 37 degrees", I'm already in bed with a quite noticeable cold.
I think that's meant to convey "not even 100 pounds".
J.W. Brewer said,
May 22, 2026 @ 7:19 am
As I was having my coffee, my smartphone gave me a perhaps-comical example of what Chester Drawers was complaining about in the form of different headlines from different stories covering the same underlying event that seemed like they could not all be true as stated. E.g.
1. Vietnam auctions convicted tycoon's Hermes handbags for over $500k
2. Jailed Vietnamese tycoon's Birkin bags sell for more than $550K
3. Two Hermes bags of convicted tycoon Truong My Lan fetch $531,000 at auction
And more with other numbers, including some with figures given in pounds sterling or Euros, and others that again seemed inconsistent with each other from an implicature perspective even if specified as non-exact (e.g. "more than \$554,000" versus "over \$539,000").
All of these numbers were apparently "translating" an original number or numbers stated in Vietnamese dong, but it's not clear to me without digging more deeply than I cared to how much of the variation in translation output is due to 1) variation in significant figures in the input (e.g. rounded to nearest billion versus nearest hundred-million); versus 2) variation in significant figures in the output; versus 3) variation in the exchange rate assumed.
J.W. Brewer said,
May 22, 2026 @ 7:26 am
Pace David M., "98 pound weakling" is sufficiently transparently a calque of "seven stone weakling" that it is "meant to convey" (to the extent an idiom can be said to actually reflect anyone's actual subjective intention?) "not even 112 pounds."
While I don't advocate reform of American usage given how alien "stone" are to our way of talking about weight, it does seem that from a "significant figures" perspective denominating the weight of adult human beings in stone is better than pounds because if you gain or lose a few pounds it is generally meaningless noise (not to mention that the sort of scales people typically use in at least non-hospital settings may in practice give a result a pound or two off in either direction from the true weight) whereas gaining or losing a stone is indeed significant.
Robot Therapist said,
May 22, 2026 @ 7:50 am
Reminds me of the old joke about the museum guide who tells a visitor that the fossil is 400,000,005 years old. "Because when I came here 5 years ago…."
anonymous said,
May 22, 2026 @ 8:02 am
@Andreas Johansson:
"it's not obvious whether 70ºF has one or two significant digits."
This is why, when it matters, we use scientific notation.
Doug said,
May 22, 2026 @ 8:16 am
I'm not sure I should believe that "98 pound weakling" came from a conversion of "seven stone weakling."
A discussion here:
https://languagehat.com/lay-metrology/
(specifically the note from ktschwartz) suggests that "97 pound weakling" was the original.
languagehat said,
May 22, 2026 @ 8:23 am
I'm not sure I should believe that "98 pound weakling" came from a conversion of "seven stone weakling."
You shouldn't; it's nonsense. As I said in that thread:
David Morris said,
May 22, 2026 @ 8:28 am
The Sydney Town Hall organ was extensively refurbished around the time that metric measurements were being introduced in Australia. Many years later the organ builder showed me a booklet which the city council had produced including eg "Open Diapason 2.44 m". He convinced them to scrap it.
Subway stations in Seoul have directions to the nearest exit, with a distance to the nearest metre eg '49 m'. Saying 50 m would mean that people reach the exit one metre sooner than they otherwise might expect (like, anyone's counting/measuring?).
J.W. Brewer said,
May 22, 2026 @ 8:30 am
Come to think of it, the examples in my earlier post about the Vietnamese handbag auction may illustrate why "significant digits" is itself a not-always-useful concept, because reality is not always usefully subdivided in a decimalized way. Take the headline that says "over \$500K." That has some implicature of "but not over \$X." But what's X? It can't be that either X is \$600K or it's \$510K or it's \$501K with no other possibilities. There are contexts in which it would be reasonable to think the headline was fine if e.g. the real number was \$519,204 but misleading if the real number was \$563,444.
Indeed, auction houses (the context of that story) often have conventions where you can't just bid a dollar above the current bid you have to offer at least a specified minimum "salient" or "significant" increment so at all times the current bid is a "round number," but whether the minimum increment is \$100 more or \$10,000 more or something else depends on what the current bid is. One major NYC house has a chart online telling you the required increments in nine specified ranges that collectively get you from a current bid of \$100 (must bid at least \$200) to one of \$190,000 (must bid at least \$200,000), while indicating that beyond \$200K the auctioneer has discretion as to how to adjust the pattern to the situation.
Doug said,
May 22, 2026 @ 8:38 am
J.W. Brewer said
"…"significant digits" is itself a not-always-useful concept, because reality is not always usefully subdivided in a decimalized way. "
I remember dealing with significant digits (or "significant figures") in my high school chemistry class, and thinking that chemists must be very strange people who think that three tenths is somehow more of a "round number" than a quarter.
Ralph Hickok said,
May 22, 2026 @ 11:30 am
I'm a bit puzzled by "98-pound weakling," since the standard weakling to me weighs 97 pounds. I got that notion for Charles Atlas, who was a 97-pound weakling before before he became the world's most perfectly developed man.
https://www.reddit.com/r/vintageads/comments/10sndot/charles_atlas_1948_97lb_weakling/
J.W. Brewer said,
May 22, 2026 @ 3:59 pm
The history of proverbial weakling-weights is complex and it was too messy to be a good example. If you check out the google books ngram viewer, you will see that (in that corpus) 97-pound came first, starting in the late 1920's, then 98-pound arrived on the scene circa 1956, was approximately as common as 97 by circa 1970, and pulled ahead consistently after circa 1985. Seven-stone doesn't turn up in the corpus until circa 1962, and unsuprisingly much more in BrEng texts than AmEng ones.
Perhaps "98 pounds" feels like the canonical form to me because that's what's specified in the opening line of the song "I Can Make You a Man," from _The Rocky Horror Picture Show_, which is transparently based on the old Charles Atlas ads. I may have been exposed to that as a teenager more than to older texts using 97.
languagehat's theory that the switch from 97 to 98 was motivated by the prosodic desire to lose a syllable and end on a stressed one does not IMHO sufficiently explain the mildly remarkable coincidence that 98 (precisely equaling 7 stone) was the strong-final syllable substitute chosen when 95, 96 or 99 would have all accomplished that while being more obvious "round" numbers in an American context. Although to be fair 97 is prime, so maybe roundness was not the desideratum?
SlideSF said,
May 22, 2026 @ 5:40 pm
I was about to type that to me, a native AmE speaker of a certain age, 98-pound weakling sounded so much better to the ear than 100-pound weakling perhaps because of seeing it so many times in the back pages of Superman an other comics as a child. This would have been in the late 1950s to mid 1960s.
Then I read Ralph Hickok's comment about the original Charles Atlas term 97-pound weakling. It gave me pause, because to me it has always been 98. Or has it? I honestly cannot remember at this point what those comic adverts said. But I do remember the buff bodybuilder kicking sand in the guy's face before taking his girl away.
Barbara Phillips Long said,
May 22, 2026 @ 6:45 pm
Wired has a new article about measurement, saying that counting and comparison are the basis of measurement and have been used since the stone age. There are a lot of photos of various measuring, counting, and timing devices, plus some commentary on "digital." Quotes:
Humans are animals that measure things. Call us Homo mensura. We have a compulsion to quantify, and for millennia we’ve been inventing new ways to go about it. For anything you can think of, there’s a device to measure it—from sphygmomanometers to spectrophotofluorometers. And of course nowhere is this more true than in science. Well, science and baseball.
…
Of course, today we have some pretty fancy instruments for this. But I’m going to let you in on a little secret: With all of our cool tools, measurement still comes down to either comparison or counting. In that sense, it hasn’t changed much since Noah built his ark from a spec sheet in cubits—the length of a human forearm from elbow to fingertip.
…
we’re used to thinking of digital as synonymous with electronic. But what makes electronic systems digital is that information can only be represented by discrete values—the binary digits 0 and 1. So yes, even though the timer above operates by ratcheting physical gears, this is a digital device.
https://www.wired.com/story/story/all-measuring-devices-run-on-two-stone-age-techniques/
unekdoud said,
May 22, 2026 @ 11:59 pm
I bought a cheap kitchen scale online that happily reports weights of 97, 98 and 100 grams, but never 99 or 101. (I believe scales are tested and calibrated using a 100-gram weight.) I've been wondering if it uses just rounding, or conversion and then rounding.
For a non-physical conversion: it is still common to see electronic displays marketed as having (more than) 16 million colors, and as we all know, the actual number is 2^24. (Hopefully.)
Michael Watts said,
May 24, 2026 @ 8:53 am
Well, the concept is good, but people can be confused over where to apply it.
The basic reality of dealing with body temperature in Fahrenheit is that the difference between a temperature that is elevated by 1.7 degrees or one that is elevated by 2.2 degrees is quite material; the difference between a temperature of +1.71 and +1.76 not so much.
It matters how accurately you can measure body temperature, and significant figures are the way we measure accuracy of measurement. But it would be a mistake to report absolute body temperatures by reference to the concept of significant figures – you want to report them by reference to the scale at which variation (1) exists, and (2) matters, which is, on the assumption that we're reporting Fahrenheit units in a decimalized form, tenths of a degree.
Applying the concept of "significant figures" directly to an absolute body temperature encounters the problem that the scale of meaningful variation is dwarfed by the absolute value. If you do want to talk about "significant figures" in a reported temperature of 98.6, the right way to do that is to treat the initial "9" as a constant that contributes zero figures. (And the better way is the approach from my earlier paragraph, treating "98.6" as a constant in its entirety and working in 'the amount of deviation from 98.6'. How well you can apply that model to a thermometer would seem to depend on the details of how the thermometer arrives at its temperature estimate.)
John Lavagnino said,
May 26, 2026 @ 4:40 am
The London newspaper The Daily Telegraph was once known for a policy of making the news as dull as possible, and in that spirit once reported Elizabeth Taylor as saying “I’m feeling like a million dollars (£357,000).”
Madeline Kalvis said,
June 1, 2026 @ 8:41 pm
Personal rule: if I have a nice round number, I un-round it up or down, or add a decimal.
E.g. if the number is 400, then it either needs to be 401, or 400.0, depending on whether legibility or accuracy is the bigger priority.
Doug said,
June 5, 2026 @ 11:27 am
I am reminded of the well-known anecdote about Mt. Everest:
"…in 1856 the British Royal Geographic Society declared the elevation of Peak XV (as Everest was then called by the British surveyors) to be 29,002 ft. after several years of careful, redundant (to double-check accuracy) mathematical calculations to correct Nicholson's data for light refraction, barometric pressure, temperature and tidal effects. In fact, Peak XV was calculated to be exactly 29,000 ft., but to avoid people thinking that they had simply rounded-off or estimated the calculation, they added two feet to make the elevation look more believable."
https://www.montana.edu/everest/facts/elevation.html
amy said,
June 18, 2026 @ 9:15 pm
A bridge that is 3168 feet ahead (0.6mi) is only 36 seconds away if you're driving at 60mph.