According to Wikipedia the two variants exist because the digits of large numbers used to be grouped into groups of six digits but in order to improve readability this was eventually changed to groups of three digits and some insisted that with that also the naming should be adjusted. A long scale trillion has three digit groups when using groups of six digits (1,000000,000000,000000) and six after the switch to groups of three (1,000,000,000,000,000,000) which then should be a short scale sextillion but somehow it ended up as a quintillion.
This is the key piece of information for making sense of it. Ultimately the OP's insight is that the number-naming system used in the west is thousands based instead of millions based, but came to that by observing the number-naming outcomes instead of the source notation that led to it.
Spanish uses the long scale, but lately I've been noticing people mistakenly using the short scale in Spanish more and more, likely due to the influence of English and the internet, sometimes even in news articles and other "professional" publications. You may see someone speaking of "un trillón de dólares" (a trillion dollars), which while it makes sense in English when speaking of federal budgets or the market cap of FAANG, in long scale that's more than the world's entire money supply.
It's especially annoying because it creates ambiguity and renders the *illón-words fairly useless.
In Dutch the word "miljard" for 10^9 is too well known and deeply ingrained to change I think, but with "triljoen" which could either mean 10^18 or a direct conversion from the American English trillion, all bets are off
Yeah, I too think that's likely the direction we're heading, and I'd be fine with either option as long as it was consistently used, this transitional phase is just painful.
In the meanwhile you can say one thousand millions (for what Americans call a billion), like the local tv news does, and for the bigger one say just say millions of millions (what Americans call a trillion), that should be unambiguous enough.
If you want to be unambiguously understood, especially in international context, it seems it's better to avoid words beyond "million" altogether.
"million of millions of dollars" or "ten to the twelfth dollars" or "one tera dollar" or even "one EEE twelve" (for programmers) will always be understood correctly, no matter which part of world listeners are from.
The only everyday context where numbers on that scale are commonly used is money/finance, and it's pretty universal in that context that 1e9=B=billion, 1e12=T=trillion. This long scale/short scale distinction gets posted a lot but it's one of those cases where in practice it seems to matter very little.
In science and engineering you'd rather use scientific notation anyway, and in math and CS notoriously only 3 numbers exist: 0, 1 and n.
You don't seem to get the point. That is only universal in current day English. In e.g. Finnish: miljoona = 1e6, miljardi = 1e9, biljoona = 1e12, triljoona = 1e18.
TIL about one more thing US misunderstood and now we have to deal with it. Another one is command key on mac, "borrowed" from road sign indicating "sight seeing place" :)
I don't see how borrowing the Swedish "point of interest" symbol for the command key is "misunderstanding" something - as I understand the story, they just liked the symbol and decided to use it.
Also, I'm certainly not a US apologist, but I also don't see how the US using the short scale is a case of misunderstanding - it sounds like they just decided that it makes more sense that way (and I would agree, although maybe that's just because I'm used to it).
this is so funny because i always envied english for it being so clear: million, billion, trillion. in german we have these "awkward" names in between: million, milliarden, billionen, billiarden. but now hearing about this long scale it actually does make quite a lot more sense when thinking about it in multiples of millions
Swedish does that as well. miljon, miljard, biljon, biljard.
This is sufficiently confusing to people that every time I see a newspaper article mention something is a biljon of something they have to mention how much it is and remind readers to not confuse it with an American billion (that is only a miljard).
In most contexts when big numbers like those show up though the metric-system comes to the rescue, since things will be referred to as being a mega-something or giga-something etc anyway. That works great until Americans attempt to do it and get the letters wrong or use K instead of k or M instead of m that causes new confusion and then we're back at having to guess what something means depending on what side of the Atlantic it was written.
same in Italian: milione (1E6), miliardo (1E9), bilione (1E12) etc.. the long scale a "one" is 1E6 bigger than the previous one, example: bilione is 1E6 bigger than milione.
As a kid I stressed our Olivetti divisumma 24 ( https://www.ithistory.org/sites/default/files/hardware/Olive... ) with a million times a million. It entered a perpetual mechanical cycle that even unplugging it could not break. Finally Dad had to attack its innards and tug and twiddle until he pulled out a spring loaded gear and it caught a cog on the next go-round. It lifted its digit arms and printed out a 'partial answer' that was a series of random numbers as wide as the whole mechanism.
He said "please don't do that again." I moved on to torture computers.
And in East Asia, we use a system based on exponents of 10000. I kind of like it, except when I have to think about it and the short/long scales at the same time.
It is used in all European countries (I don't know any European country that doesn't use it). I know the long scale under the name "European" and the short scale as "American".
>I don't know any European country that doesn't use it
With the exception of people over 70, the UK has pretty uniformly moved to the American system. All of our govt statistics, corporate finances info, day-to-day conversations involving billions refer to "one thousand million"
The same thing happened to me, except I was younger and could adapt more easily.
I'm bilingual, I watch and read content in both Spanish (my native language) and English. Back in 2021, I heard that Rick Astley's "Never Gonna Give You Up" had hit 1 billion views on YouTube. I loved that song back then.
I was really amazed, so I decided to check it out for myself. But to my surprise, the video said “1000 millones de vistas” (millón = million). Confused, I asked myself, “Why do they say the video hit one billion views if it only says one thousand million here?”
That’s when I figured out that billón doesn’t mean the same as billion.
And now, years later, I’m reading your blog post about your experience, and commenting on it in a language that’s not even my native one.
Oh I never got why there was a confusion for the value of billion and co. I always assumed I did not get the proper value, but now it makes much more sense!
I'm kinda wondering are there any countries that still use the long scale nowadays? For me the biggest thing I've had to learn is that in Russian we use a short scale, except we don't have "billion" and instead it's "milliard". So it's just that you need to be careful with translating that one word. Are there other countries where the scale "shifts"?
The bit about the name “billion” still literally meaning “million million” in long scale really shows how old language shapes modern confusion.
What’s interesting is that the long scale actually matches the literal Latin root more closely, so in a way, the “modern” short scale is less intuitive linguistically, but more practical numerically.
>imagine my disappointment when I left home for university, got access to computers and the World Wide Web, and discovered that the names I had learnt were off by several orders of magnitude
imagine discovering mega- giga- tera- then not mentioning them
It doesn't sound like English, at least in my brain it doesn't register as English, and I may have found a plausible reason: If you look up the amount of English words with the letters "iarda" on them you only find 3 words (at least according to wordmine.info), but French shows 38 words, even just "arda" the difference is huge: 317 vs 2017 words https://www.wordmine.info/french/words-with?minletters=2&max...
The Economist (British) changed from million million -> thousand million in (1944) -
"If it is objected that a billion in this country is reserved for the meaning of a million million, then it can be counter-objected that, if so, it is reserved for a use that interests nobody but astronomers and the historians of German inflation"
The US leading the way in a sensible measuring system.
According to Wikipedia the two variants exist because the digits of large numbers used to be grouped into groups of six digits but in order to improve readability this was eventually changed to groups of three digits and some insisted that with that also the naming should be adjusted. A long scale trillion has three digit groups when using groups of six digits (1,000000,000000,000000) and six after the switch to groups of three (1,000,000,000,000,000,000) which then should be a short scale sextillion but somehow it ended up as a quintillion.
So basically
I'm sorry it had to be done https://www.youtube.com/watch?v=rIB5HEcZBs8
N-illion = 1000^(n-1)
Isn't it more like:
Since the OP was saying groupings use to be by 6-digits, not 3-digits (i.e. "1,000") as seen today.The original long scale makes more sense, billion, bi million, twice six digits.
Yet, mille and milli- mean thousand.
But the suffix -one in Italian is used to indicate something big - spaghetti vs spaghettoni - so a milione is a big thousand, a million.
Thanks!
This is the key piece of information for making sense of it. Ultimately the OP's insight is that the number-naming system used in the west is thousands based instead of millions based, but came to that by observing the number-naming outcomes instead of the source notation that led to it.
Spanish uses the long scale, but lately I've been noticing people mistakenly using the short scale in Spanish more and more, likely due to the influence of English and the internet, sometimes even in news articles and other "professional" publications. You may see someone speaking of "un trillón de dólares" (a trillion dollars), which while it makes sense in English when speaking of federal budgets or the market cap of FAANG, in long scale that's more than the world's entire money supply.
It's especially annoying because it creates ambiguity and renders the *illón-words fairly useless.
It's only "mistakenly" until it becomes the norm, which as another Spanish speaking person, I bet that will be the case no long in the future.
In Dutch the word "miljard" for 10^9 is too well known and deeply ingrained to change I think, but with "triljoen" which could either mean 10^18 or a direct conversion from the American English trillion, all bets are off
[dead]
Yeah, I too think that's likely the direction we're heading, and I'd be fine with either option as long as it was consistently used, this transitional phase is just painful.
In the meanwhile you can say one thousand millions (for what Americans call a billion), like the local tv news does, and for the bigger one say just say millions of millions (what Americans call a trillion), that should be unambiguous enough.
If you want to be unambiguously understood, especially in international context, it seems it's better to avoid words beyond "million" altogether.
"million of millions of dollars" or "ten to the twelfth dollars" or "one tera dollar" or even "one EEE twelve" (for programmers) will always be understood correctly, no matter which part of world listeners are from.
The only everyday context where numbers on that scale are commonly used is money/finance, and it's pretty universal in that context that 1e9=B=billion, 1e12=T=trillion. This long scale/short scale distinction gets posted a lot but it's one of those cases where in practice it seems to matter very little.
In science and engineering you'd rather use scientific notation anyway, and in math and CS notoriously only 3 numbers exist: 0, 1 and n.
You don't seem to get the point. That is only universal in current day English. In e.g. Finnish: miljoona = 1e6, miljardi = 1e9, biljoona = 1e12, triljoona = 1e18.
TIL about one more thing US misunderstood and now we have to deal with it. Another one is command key on mac, "borrowed" from road sign indicating "sight seeing place" :)
https://brndstudio.medium.com/how-a-swedish-road-sign-inspir...
I don't see how borrowing the Swedish "point of interest" symbol for the command key is "misunderstanding" something - as I understand the story, they just liked the symbol and decided to use it.
Also, I'm certainly not a US apologist, but I also don't see how the US using the short scale is a case of misunderstanding - it sounds like they just decided that it makes more sense that way (and I would agree, although maybe that's just because I'm used to it).
It makes no sense I’d say. In many European languages it’s milliard, etc.
What was misunderstood in the command key? The link mentions nothing of the sorts
Don't know anything about misunderstandings, but the symbol in question is https://en.m.wikipedia.org/wiki/Looped_square
this is so funny because i always envied english for it being so clear: million, billion, trillion. in german we have these "awkward" names in between: million, milliarden, billionen, billiarden. but now hearing about this long scale it actually does make quite a lot more sense when thinking about it in multiples of millions
Swedish does that as well. miljon, miljard, biljon, biljard.
This is sufficiently confusing to people that every time I see a newspaper article mention something is a biljon of something they have to mention how much it is and remind readers to not confuse it with an American billion (that is only a miljard).
In most contexts when big numbers like those show up though the metric-system comes to the rescue, since things will be referred to as being a mega-something or giga-something etc anyway. That works great until Americans attempt to do it and get the letters wrong or use K instead of k or M instead of m that causes new confusion and then we're back at having to guess what something means depending on what side of the Atlantic it was written.
I think they forgot "thousandard" = 1,000,000. And million is a thousandard of those.
same in polish milion, miliard, bilion, biliard, trylion, tryliard, kwadrylion, kwadryliard...
same in Italian: milione (1E6), miliardo (1E9), bilione (1E12) etc.. the long scale a "one" is 1E6 bigger than the previous one, example: bilione is 1E6 bigger than milione.
As a kid I stressed our Olivetti divisumma 24 ( https://www.ithistory.org/sites/default/files/hardware/Olive... ) with a million times a million. It entered a perpetual mechanical cycle that even unplugging it could not break. Finally Dad had to attack its innards and tug and twiddle until he pulled out a spring loaded gear and it caught a cog on the next go-round. It lifted its digit arms and printed out a 'partial answer' that was a series of random numbers as wide as the whole mechanism.
He said "please don't do that again." I moved on to torture computers.
And in East Asia, we use a system based on exponents of 10000. I kind of like it, except when I have to think about it and the short/long scales at the same time.
10000^1 = 万 10000^2 = 億 10000^3 = 兆 10000^4 = 京
It is used in all European countries (I don't know any European country that doesn't use it). I know the long scale under the name "European" and the short scale as "American".
>I don't know any European country that doesn't use it
With the exception of people over 70, the UK has pretty uniformly moved to the American system. All of our govt statistics, corporate finances info, day-to-day conversations involving billions refer to "one thousand million"
Same in Ireland, the long scale was already an elderly person thing when I was a child
UK used to do it the European way, but has adopted American way since (IIRC) about 50 years ago. As a Brit I wish we still used the traditional way.
(And despite Brexit, UK still is a European country!)
It may take fifty years, but I think that you will eventually rejoin the EU.
I definitely hope so! (And hope it won't take that long, but it wouldn't surprise me.)
Or whatever the thing is then.
The same thing happened to me, except I was younger and could adapt more easily.
I'm bilingual, I watch and read content in both Spanish (my native language) and English. Back in 2021, I heard that Rick Astley's "Never Gonna Give You Up" had hit 1 billion views on YouTube. I loved that song back then.
I was really amazed, so I decided to check it out for myself. But to my surprise, the video said “1000 millones de vistas” (millón = million). Confused, I asked myself, “Why do they say the video hit one billion views if it only says one thousand million here?”
That’s when I figured out that billón doesn’t mean the same as billion.
And now, years later, I’m reading your blog post about your experience, and commenting on it in a language that’s not even my native one.
I just seamlessly switch scales and units with the language.
When I talk Swedish I think in terms of long scale, 24 h clock, SI units.
When I talk English I think in terms of short scale, 12 h clock, imperial units.
It's like different cultural basis vectors.
Numberphile did a video on this many years ago: https://www.youtube.com/watch?v=C-52AI_ojyQ
Long scale seems to be much better because you have to remember fewer prefixes, so with fewer easier to remember rules you get wider coverage
Why didn't this principle win?
Is the billiard (10^15) the name sake of the 15-ball game by the same name?
Oh I never got why there was a confusion for the value of billion and co. I always assumed I did not get the proper value, but now it makes much more sense!
I'm kinda wondering are there any countries that still use the long scale nowadays? For me the biggest thing I've had to learn is that in Russian we use a short scale, except we don't have "billion" and instead it's "milliard". So it's just that you need to be careful with translating that one word. Are there other countries where the scale "shifts"?
The bit about the name “billion” still literally meaning “million million” in long scale really shows how old language shapes modern confusion.
What’s interesting is that the long scale actually matches the literal Latin root more closely, so in a way, the “modern” short scale is less intuitive linguistically, but more practical numerically.
I Spanish language we have this dad joke:
¿Que es un millón? Mil miles.
¿Que es un billón? Un millón de millones.
¿Que es un semillón? ???
Una semilla muy grande.
The 80's song "One Billion is Big" by the "Fat Boys" seems very relevant here: https://www.youtube.com/watch?v=TdnLhN4SeYY
Oh thanks for completely breaking my numeracy. Gotta relearn maths real quick
>imagine my disappointment when I left home for university, got access to computers and the World Wide Web, and discovered that the names I had learnt were off by several orders of magnitude
imagine discovering mega- giga- tera- then not mentioning them
In the long system how is a billionaire called? A milliardaire? That doesn't sound right.
Milliardaire yes, of course. Why doesn't that sound right to you?
https://fr.wikipedia.org/wiki/Liste_des_milliardaires_du_mon...
It doesn't sound like English, at least in my brain it doesn't register as English, and I may have found a plausible reason: If you look up the amount of English words with the letters "iarda" on them you only find 3 words (at least according to wordmine.info), but French shows 38 words, even just "arda" the difference is huge: 317 vs 2017 words https://www.wordmine.info/french/words-with?minletters=2&max...
In Czech, which uses the long scale, yes. The equivalent of "milliardaire".
Exactly how it's called in french
Well, Trump and Musk can just get up in front of the UN and say, "to most of the world we're mere milliardaires, not billionaires!"
The Economist (British) changed from million million -> thousand million in (1944) -
"If it is objected that a billion in this country is reserved for the meaning of a million million, then it can be counter-objected that, if so, it is reserved for a use that interests nobody but astronomers and the historians of German inflation"
The US leading the way in a sensible measuring system.