How big is a billion? - Numberphile 

It's great to see how amazed he is by the word "Milliard". Greetings from the continental Europe.

5:02 - "One is one, that's fine" Key takeaway from the entire video.

I'm Russian and I used to think Americans were crazy for thinking there are 7billion people in the world but now I understand why...

Anytime I see the word "trillion" in a news article in my country I'm 100% sure it's incorrectly translated from the English short system.

In danish it's: Million = 1,000,000 Milliard = 1,000,000,000 Billion = 1,000,000,000,000 Billiard = 1,000,000,000,000,000

Always got confused with this, you know, I’m Portuguese and speak Portuguese and we use the long system, but the Brazilians (who also speak Portuguese) use the short system

I always thought until I was "corrected" in Year 8 maths that it was 1 million million = 1 billion 1 billion billion = trillion etc. I call it the longerer system.

I love how the thumbnail asks us if 1,000,000,000 is a billion or a trillion. But it is just a milliard.

4:04 "Somebody just got it wrong, and it just, sort of, caught on" - Origin story for half of the things in America.

I use the "load" system: 1 000 a load 1 000 000 a shit load 1 000 000 000 a fuck load 1 000 000 000 000 a fuck off shit load This system works best for every day speaking, eg. Premiership footballers earn a shit load of money." Or: "the national debt of [country] is a fuck off shit load of dollars"

When it gets to the really big numbers, in Ireland there are two camps - eg, "Does the government owe 'a Gazillion' Euros or 'a Gajillion' Euros"..?

7:59 whoa he quickly number-zoned the long system 😂😂😂

The worst thing is when text is translated from English to a language that uses the long system (such as Finnish.) An inattentive/ignorant translator will make an error of three orders of magnitude when translating "billion".

In Germny we use the long system. And when u start to have english classes you're going to be heavy confused that people name numbers in such a different way.

I'll add one more thing. I am from Slovakia and as you know some languages have masculine, feminine and gender neutral nouns and pronouns. Well in Slovakia we use the long system but here we alternate the genders in a way. A million is "milión", which makes it masculine (male) and a milliard is "miliarda". The "a" at the end of "miliarda" makes it feminine. Same goes for all the other ones: milón, miliarda, bilión, biliarda, trilión, triliarda... So from million up it always alternates masculine , feminine , masculine , feminine ....

"Long System" supporter from Germany ;)

I'm German and I noticed this many years ago while watching American news. the German word "Milliarde" corresponds to the American "Billion" and the German "Billion" corresponds to the American "Trillion."

am i the only one who likes to see James' pure joy while talking about milliard?

Fahrenheit, Inches, Pounds and Billion.... America has a talent to use the most illogical and impractical systems you can have.

When English adopted America's system but America still uses imperial. Top 10 anime betrayals.

The way England's economy is going they won't have to worry about any of this.

Why was I NEVER informed of this difference?

Slovakia uses the long system, so i was always confused with Milliard and Billion. Thank you for explaining this.

I live in Canada and I can confirm how annoying it is to use both

In Swedish: 10^0 = ett 10^3 = 1 tusen 10^6 = 1 miljon 10^9 = 1 miljard 10^12 = 1 biljon 10^15 = 1 biljard 10^18 = 1 triljon 10^21 = 1 triljard etc...

Here in Denmark, it is not at all unusual to see American billions mistranslated as "billion". So when seeing the word "billion" in a news item about forreign affairs, you have think about whether "milliard" or "billion" makes most sense in context.

standard form? it is called scientific notation where I live

Can we align it to mega, giga , tera etc?

As a Dutch person who was always confused as to why our words to describe these numbers differed fron the English one, I now finally see that my country still enforces the most logical system. Great vid.

In Spanish it goes like this: 10-diez 100-cien 1000-mil 10.000-diez mil 100.000-cien mil 1.000.000-millón 10.000.000-diez millones 100.000.000-cien millones 1.000.000.000-mil millones 10.000.000.000-diez mil millones 100.000.000.000-cien mil millones 1.000.000.000.000-billón It uses the long system. You can clearly see a pattern in the names. It really shocked me and annoyed me when my English teacher told me about the short system. It just doesn’t make sense, it breaks the pattern.

I look forward to the day when we avoid all confusion by using standard SI prefixes as we do in computing. So it would be £M1 (1 Megapound = £1,000,000), £G1 (1 Gigapound = £1,000,000,000) etc in the same way that we have 1 Megabyte and 1 Gigabyte etc

I came here absolutely sure of the answer and now I'm leaving with a milliard questions, omg

English, born 1965, was taught that a billion was, indeed, 1,000,000,000,000. Took me donkeys years to get past us starting to use the US system and it STILL doesn't feel right!

Ah, another system where the UK decided to something illogical to not be the SAME as continental Europe.

I love this! Not sure I ever learned of the long scale before. It makes loads more sense. Fascinated by all of this, including the Greek tidbit at the end. Cheers!

This video is pretty old, so there are a lot of comments I didn't read. Has anyone mentioned Chinese? They group powers of ten by fours. (In order for the following to make sense, you have to know that there are thousands of homonyms in Chinese that are completely disambiguated by the characters used to write them. See below.) So: 10000^0 = 10^0 = 1 - yi 10^1 = 10 - shi 10^2 = 100 - bai 10^3 = 1000 - qian 10000^1 = 10^4 = 10000 - wan (or yi wan, i.e. one ten-thousand) 10^5 = 100000 - shi wan (ten ten-thousands) 10^6 = 1000000 - bai wan (hundred ten-thousands) 10^7 = 10000000 - qian wan (thousand ten-thousands) 10000^2 = 10^8 = 100000000 - yi [different yi, see above] (one hundred-million) 10^9 = 1000000000 - shi yi (ten hundred-millions) etc. There aren't any words past yi. They just start using standard notation. I've always followed a piece of advice I got from long ago. When discussing large numbers in English with a native Chinese speaker I always use the Chinese words

Make Billion Great Again

I love that he underlined one letter in million, two for billion, three for trillion, four for quadrillion, and quintillion would be five. That means the first five number prefixes each have that number of letters.

I'm from Spain and I was taught the 'long system' at school. It makes so much more sense.

I live in Britan, and I've never heared of this before. But now that I have, I want to bring it back.

The illogicity of the short system is quickly resolved if you consider the exponent as n+1, where n is the corresponding number in the naming convention, ie trillion = 1000^(3+1), billion = 1000^(2+1), etc. Short system is more convenient in that the name endings are consistent (-illion).

In Germany its: Millonen(million) = 1.000.000 Milliarden(milliard) = 1.000.000.000 Billionen(billion) = 1.000.000.000.000

First time i heard about the short system. I have always used milliard and billiard.

There's also another little problem that comes with this language/number gap. There're lots of spanish/english translators that seem to forget that you actually also have to translate math, and the problem is bigger when the words millions, billions and trillions are basically written the same way in both languages so when, for example, they see the word "billonare" they translate it to what sounds correct in spanish, "billonario", an easy translation it seems. But then that word brakes the entire text because the number is massively huge in comparison to it's original form in english and the guy ends up having a net worth of around a $1000000000000 which is an insane number that no human can ever posses. The problem is also persistent in weight and distance measures. I remember being in elementary school and watching a drawing in an astronomy book with the weight of the earth and some other astronomical measures, everything in billions and trillions, i looked at my dad not being able to grasp the quantity of zeros those numbers could have, he looked at me an then told me this really tricky language thing, for a week I had thought the galaxy was a thousand times larger than it is.

We use the long system in Iceland (with the milliard + billiard etc inbetween too)

The logic behind the short scale, and what is used to make it not idiotic, is actually 1000x1000 to the power of. So: 1 Billion is 1000x1000^2 1 Trillion is 1000x1000^3 1 Quadrillion is 1000x1000^4 and so on...

While in every day French, "milliard" is a thousand million. But I personally don't think "billion" is often used. I often read "mille milliards" and I'm not talking about the Captain Haddock's swear "Mille milliards de mille sabords" of course.

I’m australian and we use the short system. I agree that the long system makes more sense, and I actually like milliard and billiard etc. But it just sounds so wrong to me to call it that, I simply cannot wrap my head around it.

Denmark uses the long system. Imagine the horror of reading and learning most things in english (short system) and then having to explain it in danish (long system) "there are7 billion people on earth, but not really cause someone couldn't pronouce 'milliard'"

We can't use the Long System because there would be no billionaires anymore, only millionaires and milliardaires :)

America is the centre of cultural discourse. 1000 million is a modern billion unfortunately

I've never understood the long system, but now it makes so much more sense than the short system.

Screw it. Let's abolish all the names and just use standard form for anything larger than 10,000.

here it goes million, milliard, billion, billiard, trillion, trilliard...

In French, we use the milliard…

Mathematician 1: Hey, wanna play Billiards? Mathematician 2: Quadrillion isn’t a game.

I know this varies by country, but to me this makes the most sense: 1,000 = one Thousand 1,000,000 = one Million 1,000,000,000 = one Billion 1,000,000,000,000 = one Trillion Every new "comma" gets a new name.

I'm living in Switzerland so when I'm hearing reading english, i just think billion=Millarde, is that don't familiar, in England? I think the long system is simpler. I love your pronunciation of the World Milliard. (yes my english is bad, i know that.)

I'm glad I live in a country that used the long scale and the metric system :)

In Chile we use the long system and it's a little confusing for me when I watch series in english, I still don't understand why someone would use the short one... so weird

In spanish it's: Million = 1,000,000 Milliard = 1,000,000,000 (millardo) thousand million Billion = 1,000,000,000,000 (billón) Billiard = 1,000,000,000,000,000 (billardo)

I immediately fell in love with the long system thanks to this video

In Norway, we use the long system, however, we are de fact bi-lingual, using English a lot, so we kinda get our values wrong when speaking to English speaking people

Even though I've learnt in school that a billion is a thousand million, I prefer the long scale system which was traditionally used in Britain prior to 1974. This is where a billion is a million million, a trillion is a million billion, a quadrillion is a million trillion, etc. I understand that the long scale system may be more cumbersome than the short scale system, but I agree that the long scale system makes more logical sense. The biggest key difference is that in the long system, a vigintillion is bigger than a googol, whereas it's smaller in the short system. The formula for the two systems can be shown here. Short scale system: 10^(3n+3) Long scale system: 10^6n Here is a list of key dictionary numbers in the long scale system: Million - 1e+6 Billion - 1e+12 Trillion - 1e+18 Quadrillion - 1e+24 Quintillion - 1e+30 Sextillion - 1e+36 Septillion - 1e+42 Octillion - 1e+48 Nonillion - 1e+54 Decillion - 1e+60 Googol (for comparison) - 1e+100 Vigintillion - 1e+120 Centillion - 1e+600 Millinillion - 1e+6000 Milli-millinillion - 1e+6000000 Here's an extension to the system based on SI prefixes (this extension is derived from the Epstein system, devised by Louis Epstein): Megillion - 1e+6000000 Gigillion - 1e+6000000000 Terillion - 1e+(6e+12) Petillion - 1e+(6e+15) Exillion - 1e+(6e+18) Zettillion - 1e+(6e+21) Yottillion - 1e+(6e+24) Ronnillion - 1e+(6e+27) Quettillion - 1e+(6e+30) Still quite far from a googolplex, which has one followed by a googol (ten thousand sedecillion; ten duotrigintillion in the short scale) zeroes. A quettillion has a one followed by six quintillion zeroes (six nonillion in the short scale).

I am German and we use the long system, I then learned to count in French, a language that honestly needs to sort out the naming of their numbers! Then I was blessed in school learning to count in the English way, which actually added quite a lot of confusion because when you look up 'Milliarde', the German word for 10^9, you get two translations 'billion' and 'milliard'.... well and then I learned Korean which instead of using any of those systems has a system where the numbers receive new names for every multiplicative of 10.000.... Im planning on learning more languages and it would really make things easier if everyone could just sign a convention already that from now on in any place on earth things are counted in 10 to the power of...

in italy: 10^6: Milione 10^9: Miliardo 10^12: Bilione 10^15: Biliardo (Number, it could also mean the game without context) 10^18: Trilione 10^21: Triliardo

In the whole Spanish speaking we use the correct one. That is, a billion is a million million.

I was born in Israel and moved to the US. when I was young...I remember always being confused and not understanding where the billiard disappeared...now it all makes sense!

In Norway we use the long system, the words Million and Milliard are really common, not so much Billion and Billiard.. When I was younger I was really confused why what we call Milliard was called Billion in english, tho we also have the word Billion, but it wasn't the same thing as in english. I also didn't really know the difference between Billion and Billiard, I would sometimes think they were the same number. This video suddenly makes sence of it all!

Miljoona 1 000 000 Miljardi 1 000 000 000 Biljoona 1 000 000 000 000 Triljoona 1 000 000 000 000 000 000 Kvadriljoona 10^24 Sentiljoona 10^600 In finnish that is

In germany everybody uses the large system

I like how James explains the details. Then the other input is just " Grrr, this is rubbish!"

go old English! let's bring the milliards back!!!

Heyyyy, so the French counting system makes more sense that the english one I knew it ! -But what about 99 ? -I SAID "I KNEW IT" !

1 billion has 1 billion 0's. sooooo it would be 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I had no idea this was a thing. As a Brit living in the UK and only ever being taught the short form, I never even questioned it, but a lot of what they say makes sense.

Slovak has milliards as well. English should get its s*&t together.

I’ve grown up in English speaking Canada and knew nothing of the long system until now and now I’m pissed we don’t use it. This makes so much more sense

The way I thought about the short system which makes perfect sense is the amount of extra sets of three zeros after a thousand. Aka 1000(1000)^x

I'm Greek and I didn't notice the myriad and 100 connection thanks. It also makes perfect sense linguistically at the etymology (as a connection of two words), both in ancient and modern greek variations of the language.

So the moral of the story is, just use standard form. It's a lot easier than having 2*10^3 different numbering systems.

in french 1 000 mille 1 000 000 million 1 000 000 000 milliard 1 000 000 000 000 billion

I never new that a thing like a milliard exists outside of Germany... I always wondered about the difference between higher numbers back when I was younger, thanks for clarifying that :)

Guys, I just loved this video and how well you explained all the small nuances. Thank you for the great work.

I didn't even know the short system existed. The long system is just logical!

Polish names are the best. 1 000 tysiąc 1 000 000 milion 1 000 000 000 miliard 1 000 000 000 000 bilion 1 000 000 000 000 000 biliard

swedish names: 1 000 - Tusen 1 000 000 Miljon 1 000 000 000 Miljard 1 000 000 000 000 Biljon 1 000 000 000 000 000 Biljard

Eastern Europe here, Romania to be more precise. Had a course in uni on English from an economics pov... we actually had a few hours discussing this exact topic because it's so alien to us.

I was brought up on the short system, and learned of the long system while still in school. And like James, I find the latter more logical, but will stick to the former. If, however, there were a move on to switch to the long system, I would support that.

I understand the logic, but I don't like the long system personally. For one thing, I'm used to the short system. It sounds as though it can also get confusing. "Milliard" sounds quite a lot like "Million". It's the "mill" bit. Meanwhile, listen to the short system: million, billion, trillion, quadrillion... it's more easily distinguishable.

I think it would all make a lot more sense if we just called 1,000 a "million," 1,000,000 a "billion" and so on.

My father use to say there were two ways a billion was defined depending on the language. This clears it up. I remember when Canada underwent the metric conversion. I was in grade 2 in 1974..

When I'm speaking English I always think of a billion as 10^9. But in my local language of Dutch 10^9 is called 'Miljard' and we also have 'Biljoen' which is 10^12

Even in the United States, "milliard" is still used on a limited basis. Specifically, in financial trading. My first job in banking was doing treasury trade support. The funds traders would call us up and tell us to move funds virtually on the computer as they made real time trades. For trades of a billion, they would call it a "yard", shorthand for a milliard. So I would get a call like "500 million to BOA, a yard to Citizens, 3 yards to Chase!"..."ok confirmed!".

You missed thousand in long system, is it then oneard? :-) Just kidding, we use long system in Finland too, "miljardi" being thousand millions. Though, wouldn't the most logical system be short system that is fixed one step down. Especially since "mill" in million is actually referring to thousand. 1 = One = (1000)^0 1 000 = Million = (1000)^1 1 000 000 = Billion = (1000)^2 1 000 000 000 = Trillion = (1000)^3 ...

The long scale is made to make it bigger over time as new numbers are discovered, so it can be updated always. Ex: the grahham number grahham = (grahham's number)¹ grahhard = 1000 times grahham bigrahham = (grahham's number)² bigrahhard = 1000 times bigrahham trigrahham = (grahham's number)³ And so on (the scale can be bigger that this, but that is the point of the long system, this is just an example of how it works with a given number past the million)

German speaking: 1.000.000 = Eine Million 3.000.000 = Drei Millionen 1.000.000.000 = Eine Milliarde 3.000.000.000 = Drei Milliarden 1.000.000.000.000 = Eine Billion 3.000.000.000.000 = Drei Billionen and so on

What they should have done is put prefixes to million, like the way computers do it. kilomillion, megamillion, gigamillion, teramillion. There is no dispute in k/m/g/t of their meaning, and keep the long system without reusing words, therefore there would be no confusion, for instance 1 megamillion = 1 billion

as a canadian who grew up speaking english at home and french at school, i can confirm this messed me up so much

Growing up in Australia, I remember learning the two billions (thousand million/million million) as well as the ton (metric) vs. tonne (imperial). This was in the 1990s, but it was still evident that the million million interpretation was logically preferred, and the thousand million was considered an unhelpful Americanisation that was useful for talking about money but deeply inelegant in mathematical terms!