How big is a billion? – Numberphile


JAMES GRIME: As an antipathian, how big is a billion? TONY PADILLA: No, I’m not even
going to go there, man. JAMES GRIME: Well, what
were you taught? What were you taught
at school? TONY PADILLA: OK. So there’s basically two
ways of interpreting what a billion is. There is the correct
English way. And there’s the incorrect
American way. I think I was taught a billion
is 1,000 million. JAMES GRIME: Right, exactly. Now, that’s what I was taught
at school as well. Although in Britain the older
generation would say a billion is not 1,000 million. They would say it was
a million million. TONY PADILLA: There’s a
beautiful mathematical logic to the old way of doing and it,
which I just don’t see in the new way. JAMES GRIME: If we ask our
viewers, I reckon about half of them will answer a billion
has nine zeroes. That’s 1,000 million. And I reckon the rest of them
will say a billion has 12 zeroes, which is a
million million. And it depends on how old
you are and where in the world you live. Let’s be honest. Real mathematicians and real
scientists, if they’ve got a large number, they’re not really
going to use billions and trillions. They actually use
standard form. So if I want to say something
with 27 zeroes, you’d write something like this. You’d be 5 times
10 to the 27th. But if you’re reading articles
in the newspapers, on BBC website, they’re going
to use words like billions and trillions. Now, there is dispute. There are two systems. There’s the short system
and the long system. So let’s have a look at the
short system first. So the short system is based
on powers of 1,000. Let’s start off with
the number 1. Now, it is a power of 1,000. It’s 1,000 to the power
0, So that’s 1. What’s the next step up? Well, you get 1,000,
don’t you? That is 1,000 to the power 1. That’s three zeroes. I’ll put that over here. We’ve got three zeroes there. What’s the next step up? It’s a million. Right, let’s do a million. 1,000 squared, that’s six
zeroes we’ve got. What’s next up, after that? Well, in the short system, the
next one is a billion. So a billion, that’s
1,000 cubed. And that’s 10 to the power
9, nine zeroes. After that, you get a trillion,
which is 1,000 to the power 4. And that’s 10 to the power 12. That 12 zeroes. And we can keep going
after that. So let’s see, million,
billion, trillion. The next one is quad,
quintillion, sextillion, septillion. This is what America uses. And it’s what Britain uses. And it’s what the English-speaking world now uses. Britain adopted this
officially– the government officially
adopted the short system in 1974. So there is a generation gap for
people who are used to the long system. You are aware that the UK
has adopted 10 to the 9. TONY PADILLA: Yeah, you know,
the UK has been on the slide for a while, right? So they should have stuck to
their guns because the 10 to the 12 version makes
loads more sense. JAMES GRIME: The thing that
annoys me with this, though, is, you see, bi means
two, like bicycle. But it’s not 1,000
to the power 2. It’s 1,000 to the power 3. It’s horrible, isn’t it? TONY PADILLA: Well, maybe it’s
just someone wanted to say, oh, we could say a
billion, right? We can say someone’s
a billionaire. And we can say it more quickly
if we use this different definition of a billion. But, you know. JAMES GRIME: Yeah, it’s
pretty horrible. A trillion, which should be
a three then, is 1,000 to the power 4. Not very nice, because, if you
ask me, the long system is more logical. TONY PADILLA: I can’t
understand it. I suspect somebody– I could be wrong about this. But I expect somebody
just got it wrong. And it sort of caught on. JAMES GRIME: So the long system
is used by most of continental Europe and the
non-English-speaking world. And it’s based on powers
of 1 million. So let’s start off in the same
place we started before, with the number one. That is a million to the power
0, so same as before. The next power is going
to be here, a million. So that’s a million– let’s write it down– to the power of 1. Now, the next power of a million
will be– and in the long system, it is called
a billion, which is 1 million squared. It is a bi-million. And that’s where the word
billion comes from. So it’s a million
to the power 2. So let’s just join those up. So 1 is 1. That’s fine. Million and million
are the same. But here 12 zeroes
was called in the short system a trillion. I actually prefer billion
in the long system. The next power up is now
called a trillion, a tri-million. It’s a million cubed, 3
powers of a million. So that would line up with
what’s called a quintillion. TONY PADILLA: Well, I’ve
always thought the only dispute was between a billion. But they all fall out. JAMES GRIME: They all
fall out of order. You’re absolutely right. The long system, though,
is more logical. The naming of the numbers
are more logical. Billion, trillion has meaning,
whereas they lose their meaning in the short system. OK. And you can carry
on like this. A quadrillion– I mean, I could go on for a
long time with this if you want me to– is 1 million. What is it? 1 million, Well, quad is
4, 1 million to the 4. OK, and you can really
extend it. Let’s go right the way down. OK, what’s a centillion? According to this logic,
1 centillion– well cent, so that’s 1 million
to the power of 100, which is 10 to the 600. So that, incidentally, if
you do it that way, is bigger than a googol. Well, you do have
some gaps now. And it might be useful to have
a name for these gaps. It might be useful to have
a name for 1,000 million. We don’t seem to have one now. Well we do. The name for 1,000 million
in the long system– and I love this word. It’s called a milliard. A milliard, that’s
1,000 million. It’s fallen out of
favor, that word. It’s still used, I think,
in continental Europe. But in Britain when we use
the long system, it kind fell out of favor. I think it’s a great word. I want to bring back
the milliard. TONY PADILLA: So what
have we got? Have we also got a billiard? JAMES GRIME: Exactly. We’ve got a billiard
right there. That’s called a billiard, like a
posh person playing snooker, yeah, a billiard. In the financial world,
they actually have a term called a yard. And it actually comes from
the word milliard. And it means 1,000 million. And they use the word yard
instead of saying billion, or 1,000 million, because
it’s unambiguous. TONY PADILLA: This is great. Why have we gone to this silly
system that has no mathematical logic
to it, which– it’s just because somebody
didn’t really understand numbers that it got created. And we should have gone back
to the old English way. And I think to celebrate the
Queen’s 60th Jubilee, this is what we should do. We should all go back
to old English way of writing numbers. JAMES GRIME: I prefer the
long system, but I won’t be using it. I won’t be using the
long system. I’ll be using the
short system. It’s the standard in the
English-speaking world. Asia don’t really use
these systems. They have their own systems. Countries like Canada,
bilingual countries– even more confusing– will use both, one for
each language. So they’ll be using short system
in one language and then long system in the other. But you’re shaking your head,
like that’s not true. TONY PADILLA: No, it’s
just disgusting. JAMES GRIME: You’re
amazed aren’t you? Imagine, imagine. The Greeks have an interesting
system because what they do– TONY PADILLA: They need
it with the kind of money they owe. JAMES GRIME: Oh, don’t get
me started, right. They don’t use the
word million. Here’s an interesting
story as well. Million means large 1,000. Mil means 1,000. Million means a large 1,000. Now, what the Greeks use
is a word called– I’ll put it here– myriad. Now, myriad, in English, means
many, uncountably many, lots. It actually originally
means 10,000. Myriad means 10,000. So instead of million, they
don’t say million. They call that 100-myriad. And the Greeks use
the long system. But instead of million,
we have this word– 100-myriad. So they’ll now have, not a
bi-million, not a billion, but a bi-100-myriad. TONY PADILLA: Oh, it
just annoys me. I just think it’s rubbish. The way everyone has started to
do it, it makes no sense. At least I can’t see
the sense in it.