How big is a billion? - Numberphile

Uploaded by numberphile on 24.05.2012

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?
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,
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
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.
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?
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--
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--
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.