PDA

View Full Version : can't figure million million million

Tinaa
2007-Oct-30, 05:38 PM
How could one write million million million in a shorter term? Is it a million billion? I can't seem to get the answer out of my own head.

The Supreme Canuck
2007-Oct-30, 05:42 PM
1x10^18?

WaxRubiks
2007-Oct-30, 05:43 PM
isn't it, a billion billion. -> (1000*million)*(1000*million)

eta: are you trying to go through your bills?:D

Moose
2007-Oct-30, 05:43 PM
A million trillion, I think.

2007-Oct-30, 05:49 PM
According to Wikipedia (http://en.wikipedia.org/wiki/Names_of_large_numbers), it is called a quintillion.

Or simply a trillion for those traditional Britons.

PetersCreek
2007-Oct-30, 05:52 PM
In nontechnical (ex: business) writing, large numbers are sometimes abbreviated as 1K for 1000, 2M for two million, etc.

So the shortest shorthand I could come up with for 1 million-million-million is: 1M³

tdvance
2007-Oct-30, 06:08 PM
million=mega
billion=giga
trillion=terra
quintillion=exa

so, a shorter shorthand is "1E".

Todd

agingjb
2007-Oct-30, 06:34 PM
Traditional Britons didn't entirely win this particular dispute.

http://en.wikipedia.org/wiki/Long_and_short_scales

Such of the British media that distinguish any numbers above four (the Financial Times and some diminishing enclaves within the BBC) now use billion for 10**9 and trillion for 10**12.

So 10**18 would be quintillion.

Peptron
2007-Oct-30, 06:56 PM
That's why I prefer the "long scale" over the short.

Million million million is "million" 3 times, so it's "trillion" 10^18 or (10^(6*3))
"million" 5 times would be "quintillion" 10^30 or (10^(6*5))
"million" 10 times would be "decillion" 10^60 or (10^(6*10))
"million" 100 times would be "centillion" 10^600 or (10^(6*100))

So if you have a random number, like 10^42, just divide the power by 6 and you got the "name". 42/6 = 7 so it's "septillion".

I'm not sure what is the logic behind the short scale, it doesn't make much sense to me. To me it just makes a lot more sense that "billion" is "million two times", and that "trillion" is "million three times".

Mister Earl
2007-Oct-30, 07:00 PM
Here's how we were taught in school:
Million = 1,000,000
Billion = 1,000,000,000
Trillion = 1,000,000,000,000
Quintillion = 1,000,000,000,000,000,000
Sextillion = 1,000,000,000,000,000,000,000
Septillion = 1,000,000,000,000,000,000,000,000
Octillion = 1,000,000,000,000,000,000,000,000,000
Nintillion = 1,000,000,000,000,000,000,000,000,000,000
Decillion = 1,000,000,000,000,000,000,000,000,000,000,000

Learned that as a young boy, and remember it well because I was enraptured by the big numbers. Nerd then, nerd now.

Peptron
2007-Oct-30, 07:10 PM
Yeah, that's why I don't like it. To me, the "bi" in "billion" only makes sense if it means "two something". And the "tri" in "trillion" means "three something".

It doesn't follow that logic in that case:
Million = 1,000,000
Billion = 1,000,000,000
Trillion = 1,000,000,000,000

But does in that case:
Million = 1,000,000
Billion = 1,000,000,000,000 (being "double", a million million)
Trillion = 1,000,000,000,000,000,000 (being "triple", a million million million)

agingjb
2007-Oct-30, 07:15 PM
Let me say that I would have preferred long scale to have prevailed, but, I suppose, consistency has some discernable merit.

Mister Earl
2007-Oct-30, 07:17 PM
Yeah, that's why I don't like it. To me, the "bi" in "billion" only makes sense if it means "two something". And the "tri" in "trillion" means "three something".

It doesn't follow that logic in that case:
Million = 1,000,000
Billion = 1,000,000,000
Trillion = 1,000,000,000,000

But does in that case:
Million = 1,000,000
Billion = 1,000,000,000,000 (being "double", a million million)
Trillion = 1,000,000,000,000,000,000 (being "triple", a million million million)

So what would you call 1,000,000,000 and 1,000,000,000,000,000?

Peptron
2007-Oct-30, 07:24 PM
In French (and some other languages) we suffix the "mid-points" by "-ard" instead of "-on"

So
1,000,000,000 = milliard
1,000,000,000,000,000 = billiard

So you get
1,000,000 = million
1,000,000,000 = milliard
1,000,000,000,000 = billion
1,000,000,000,000,000 = billiard
1,000,000,000,000,000,000 = trillion
1,000,000,000,000,000,000,000 = trilliard

But then it's also accepted to simply say "a thousand millions" and "a thousand billions".

John Mendenhall
2007-Oct-30, 07:36 PM
(1x(10^6))*(1x(10^6))*(1x(10^6)) = 1x(10^18) = 1,000,000,000,000,000,000 = 1 quintillion (in American English).

mike alexander
2007-Oct-30, 07:51 PM
In politics it's called a 'budget'.

Tinaa
2007-Oct-30, 10:23 PM
I'm trying to explain it to sixth graders. A student asked me the question so I'd like to come up with a good answer. I told her to give me a day.

2007-Oct-30, 10:52 PM
I'm trying to explain it to sixth graders. A student asked me the question so I'd like to come up with a good answer. I told her to give me a day.

Cool, I think they would also find googol and googoleplex interesting.

http://en.wikipedia.org/wiki/Names_of_large_numbers

Interesting fact: Google was actually a typo for googol; A 160 billion dollar typo (http://valleywag.com/tech/genius-at-work/the-160-billion-typo-315279.php#).

The concept of scientific notation may also be useful for them.

Disinfo Agent
2007-Oct-30, 11:05 PM
Remember that you can find absolutely anything (http://www.bautforum.com/general-science/9872-meaning-billion.html) in the BAUT forums.

publius
2007-Oct-31, 12:17 AM
The short scale goes right along with the SI prefix convention, and this is sometimes called the "engineering" scaling.

It is simply this 10^(3*n), where n = 0 is the base, n = 1 is a kilo-, n=2 is mega-, n = 3 is giga-

n = 2 is a million, n = 3 a billion, n = 4 a trillion. If you want the "one", "two", progression, just use n = m + 1, and count on m. A million is m = 1, billion is m = 2, trillion is m = 3, etc, etc. Each step is 1000 times the previous.

The long scale just uses 10^(6n). Each step is a million times the previous. And that will not agree with the SI prefix progression, which is based on the short scale.

And what's so special about either of them? You can do a geometric progression. A million is a thousand thousand. A billion is a million million. This is the long scale so far. But now let a trillion be a billion billion. The next step, a quadrillion would be a trillion trillion, and so on.

That's just squaring each one, or the progression can be written,

10^(3*2^n).

One thousand is n = 0. n = 1 is a million. n = 2 would be a billion. And the trillion = a billion billion would be n = 3.

See, there's all sorts of ways you could do this.

-Richard

2007-Oct-31, 08:00 AM
I think this is the first time publius made a post that I could understood all of what was said . . . :)

mugaliens
2007-Oct-31, 12:34 PM
How could one write million million million in a shorter term? Is it a million billion? I can't seem to get the answer out of my own head.

A million billion would work. Since a million is 1x10^6, a million million million is 1x10^18.

Here's an accepted way with a few less characters: 1e18.

tdvance
2007-Nov-01, 03:04 PM
grows too slowly--use the (base 10 verson of the) inverse of the Ackerman function (I don't know what the inverse is called, if anything beside "inverse of the Ackerman function"):

Million=10 (we start small here)
Billion=10^10
Trillion=10^(10^10)=10^Billion

Then, there are fewer than a trillion particles in the (observable) universe, it's been around for fewer than a trillion plank-times, it's width is less than a trillion plank-widths, and its mass is less than a trillion electron-masses. We need fewer numbers--since we would rarely need anything over a trillion. Of course, if the national debt reaches a trillion, we're not paying it off.

Todd

The short scale goes right along with the SI prefix convention, and this is sometimes called the "engineering" scaling.

It is simply this 10^(3*n), where n = 0 is the base, n = 1 is a kilo-, n=2 is mega-, n = 3 is giga-

n = 2 is a million, n = 3 a billion, n = 4 a trillion. If you want the "one", "two", progression, just use n = m + 1, and count on m. A million is m = 1, billion is m = 2, trillion is m = 3, etc, etc. Each step is 1000 times the previous.

The long scale just uses 10^(6n). Each step is a million times the previous. And that will not agree with the SI prefix progression, which is based on the short scale.

And what's so special about either of them? You can do a geometric progression. A million is a thousand thousand. A billion is a million million. This is the long scale so far. But now let a trillion be a billion billion. The next step, a quadrillion would be a trillion trillion, and so on.

That's just squaring each one, or the progression can be written,

10^(3*2^n).

One thousand is n = 0. n = 1 is a million. n = 2 would be a billion. And the trillion = a billion billion would be n = 3.

See, there's all sorts of ways you could do this.

-Richard

publius
2007-Nov-02, 04:28 AM
grows too slowly--use the (base 10 verson of the) inverse of the Ackerman function (I don't know what the inverse is called, if anything beside "inverse of the Ackerman function"):

Million=10 (we start small here)
Billion=10^10
Trillion=10^(10^10)=10^Billion

Todd

I don't know much about the Ackerman function, other than the name and it gets big quickly, much less the inverse. But that sequence above is a "tetration", or hyperpower, or power tower, amongst other names.

The notion of tetration comes from it being the forth operation, with addition being the first, multiplication second, and raising to a power being third.

There are variety of notations, but one is a pre supersuperscipt:

na

That is a power tower of a^(a^(.....^a)...) n times.

You can then even extend that to "pentation", with a tetration tower, and so on.

Tetration for non-integer reals hasn't been successfully defined yet, I don't think. :)

And there are some surpises. For example, the sqrt(2) to the infinite tetration is 2! That just seems crazy. a^x diverges for a > 1, so you'd think an infinite tetration would certainly diverge as well. But for a range of a, it has a limit.

Just pull out the calculator and take a power tower stack of sqrt(2) and you'll see it gets closer and closer to 2.

-Richard