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.

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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

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

Moose

2007-Oct-30, 05:43 PM

A million trillion, I think.

The_Radiation_Specialist

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.

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

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

quadrillion=peta

quintillion=exa

so, a shorter shorthand is "1E".

Todd

billion=giga

trillion=terra

quadrillion=peta

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.

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".

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

Quadrillion = 1,000,000,000,000,000

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.

Million = 1,000,000

Billion = 1,000,000,000

Trillion = 1,000,000,000,000

Quadrillion = 1,000,000,000,000,000

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)

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?

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".

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.

The_Radiation_Specialist

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.

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

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

The_Radiation_Specialist

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.

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

Quadrillian=10^Trillion, and so on!

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

Million=10 (we start small here)

Billion=10^10

Trillion=10^(10^10)=10^Billion

Quadrillian=10^Trillion, and so on!

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

Quadrillian=10^Trillion, and so on!

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

Million=10 (we start small here)

Billion=10^10

Trillion=10^(10^10)=10^Billion

Quadrillian=10^Trillion, and so on!

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

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