Number Names

Here are large number names and their scientific notation equivalents.

1,000,000 = one million = 10^6

1,000,000,000 = one billion = 10^9

1,000,000,000,000 = one trillion = 10^12

1,000,000,000,000,000 = one quadrillion = 10^15

1,000,000,000,000,000,000 = one quintillion = 10^18

1,000,000,000,000,000,000,000 = one sextillion = 10^21

1,000,000,000,000,000,000,000,000 = one septillion = 10^24

1,000,000,000,000,000,000,000,000,000 = one octillion = 10^27

1,000,000,000,000,000,000,000,000,000,000 = one nonillion = 10^30

1,000,000,000,000,000,000,000,000,000,000,000 = one decillion = 10^33

= one undecillion = 10^36

= one duodecillion = 10^39

= one tredecillion = 10^42

= one quattuordecillion = 10^45

000 = one quindecillion = 10^48

000,000 = one sexdecillion = 10^51

000,000,000 = one septendecillion = 10^54

000,000,000,000 = one octodecillion = 10^57

000,000,000,000,000 = one novemdecillion = 10^60

000,000,000,000,000,000 = one vigintillion = 10^63

There are other named numbers but this is as far as the standard names go, according to Philip Davis in _The Lore of Large Numbers_. One reason is that there is no setting (other than theoretical mathematics, where I live) where any numbers any bigger have any use. He mentions that Kasner and Newman, in _Mathematics and the Imagination_, named two others:

10^100 (1 followed by one hundred zeroes) = one googol and 10^googol = 10^(10^100) = one googolplex.

That would mean one googol is


and one googolplex would be a 1 followed by 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000 zeroes.

A while back I received an e-mail from Chris Meador. Chris wrote:
"One of my high school teachers (Ben Cook) told us that there are slight differences in the naming conventions between America and England (if I remember right). A million is 10^6, a billion is a million squared 10^12, and a trillion is a million cubed (10^18). I might have those numbers wrong, but if there is a difference it may be worth mentioning on your web page. I'll keep an eye out for reliable verification (I'm pretty sure I didn't dream this up but I suppose it's possible)."

Having been unfamiliar with this, I e-mailed my friend, John Duncan, a Scottish mathematician at the University of Arkansas-Fayetteville, who replied:

"The above gives the official British definitions - and there is a clear logic to it. Unfortunately the US definition of billion is beginning to appear more and more in UK - yet another example of the insidious US corruption of the English language!!! A US billion is 10^9 - where is the "bi" in that? Perhaps the square of 10^(9/2)???"

Of course, at the risk of disputing with John, there is a way in which the US terms make sense.  One million is 1000^1*1000, one billion is 1000^2*1000, one trillion is 1000^3*1000, etc.  

On 11/26/2007, I received an email from the UK informing me that, in 1999, the UK officially adopted the US billion.  "[S]o a UK billion is 10^9 now, just the same as a US one."


I recently received an e-mail from Lisa Coulter, a teacher of 4th - 6th graders at Children's House Montessori School in DeLand, Florida. She and her students had some very nice suggestions for some other number names.

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