Names for extremely large numbers

Names for extremely large numbers are kinda pointless. The purpose of a name is to communicate something, and if the meaning of the name is not widely known, the name doesn't serve that purpose. It's even counterproductive if two people have incompatible ideas what the word means. It's much safer to simply use scientific notation for extremely large numbers.

Obscure or confusing

Everyone knows what a million is. Any larger than that and you may run into trouble. The next large number name, billion, means 10⁹ to some people and 10¹² to others.

When writing for those who take one billion to mean 10⁹, your audience may or may not know that one trillion is 10¹² according to that convention. You cannot count on people knowing the names of larger numbers: quadrillion, quintillion, sextillion, etc.

To support this last claim, let's look at the frequency of large number names according to Google's Ngram viewer. Presumably the less often a word is used, the less likely people are to recognize it.

Here's a bar chart for the data from 2005, plotting on a logarithmic scale. The chart has a roughly linear slope, which means the frequency of the words drops exponentially. Million is used more than 24,000 times as often as septillion.

Here's the raw data.

 |-------------+--------------| | Name | Frequency | |-------------+--------------| | Million | 0.0096086564 | | Billion | 0.0030243298 | | Trillion | 0.0002595139 | | Quadrillion | 0.0000074383 | | Quintillion | 0.0000016745 | | Sextillion | 0.0000006676 | | Septillion | 0.0000003970 | |-------------+--------------|

Latin prefixes for large numbers

There is a consistency to these names, though they are not well known. Using the convention that these names refer to powers of 1000, the pattern is

[Latin prefix for n] + llion = 1000ⁿ⁺¹

So for example, billion is 1000²⁺¹ because bi- is the Latin prefix for 2. A trillion is 1000³⁺¹ because tri- corresponds to 3, and so forth. A duodecillion is 1000¹³ because the Latin prefix duodec- corresponds to 12.

 |-------------------+---------| | Name | Meaning | |-------------------+---------| | Billion | 10^09 | | Trillion | 10^12 | | Quadrillion | 10^15 | | Quintillion | 10^18 | | Sextillion | 10^21 | | Septillion | 10^24 | | Octillion | 10^27 | | Nonillion | 10^30 | | Decillion | 10^33 | | Undecillion | 10^36 | | Duodecillion | 10^39 | | Tredecillion | 10^42 | | Quattuordecillion | 10^45 | | Quindecillion | 10^48 | | Sexdecillion | 10^51 | | Septendecillion | 10^54 | | Octodecillion | 10^57 | | Novemdecillion | 10^60 | | Vigintillion | 10^63 | |-------------------+---------|

Code

Here's the Mathematica code that was used to create the plot above.

 BarChart[ {0.0096086564, 0.0030243298, 0.0002595139, 0.0000074383, 0.0000016745, 0.0000006676, 0.0000003970}, ChartLabels -> {"million", "billion", "trillion", "quadrillion", "quintillion", "sextillion", "septillion"}, ScalingFunctions -> "Log", ChartStyle -> "DarkRainbow" ]