# 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 |
| 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 |
| 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"
]
```

## 4 thoughts on “Names for extremely large numbers”

1. Clint Hepner

In the long scale, the Latin prefixes simply refer to powers of 1,000,000: one billion is (1,000,000)^2, one trillion is (1,000,000)^3, etc.

The long scale also provides names constructed from the prefixes + *-lliard* (milliard, billiard, etc) for 1000^(n+4). One wonders how frequently trilliard and above are used outside of dictionaries that define them; Google Ngram only shows results for “milliard” and “billiard”, and the latter is inflated by references to the game.

2. Saurish Chakrabarty

The predictable trend beyond quintillion is surprising to me. I would have expected the frequencies above trillion to be somewhat similar. The log scale brings out the difference! By the way, my spell check does not know the word quintillion.

3. Very nice! Thank you, John.

4. Steve Hollasch

I think it’s a stretch to say frequency of use corresponds exactly with understanding. I understand the rationale, but this does *not* categorically demonstrate the probability that an average person will understand a particular quantity. If anything, it just shows that our need to work with large numbers falls off in direct logarithmic relation to their sizes, which seems kind of obvious.