Long scale is better than short scale
Dan Dart's Blog: Software, Mathematics, Radio, Music [Unofficia…
May 4, 2026
Hi!
It's been a bit since I've posted anything quite as substantial, so here we go!
I was brought up with what we were led to believe was the "British/French" system of numbers, known as "long scale", which many countries still use, as opposed to the "American/German" version, which apparently Britain now uses, also known as "short scale".
The difference? The powers of ten:
10^n | 1000^n | Short scale | Million^n | Long scale, -ard | Long scale, thousand
---|---|---|---|---|---
3 | 1 | Thousand | 0.5 | Thousand | Thousand
6 | 2 | Million | 1 | Million | Million
9 | 3 | Billion | 1.5 | Milliard | Thousand million
12 | 4 | Trillion | 2 | Billion | Billion
15 | 5 | Quadrillion | 2.5 | Billiard | Thousand billion
18 | 6 | Quintillion | 3 | Trillion | Trillion
21 | 7 | Sextillion | 3.5 | Trilliard | Thousand trillion
24 | 8 | Septillion | 4 | Quadrillion | Quadrillion
27 | 9 | Octillion | 4.5 | Quadrilliard | Thousand quadrillion
30 | 10 | Nonillion | 5 | Quintillion | Quintillion
33 | 11 | Decillion | 5.5 | Quintilliard | Thousand quintillion
36 | 12 | Undecillion | 6 | Sextillion | Sextillion
39 | 13 | Dodecillion | 6.5 | Sextilliard | Thousand sextillion
42 | 14 | Tredecillion | 7 | Septillion | Septillion
45 | 15 | Quattuordecillion | 7.5 | Septilliard | Thousand septillion
48 | 16 | Quindecillion | 8 | Octillion | Octillion
51 | 17 | Sexdecillion | 8.5 | Octilliard | Thousand octillion
54 | 18 | Septendecillion | 9 | Nonillion | Nonillion
57 | 19 | Octodecillion | 9.5 | Nonilliard | Thousand nonillion
60 | 20 | Novemdecillion | 10 | Decillion | Decillion
...etc.
The details of this table is probably my best backup as to why I prefer long scale to short scale.
As you can see, the long scale directly comes from the Latin of the power of a million, but short scale comes from what seems to be a hack: "a thousand times the power of a thousand"? "One less than the power of a thousand"?
If you're intent on using a thousands-based system, I have suggested a "power of a thousand" name below,with the added benefit that it divides directly into the long scale without having to add such a "hack factor"!
10^n | 1000^n | Silly name
---|---|---
3 | 1 | Thousand
6 | 2 | Bisand
9 | 3 | Trisand
12 | 4 | Quadsand
15 | 5 | Quintsand
18 | 6 | Sexsand
21 | 7 | Septsand
24 | 8 | Octsand
27 | 9 | Nonsand
30 | 10 | Decsand
33 | 11 | Undecsand
36 | 12 | Dodecsand
39 | 13 | Tredecsand
42 | 14 | Quattuordecsand
45 | 15 | Quindecsand
48 | 16 | Sexdecsand
51 | 17 | Sepdecsand
54 | 18 | Octdecsand
57 | 19 | Nondecsand
60 | 20 | Viginsand
This is obviously very tongue-in-cheek, but it's one of the times that a common usage of numbers (which I like very much) has disappointed me.
Till next time.
Discussion in the ATmosphere