Comments

Cyril wrote:

In French, we use the long scale almost as is. We have milliard, trilliard, etc.

We always have to convert the English's billion to French's milliard, and so on. Yet, we haven't learned the rule for the "scale", since there's none for the long scale's -iard numbers. Each multiple-of-3 power of 10 has a name and that's it.

Raúl Ward wrote:

In Spanish speaking countries, a billion is a million millions.

The problem is that sometimes, when translating news or articles from English, they do it literally, so an English billion (one thousand millions) is put in Spanish as a "billón" (a million millions). That is a source of mistaken amounts.

Jon wrote:

I'm from Denmark were we use the long scale. I didn't know a long scale form existed in English! It happens quite often that a billion, in English, gets translated to a billion in Danish, which is off by \( 999 \times 10^9, \) and of course, should have been a milliard. ;-)

Marek Madejski wrote:

I grew up with the long scale (in Poland), so I may biased, but I find \( 10^{6n} \) more intuitive and easier to use than the short scale's \( 10^{3n+3} \) (with \( n \) being the Latin prefix). It's mentally easier to divide the exponent by 6 than to subtract 3 and divide by 3.

Also, the long scale covers more orders of magnitude, and between each \( n \)-illion and \( (n+1) \)-illion there is a \( 10^{6n+3} \) \( n \)-illiard (\( 10^9 \) = "milliard", \( 10^{15} \) = "billiard" and so on), so one doesn't need to operate with "thousands of -illions".

Said that, I still prefer the scientific notation \( k × 10^n \) to names of large numbers, precisely because both scales co-exist, and lead to mistakes literally off by multiple orders of magnitude.