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- "Ten, a hundred, a thousand, …

# "Ten, a hundred, a thousand, a million, a billion"

## Translation:Dek, cent, mil, miliono, miliardo

## 23 Comments

I just search it again... and it looks that a million is still 10^6 and billion still 10^12 for Esperanto. The rest of the world is still divided: https://en.wikipedia.org/wiki/Long_and_short_scales#Short_scale_users

- 379

Just want to leave here the reason why the **long scale** (used e.g. in Esperanto) is logical and the **short scale** (used e.g. in Usonia and recently also in UK) is irrational:

In the **long scale** n-illion is:

- 10 ⁶ⁿ
- 10 ³ ⁽²ⁿ⁾
- 1 000 000 ⁿ
- n-times as long as a million (n-lengths of million = n-illion)

In the **short scale** n-illion is:

- 10 ³ ⁺ ³ⁿ
- 10 ³ ⁽¹ ⁺ ⁿ⁾
- 1 000 · 1 000 ⁿ
- n-times as long as a thousand and a thousand more(?)

- 379

If the short scale was indeed counting in thousands, that would be perfectly fine for me. :) But short scale **does not** count in thousands. It's just an irrational modification of the original invention, which only makes it less useful. “Counting in thousands” would require the n-illion being n times as long as a thousand, thus:

- 1 000 — thousand
- 1 000 000 — bousand
- 1 000 000 000 — trousand
- etc.

Remember, that both long and short scale have the same goal: to communicate very large numbers in the easiest and most logical way possible. Let us test both!

In the long scale when you hear **decillion**, you just interpret it as being ten times as long as a million. 1 000 000 ¹⁰ = (10 ⁶) ¹⁰ = 10 ⁶⁰. When you hear **quintillion**, you just understand it as being five times as long as a million. 1 000 000 ⁵ = (10 ⁶) ⁵ = 10 ³⁰. When you hear **octodecillion**, you just know it is eighteen times as long as a million. 1 000 000 ¹⁸ = (10 ⁶) ¹⁸ = 10 ¹⁰⁸.

In the short scale, on the other hand, when you hear **decillion**, you either have to remember the formula 10 ³ ⁽¹ ⁺ ⁿ⁾, interpret is as being a thousand multiplied by a number ten times as long as a thousand (then why call it a **dec-** of **-illion**s?) or perform the chain formula *decillion is thousand nonillions, which is thousand octillions, which is thousand septillions, which is thousand sextillions, which is thousand quintillions, which is thousand quadrillions, which is thousand trillions, which is thousand billions, which is thousand millions, which I understand, so* 1 000 ¹⁰ · 1 000 000 = 10 ³⁶. *No, damn it! I've expanded decillion only nine times, not ten times, so that'll be* 1 000 ⁹ · 1 000 000 = 10 ³³.

That's even worse than not taking a lesson from kindergarten play of stacking smaller cylinders on larger cylinders when writing dates:

No, you don't have to remember any formula. In the long scale, one billion is a million millions, while in the short scale a billion is a thousand millions. Or, as you may prefer: long scale : (10^6, 10^12, 10^18...); short scale: (10^6, 10^9, 10^12...). (million, billion, trillion). In any case, if you insist that the short scale makes no sense, that's your opinion and I'll respect it.

Oh, and I thought I might add: you're overcomplicating the formulas. The long scale follows this geometric progression: n-illion = 10^6 * 10^6n Where n1 = 0 Million = 10^6 * 10^0 = 10^6. Billion = 10^6 * 10^6 = 10^12 Decillion = 10^6 * 10^54 = 10^60. The short scale follows the same formula, except it multiplies by 10^3n instead. So: n-illion = 10^6 * 10^3n Where n1 = 0 Million = 10^6 * 10^0 = 10^6. Billion = 10^6 * 10^3 = 10^9 Decillion = 10^6 * 10^27 = 10^33. It's like comparing a ruler measured in inches to one measured in centimeters.

I often fail to translate all the words. In this, I entered "Ten, cent, mil, miliono, miliardo". I know the right answer but type the wrong thing. Sometimes I even think it, maybe even say it out loud correctly, then type one or more words in the wrong language. Works either direction. I assume this will get better with more practice and time but if anyone has any tricks to speed up not doing this, let me know.

- 379

Yes, in Esperanto the correct form is simply *dek* for 10, *cent* for 100 and *mil* for 1000.

With tens and hundreds the case is clear: the sequences are *dek*, *dudek*, *tridek* etc. and *cent*, *ducent*, *tricent* etc. — the words **unudek** and **unucent** simply don’t exist. Theoretically one could say *unu mil*, but that would be quite unusual.

- 379

In UK it was officially changed some time ago: from the logical and etymologically correct long scale to the usonian and irrational short scale. :)

- 379

Maybe it would be more logical, but in the same time it would be less international. So because of that, the words in use are *miliono* and *miliardo*.

Bigger numbers are used quite rarely and to solve the problem of “a billion” meaning different things in different countries, the endings “-iliono” and “-iliardo” we've abstracted and it seems to be a solution, which won in the language.