Long and short scales Totally Explained

Everything about The Long And Short Scales totally explained

The long and short scales are two different numerical systems used throughout the world: ť Short scale is the English translation of the French term échelle courte. It refers to a system of numeric names in which every new term greater than million is 1,000 times greater than the previous term: "billion" means "a thousand millions" (10⁹), "trillion" means "a thousand billions" (10¹²), and so on. ť Long scale is the English translation of the French term échelle longue. It refers to a system of numeric names in which every new term greater than million is 1,000,000 times greater than the previous term: "billion" means "a million millions" (10¹²), "trillion" means "a million billions" (10¹⁸), and so on.

Note that the difference between the two scales grows as numbers get larger. Million is the same in both scales, but the long-scale billion is a thousand times larger than the short-scale billion, the long-scale trillion is a million times larger than the short-scale trillion, and so on.
For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, Although some residual long-scale usage still continues, the terms "British" and "American" no longer represent accurate terminology.

Comparison

For a more extensive table, see names of large numbers.

Value	Value Expanded	Short Scale	Short Scale Logic	Long Scale	Long Scale Logic
10⁰ =	1	one	1,000 ^{1 - 1}	one	1,000,000 ^0.0
10³ =	1,000	thousand	1,000 ^{1 + 0}	thousand	1,000,000 ^0.5
10⁶ =	1,000,000	million	1,000 ^{1 + 1}	million	1,000,000 ^1.0
10⁹ =	1,000,000,000	billion	1,000 ^{1 + 2}	thousand million (or milliard)	1,000,000 ^1.5
10¹² =	1,000,000,000,000	trillion	1,000 ^{1 + 3}	billion	1,000,000 ^2.0
10¹⁵ =	1,000,000,000,000,000	quadrillion	1,000 ^{1 + 4}	thousand billion (or billiard)	1,000,000 ^2.5
10¹⁸ =	1,000,000,000,000,000,000	quintillion	1,000 ^{1 + 5}	trillion	1,000,000 ^3.0
10²¹ =	1,000,000,000,000,000,000,000	sextillion	1,000 ^{1 + 6}	thousand trillion (or trilliard)

Since bi refers to 2 and tri refers to 3, the logic in the names is:

short scale: Billion is thousand × (thousand)² = 10⁹. Trillion is thousand × (thousand)³ = 10¹².

ť :To get from one named order of magnitude to the next, multiply by a thousand.

long scale: Million is (million)¹ = 10⁶. Billion is (million)² = 10¹². Trillion is (million)³ = 10¹⁸. ť :To get from one named order of magnitude to the next, multiply by a million. In other words, a billion (bi / two) has twice as many zeros as a million, and a trillion (tri / three) has three times as many zeros as a million, etc.

The old word "milliard", also found in many other languages, can be used for 10⁹ but is unknown in American English and not used in British English - however, "yard", which derives from "milliard", is used on financial markets, as unlike "billion", it's unambiguous.

Historical and language context

The existence of the different scales means that care must be taken when comparing large numbers between languages or countries, or when using old documents in countries where the dominant scale has changed over time. For example, British English documents from 1900 used long scale values, which are different from current British short scale usage. Both scales were used in France and Italy at various times in their history, but these countries (and most other European countries) now officially use long scale. For example, the French word billion, the German word Billion and the Dutch word biljoen all refer to 10¹². This translates to the short-scale term "trillion" (10¹²), not "billion" (10⁹ in the short scale). See Current usage below.

History

Further Information

Get more info on 'Long And Short Scales'.

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