A Billion or a Trillion

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The origin of the words Billion and Trillion.

The word “Billion” was created by the French in the 15th century.


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The French physician and mathematician Nicolas Chuquet (1445-1488) apparently coined the words byllion and tryllion and used them to represent 1012 and 1018

a million is worth a thousand thousand units
a byllion is worth a thousand thousand millions
a tryllion is worth a thousand thousand byllions
a quadrillion is worth a thousand thousand tryllions

A Billion 1012 would be defined as a million to the power of 2 (bi).
A Trillion 1018 would be a million to the power of 3, ie tri.

These numbers would be:

Billion: a million to the power of 2 = 1,000,000,000,000 (1,000,000 x 1,000,000)
Trillion: a million to the power of 3 = 1,000,000,000,000,000,000 (1,000,000 x 1,000,000 x 1,000,000)


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Numbers to the Power of… explained

2 to the power of 1 = 2
2 to the power of 2 = 4 (2×2)
2 to the power of 3 = 8 (2x2x2)
2 to the power of 4 = 16 (2x2x2x2)

1 Million to the power of:

1 = 1,000,000
2 = 1,000,000,000,000
3 = 1,000,000,000,000,000,000

Confusion over numbering from the 1800’s

From the 1500’s to the late 1700’s and early 1800’s, ALL countries used the single system of Billion (million x million) and Trillion (million x billion).

However, in  the early 1800’s France and the United States elected to use a shorted numbering system, but still used the original wording that other countries used for these numbers.

This caused confusion, with the USA having chosen a different meaning in their language.

For example 1012 now equals 109. This follows the US changing to anew systems and sticking with it

In the United States a million to the power of 2 (a Billion) is actually called a Trillion.
A United States Billion is not the same as the origin of the name, but just a simplified 1,000 times a Million.

The French created the terms ‘Long scale’ and ‘Short Scale’ to differentiate the systems being used, after reverting back to the original system.

Long Scale and Short scale Millions

In the long scale the prefixes beyond one million indicate the actual power or exponent.
The numbering sequence of million times the last (eg: million x million)

In the short scale, the prefixes refer to one less than the exponent..
The numbering sequenced of one thousand times the last (eg: thousand x million)

Long Scale:

Billion means a million millions
Trillion means a million billions

Short Scale:

Billion means a thousand millions
Trillion means a thousand billions

Timeline:

1520: France creates the terms Billion a thousand thousand Millions and Trillion a thousand thousand Billions.

1729: The US published “Greenwood Book”, published in 1729, made the first reference of the use of 1,000,000,000 (a thousand million) as being a billion. (Short Scale)

1800: France changed to the Short scale in the early 1800’s

1800: The United States officially changed to the short scale, shortly after France.

1961: France reverted back to the original Long scale in 1961. Journal officiel ‘PDF’, the official French Government gazette.

1974: Britain changed official numbers to the Short scale in 1974. Hansard, the official British Government gazette.
In 1974, the government of Prime Minister Harold Wilson announced that henceforth “billion” would mean 109 and not 1012 in official British reports and statistics

1975: France created the terms ‘Long scale’ and ‘Short Scale’ in 1975, to distinguish the two numbering systems.

Many British people, especially those educated pre 1974, still think of the billion and trillion in its original meaning.

Worldwide usage of Billion and Trillion terms

Countries that still use the original Billion include: France, Sweden most of Europe.

Countries that have changed to the shorter Billion include: United States, China, Brazil, Australia, New Zealand

Hansard 20 December 1974 vol 883 cc711-2W 711W

Mr. Maxwell-Hyslop asked the Prime Minister whether he will make it the practice of his administration that when Ministers employ the word “billion” in any official speeches, documents, or answers to Parliamentary Questions, they will, to avoid confusion, only do so in its British meaning of 1 million million and not in the sense in which it is used in the United States of America, which uses the term “billion” to mean 1,000 million.

The Prime Minister No. The word “billion” is now used internationally to mean 1,000 million and it would be confusing if British Ministers were to use it in any other sense. I accept that it could still be interpreted in this country as 1 million million and I shall ask my colleagues to ensure that, if they do use it, there should be no ambiguity as to its meaning.

The First United States use of the new billion

It appears that this was all started by Isaac Greenwood, an alcoholic who lost his position of Hollis Chair of Mathematics, Harvard University, and then his life to his alcohol addiction.

Comparisons

European to US

A European million is equal to a US million
A European billion is equal to a US trillion
A European trillion is equal to a US quintillion
A European quadrillion is equal to a US septillion
A European quintillion is equal to a US nonillion
A European sextillion is equal to a US undecillion
A European septillion is equal to a US tredecillion
A European octillion is equal to a US quindecillion
A European nonillion is equal to a US septendecillion
A European decillion is equal to a US novemdecillion

US to European

A US million is equal to a European million
A US billion is equal to a European milliard
A US trillion is equal to a European billion
A US quadrillion is equal to a European billiard
A US quintillion is equal to a European trillion
A US sextillion is equal to a European trilliard
A US septillion is equal to a European quadrillion
A US octillion is equal to a European quadrilliard
A US nonillion is equal to a European quintillion
A US decillion is equal to a European quintilliard

There is so much confusion, not only about the values of these numbers, but also of who uses which system.

I read an American recently saying;  to the Americans and the French, a billion means a thousand millions [Short Scale] and that the British Empire and Commonwealth, use the term billion [Long Scale] to describe an American trillion [Short Scale].

However, he didn’t realise that the French changed back to Long Scale, and the British (reluctantly) now use the Short Scale.

 


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