Billions and trillions

An explanation of short scale and long scale naming systems

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Shutterstock / Nishi’s Images / Night landscape showing the billions of stars in the Milky Way galaxy over tall, snow-covered mountains and a lake.

As a research scientist and a science editor, I’m used to hypotheses being proved wrong and theories being changed as new evidence comes to light. One thing scientists aren’t used to changing is how we express and write numbers. We know for a fact that 2 + 2 = 4, don’t we? However, when it comes to really large numbers, those over a million, our relationship wavers. Let me introduce the “short scale” and “long scale” nomenclature (naming) systems for integer powers of 10.

What? A billion isn’t always a billion?

That’s right – a billion isn’t always a billion. It depends on whether the author is using the short scale or the long scale, which in turn depends on what language they are speaking or what country they come from.

For numbers up to and including a million, or 10 to the power of 6 (10⁶), the long scale and the short scale are identical. For numbers larger than a million, the scales differ.

The short scale is used in most English-speaking and Arabic-speaking countries, as well as Brazil.

The long scale is used in most of continental Europe, including France, Germany, Spain and Portugal. Other countries that have derived their languages from this region, such as many in South America, like Brazil, also use the long scale.

Some languages, particularly those used in East Asia and South Asia, have even more large-number naming systems. In this blog, however, I’m focusing on the short and long scales.

Long scale

The long scale began its use in the English language in about the 14th century. The terms “billion” and “trillion” then came into common use in France in the 15th century.

Every “-illion” term in the scale is a million (10⁶) times larger than the previous term. Because these are quite large jumps, the long scale has interim steps in between the “-illion” terms. These interim steps have terms that end with “-illiard”.

The long scale proceeds like this:

• a million is a thousand thousand, or 10⁶
• a milliard is a thousand million, or 10⁹
• a billion is a million million, or 10¹²
• a billiard is a thousand billion, or 10¹⁵
• a trillion is a million billion, or 10¹⁸.

Short scale

Sometime in the 17th century, in France and Italy, the meanings of the “-illion” terms were changed, which resulted in the short scale. In the short scale, every “-illion” term is a thousand (10³) times larger than the previous term.

The short scale proceeds like this:

• a million is a thousand thousand, or 10⁶
• a billion is a thousand million, or 10⁹
• a trillion is a thousand billion, or 10¹².

International adoption

By the 18th century, France and most of Europe were using the short scale, and Britain was using the long scale.

But to make a long story short … after another hundred years or so, they had swapped – France and Europe to the long scale, and Britain the short. As colonies gained independence, they chose the scale they most preferred. And that is how the world ended up with two different naming systems for integer powers of 10.

We have a French mathematician to thank for the terms “long scale” and “short scale”. Geneviève Guitel was the first to publish the terms in her 1975 book, Histoire comparée des numérations écrites (Comparative history of written numerals).