Some numbers are less certain than they appear

We think English words for numbers are precise. But language is slippery, and a hundred is not always 100, nor is a billion always 1,000,000,000.

Staff

When is a hundred not a hundred? This might sound like a riddle, but it’s an interesting question. We tend to think of English words for numbers as precise terms, having stable, unique relationships with particular referents. These words can almost seem like parts of a mathematical equation: one hundred = 100, just as 102 = 100. But language is slipperier than that, and a hundred is not always 100, nor is a billion always 1,000,000,000.  

The Anglo-Saxons had two different hundreds, hund-teontig (100, “the short hundred”) and hund-twelftig (120, the “long” or “great hundred”). They followed the Germanic practice of counting in tens up to 120, according to historian Julian Goodare. In fact, the word hundred was more likely to refer to 120 than 100 until the 16th century. If you bought a “hundred” eels or chickens, or sold “one hundred” measures of oatmeal, you were really talking about 120. Professor Goodare speculates that the popularity of the long hundred might be partly attributed to tax evasion. In the Middle Ages, duties were levied on merchants as flat fees per hundred units, so if your “hundred” was actually 120, you could charge your customer more but pay the same tax.

Sometimes, however, one hundred wasn’t 120, either. “A hundred pounds” of groceries in 18th-century London actually weighed 104; there were 124 cod to the hundred, 128 herring, 132 mackerel, and 240 crabs. Most long hundreds became short hundreds in the 16th to 17th centuries, when arithmetic began to be taught in schools, but they lingered on when counting agricultural commodities. 

Billion and trillion were defined along scientific principles, but they can be almost as unreliable. Fifteenth- and 16th-century French mathematicians wanted to be able to talk about numbers greater than a million, so they named 1,000,0002   a billion, 1,000,0003 a trillion, 1,000,0004 a quadrillion, and so on. This is a rational system – the word for a million squared uses bi-, a Latin prefix meaning “two”; a million cubed is tri-, meaning “three”; to the fourth power is quad-, etc. This makes a billion 1012 and a trillion 1018 , the values they hold in Europe and many French- and Spanish-speaking countries around the world, which use this “long scale.”

Other mathematicians advocated for a scale that instead went up by multiples of 1,000, which made for finer verbal differentiation. On this “short scale,” a billion is 109 and a trillion 1012 , the definitions we’re familiar with in the United States and in Britain, at least since 1974. Before then, Britain used the long scale, and 109 was a milliard

If you could count a billion herring, how many would there be? Let’s be content with “a lot.”

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