Suitable Names for Large Numbers

One year ago, there were just two centibillionaires, Jeff Bezos and Bill Gates. Recently, Facebook’s Mark Zuckerberg has joined the Amazon and Microsoft founders. Elon Musk, CEO of Tesla and SpaceX, is tipped to be next to join this exclusive club [TM194 or search for “thatsmaths” at irishtimes.com].

Shot from “A Suitable Boy” with Maan Kapoor (Ishaan Khatter), Mrs. Mahesh Kapoor (Geeta Agarwal) and Bhaskar (Yusuf Akhtar), covered in colours during the Holi festival [image from Instagram.  See also here].

The word centibillionaire has slithered into common usage for someone with a nett worth of more than a hundred billion dollars. The term is a linguistic travesty: the prefix “centi” normally connotes one hundredth part of something, as when it precedes metre or gram. So, a centibillion is suggestive of one hundredth of a billion, or ten million. Alas, the misuse is probably irreversible.

The problem arises from the paucity of terms in common language for large numbers. In our decimal system, the magnitude of numbers increases by a factor of ten for each additional digit; there should be a unique name for each power of ten up to 20 or so.

Bhaskara

We are indebted to ancient Indian mathematicians for the development of the decimal number system. These mathematicians were fascinated by large numbers, and had names for powers of ten far beyond anything in common use today. Bhaskara, who flourished in the seventh century, was the first mathematician to write numbers using a circle for the zero. This zero – this “nothing” – gives the number system enormous power and versatility.

Bhaskar, a mathematically gifted seven-year-old named after the ancient savant, was a character in Vikram Seth’s blockbusting novel “A Suitable Boy”, a story recently adapted for TV. Speaking to Haresh, a love interest of Lata, the main character, Bhaskar points out a shortcoming in our counting system: names are lacking for some of the powers of ten. “First you have ten, that is, ten to the first power. Then you have a hundred, which is ten times ten, which makes it ten to the second power. Then you have a thousand, which is ten to the third power. But for the next power, ten thousand or ten to the fourth power, there is no special word.”

The fifth, sixth and seventh powers of ten – one followed by five, six and seven zeros – are a lakh, a million and a crore. Two of these names, popular in India, are also familiar to cross-word solvers. The eighth power of ten, a hundred million, has no particular name, the ninth power is a billion, and the tenth power is again anonymous. Bhaskar concludes that “it’s amazing that we don’t have a word in either English or Hindi for a number that is as important as ten to the tenth.”

A Suitable Name

Haresh recalls that Chinese merchants use ten-thousand as a natural measuring point “just as we use a lakh”. He consults a Chinese colleague in Kanpur and learns that the missing terms are wan (to rhyme with ‘kaan’) and ee (to rhyme with ‘knee’). This gives, in order of powers of ten: one, ten, hundred, thousand, wan, lakh, million, crore, ee, billion. For ten to its own power Haresh found no special word, and wrote to Bhaskar “you will have to invent one for yourself. I suggest bhask.”

Here is a challenge for inventive readers: devise a number-naming system that is lucid, unambiguous and aesthetically pleasing and that will rid us of the dogs dinner that is a centibillion.

ADDENDUM

Here are some responses to the challenge.

Vincent H, Galway, suggests: Alpha = to the power of 10, Beta to the power of 100, Gamma to the power of 1000 etc. (there are 24 letters in the Greek alphabet!)

Marcin C suggests a mention of the Greek myriad and its square, the myriad myriads.

Frank McK, Longwood, takes an Irish perspective, and suggests Deich and Cèad, “As Gaeilge”, as prefixes for multiplication by ten and a hundred . This gets us from a million to a billion, a billion to a trillion, and so on.

Brendan C, Dublin, proposes a simple Zero based system: 10 = unizero, 100 = duozero, 1,000 = trizero, and so on. Thus, a centibillion (11 zeros) becomes an evtekazero.

Joe Dunne, Shanakiel, Cork, in a letter to The Irish Times, writes:

I propose a simple “Power X” where the incorrectly named centibillion would be called Power 11, a billion would be Power Nine and a million would be Power Six. The word “power” denotes “ten to the power of” and the number represents the number of zeroes following a one. The system is also applicable to small numbers. If you only have a euro to your name, then you’re a Power Zero.

John L, Letterkenny, Donegal proposes to just follow the polygon and polyhedron models: He uses the suffix -nils. So for example a Tridecanil is 1013 . The dreaded centibillionaire becomes a hendecanil.

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