A few weeks back, Nina Stössinger asked on Twitter:
Isn’t it odd that the percent sign looks like “0/0” rather than, say, “/100” or “/00”?
This, it turns out, is a very good question. Like Nina, I had assumed that the percent sign was shaped so as to invoke the idea of a vulgar fraction, with a tiny zero aligned on either side of a solidus ( ⁄ ), or fraction slash. That said, something about those zeroes had always nagged at me. Specifically, as you divide any non-zero quantity by a smaller and smaller number the result tends ever closer to infinity (or rather, ±∞ as appropriate), until finally, when dividing by zero itself, you reach a mathematical singularity where the result cannot be computed — a numerical black hole of exotic properties and mind-bending implications. Throw in another zero as the numerator and you have a thoroughly nonsensical fraction. Though this is all terribly exciting from a philosophical point of view, it is not an especially useful situation to be in when trying to communicate the simple concept of division into hundredths. Either the ‘%’ had stumbled, blinking, from some secret garden of esoteric mathematics and into the real world, or there was more to the story. And so there was.
Writing in 1908, David Eugene Smith, later to be president of the Mathematical Association of America,1 reported on a peculiar find he had made in an Italian manuscript written sometime during the early part of fifteenth century. (Smith was cataloguing the mathematical holdings of one George Arthur Plimpton, a publisher and philanthropist who had amassed a huge library of ancient books.) What had caught Smith’s eye was an oddly attenuated abbreviation comprising a ‘p’, an elongated ‘c’, and a superscript ‘o’, or ‘o’, balanced upon the extended upper terminal of the ‘c’, as seen at top. From its context, Smith deduced that pco was a stand-in for the words per cento, or “per hundred”, more often abbreviated to per 100, p cento, or p 100.2 It was the first step towards a distinct percent sign — and, counterintuitively, it had precisely nothing to do with the digit zero.
Smith picked up the trail with his weighty two-volume History of Mathematics, published in 1923,3 wherein he printed an image of the percent sign caught midway between pco and ‘%’. Taken from an Italian manuscript of 1684, as seen above, by now the word per had collapsed into the tortuous but common scribal abbreviation seen here while the ‘c’ had morphed into a closed circle surmounted by a short horizontal stroke. The imperturbable ‘o’ sat atop it. All that remained was for the vestigial per to vanish and for the horizontal stroke to assume its familiar diagonal orientation — a change that occurred sometime during the nineteenth century — and the evolution of the percent sign was complete.
Since then the ‘%’ has gone from strength to strength, and today we revel in a whole family of “per ————” signs, with ‘%’ joined by ‘‰’ (“per mille”, or per thousand) and ‘‱’ (per ten thousand). All very logical, on the face of it, and all based on a fundamental misunderstanding of how the percent sign came to be. Nina and I can comfort ourselves that we are not the first people, and likely will not be the last, to have made the same mistake.