Excerpted from “The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life.“
Numbers were invented to describe precise amounts: three teeth, seven days, twelve goats. When quantities are large, however, we do not use numbers in a precise way. We approximate using a ‘round number’ as a place mark. It is easier and more convenient. When I say, for example, that there were a hundred people at the market, I don’t mean that there were exactlyone hundred people there. And when I say that the universe is 13.7 billion years old, I don’t mean exactly 13,700,000,000, I mean give or take a few hundred million years. Big numbers are understood approximately, small ones precisely, and these two systems interact uneasily. It is clearly [amazon asin=1451640099&template=*lrc ad (left)]nonsensical to say that next year the universe will be ‘13.7 billion and one’ years old. It will remain 13.7 billion years old for the rest of our lives.
Round numbers usually end in zero. The word round is used because a round number represents the completion of a full counting cycle, not because zero is a circle. There are ten digits in our number system, so any combination of cycles will always be divisible by ten. Because we are so used to using round numbers for big numbers, when we encounter a big number that is non-round – say, 754,156,293 – it feels discrepant. Manoj [amazon asin=1416588280&template=*lrc ad (right)]Thomas, a psychologist at Cornell University, argues that our sense of unease with large, non-round numbers causes us to see these numbers as smaller than they are: ‘We tend to think that small numbers are more precise, so when we see a big number that is precise we instinctively assume it is less than it is.’ The result, he claims, is that we will pay more for an expensive object if the price is non-round. In one of Thomas’s experiments, respondents viewed pictures of several houses together with their sale prices, which were randomly assigned either a round number, such as $390,000, or a slightly larger, precise one, such as $391,534. Asked whether they considered each price high or low, on average the respondents judged the precise prices to be lower than the round ones, even though the precise numbers were actually higher. Thomas and his collaborators argued that whatever other inferences the respondents were making about why the price was precise – such as that the seller had thought more carefully about it, and so the price was fairer – [amazon asin=0544105850&template=*lrc ad (left)]they still made the subconscious judgment that non-round numbers are smaller than round ones. A tip to readers selling their homes: if you want to make money, don’t end the price with a zero.
The practice of subtracting 1 from a round number conveys a potent message. When we read a number, we are more influenced by the leftmost digit than we are by the rightmost, since that is the order we read, and process, them. The number 799 feels significantly less than 800 because we see the former as 7-something and the latter as 8-something, whereas 798 feels pretty much like 799. Since the nineteenth century, shopkeepers have taken advantage of this trick by choosing prices ending in a 9, to give the impression that a product is cheaper than it is. Surveys show that anything between a third and two-thirds of all retail prices now end in a 9.Though we are all[amazon asin=0486270785&template=*lrc ad (right)] seasoned shoppers, we are still fooled. In 2008, researchers at the University of Southern Brittany monitored a local pizza restaurant that was serving five types of pizza at €8 each. When one of the pizzas was reduced in price to €7.99, its share of sales rose from a third of the total to a half. Dropping the price by one cent, an insignificant amount in monetary terms, was enough to influence customers’ decisions dramatically.
Our response to prices ending in 9, however, is subject to more complex influences than a bias towards the leftmost digit. A price ending in 9 feels like a bargain, even when it isn’t. Eric Anderson of the University of Chicago and Duncan Simester of MIT arranged for the same dress to be priced at $34, $39 and $44 in three otherwise identical mail order catalogues. The dress sold best at $39, rather than the cheaper price of $34. Similar results have been found in other studies: the 9-ending is a cue that the item has been discounted and is therefore a good deal. But the association of 9 with bargains can also mean that a 9-priced product looks cheap, or can give the impression that the seller is somehow manipulating you. An upmarket restaurant, for example, would never dream of pricing a main course at, say, $32.99. Nor would you trust a therapist who charged $99.99 a session. The prices would be $33 and $100, which feel both classier and more honest. Our response to the number 9 is conditioned by a mixture of cultural and psychological factors. Numbers are not impartial and straightforward; they have baggage.
