The psychology of numbers: Why is 100 better than 101?

A number like any other is just as useful, is it not? But not all numbers are equal. Ask a mathematician and they’ll wax lyrical about pi (3.142…), Prime, Fibonacci and so on. They are fascinated with patterns of recurrence, (in)divisibility and oddness of properties. You may think that that’s just geeky but us mere mortals also impose an order and significance onto numbers that’s not objectively there. 

Last year BBC Radio’s More or Less programme asked 9 experts about their favourite numbers in 2012. A Soduku fan, Dr James Grime at the University of Cambridge offered 17 and explains why in his video. Dr Pippa Wells a physicist at CERN offered 5 because the certainty for finding the Higgs Boson particle was at the “5 sigma” level (i.e. a one-in-3.5 million probablity that it’s down to chance). Robert Peston offered the ratio of bank finance to other financing sources for businesses and households. It’s 80:20 in Europe and 20:80 in the United States. This, according to Peston (and Jean Claude Trichet) explains why Europe’s (and UK’s) economy has singularly failed to recover since 2008 as banks deleveraged. Bill Edgar, football statistician offered 1 in 10,000,000,000,000,000,000,000. That’s the probability that there’s not been a gay player in the Premier League since Justin Fashanu.

Today, we live in a largely decimal world filled with natural (or whole) numbers represented by ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When we count, we think in tens, multiple of tens and divisions of ten; leaving aside the comfortable familiarity of olde world Imperial measures. 

Why is 100 better than 101? Our perception of numbers is affected by our experience with them. In a classic paper in Cognition, Sharon Armstrong, Lila Gleitman and Henry Gleitman pointed out that round numbers like 100 are considered better exemplars of numbers than less frequently noticed numbers like 101, 99, or 171. Cognitively, we focus on these round numbers and the easy divisions of these numbers. We think of these as more typical examples of numbers. In a world that is decimal, we also recognise them faster and generally regard them as better numbers than less typical numbers.

As a scientist, round numbers communicate a level of precision to other people. If somebody tells you that during their holiday it was -10C, then you assume they mean a number in the neighborhood of 10. It might have been -9C or -11C, but probably not -20C. But if someone tells you that they were locked out in -13C weather, you believe they are communicating something more precise (probably because they read it off their smart phones). Conversely, if a politician tells you that net migration will fall by 20.35% to 134,063 in 2015 or that after staffing will be 203,351.4 after cuts, you’ll know it’s a guesstimate because the level of precision implied is unattainable.

This focus on round numbers also gives us a reason to mark landmarks in our lives. We measure the performance of new Presidents by the activity in their first 100 days in office (Peter Cheese CIPD’s new CEO marked his 100 days with an org-wide announcement of his direction of travel).

We use the "good" numbers as milestones for marking large passages of time. We go to (or avoid) class reunions after 10, 20, or 25 years (although not a round number, 25 is a clean division of 100 into quarters).  We choose to acknowledge 50 years of marriage to the same person or 20 years in a company, using the anniversary to reflect on all that has been accomplished in that time. It is also an opportunity to take stock and think about what you’d like to do differently in the future.

In short, the system of numbers doesn't play favorites, but the psychology of numbers does.

This year, the Chartered Institute of Personnel and Development celebrates its Centenary.   As the CIPD reflects on its 100 years of triumphs and change, it is also looking forward to its next 100 years.  May I wish our 134,437 members and this grande dame a year of jubilation.

Thank you for your comments. There may be a short delay in this going live on the blog page as we moderate the comments added to our blogs.

  • Hi Wilson, this is Helena and Cecilia from Exeter, we would like to get in contact my email is I am in Sydney but meeting Helena in KL. She sends her regards.

  • Please,I need any one who can help me to find relation between "Psychology" & "Numbers"'s urgent :)

    Thank You.

  • Ahh... Michael..

    As you've quietly flagged up..better for whom?  There is a whole body of marketing research that looks at how you can alter perceptions by changing the anchor or the frame. £9.99 is one where cognitively most buyers will register the fact that it doesn't breach the nice round number of 10 which is an easier checkpoint for spending limits.

    During sales, when you frame the offer as 30-50% off, experiments find that most people will take the lower figure as the mean (average) and 50% as the exception. To increase attention, marketeers use "Up to 50% off" so you register the more attractive 50% BUT you cannot fool all the people all of the time. If the punters go to your store or your website and find hardly anything at more that 30% off, there'll probably never come back...

  • Interesting, and yet in retail an item priced at 9.99 will sell better than 10

    So is 99 better than 100? I guess it depends what it is you are trying to communicate/ influence

  • Thanks for your story Ann : ) I guess the risk is that every smug moment can be gazumped by the next. I do sympathise.

    Thanks Frank and Paul. The question of 'zero' is an interesting one. It's not a natural number but 'zero' is an integral part of the system of real numbers. More to the point, it marks an absence. The comments section to the article on HR is an absence which can then be interpreted to mean there are no defenders. It's also possible to say that no one read it, bothered to comment or disagreed. We just cannot tell from an absence. 'Zero' is such an elegant construct though!