The promise of 2010

fireworks-copyHumans have a fascination with round numbers. No wonder, for round numbers do simplify our lives. It’s easier to multiply 10 by 3 than 9.98 by 3, and for most practical purposes the difference in the end result is negligible – except in retail situation. No matter what amount of rounding off we do in our head, a price tag of R299.99 somehow always turns out to be R200-something, instead of about R300. And therein lies the retailers’ infatuation with non-round numbers…

You should have learned how to round off numbers in primary school. In case you slept thought that lesson, here’s a song to remind you how it’s done. Alternatively, let Excel do the rounding-off for you.

As for definitions, Wikipedia says that a round number is “a number that ends with one or more zeroes (0), meaning that they are multiples of 10, 100, 1000, and so on”, and notes that some variations “allow multiples of 5 or 25 to be also considered round.”

Wolfram Math World definition is a tad more involved. According to these guys:

  • A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48);
  • Round numbers are very rare. As Hardy (1999, p. 48) notes, “Half the numbers are divisible by 2, one-third by 3, one-sixth by both 2 and 3, and so on. Surely, then we may expect most numbers to have a large number of factors. But the facts seem to show the opposite.”
  • A positive integer n is sometimes said to be round (or “square root-smooth”) if it has no prime factors greater than the square root of n. The first few such numbers are 1, 4, 8, 9, 12, 16, 18, 24, 25, 27, 30, 32, … (Sloane’s A048098). Using this definition, an asymptotic formula for the number of round integers less than or equal to a positive real number x is given by round-numbers

Huh?

Definitions aside, we love round number so much that we always expect great things to happen in the years with round numbers. Here’s wishing that this expectation comes true for you!