Humans have a fascination with round numbers. No wonder, for round numbers do simplify our lives. Itâ€™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 retailersâ€™ infatuation with non-round numbersâ€¦
You should have learned how to round off numbers in primary school. In case you slept thought that lesson, hereâ€™s a song to remind you how itâ€™s done. Alternatively, let Excel do the rounding-off for you.
As for definitions, Wikipedia says that a round number is â€œa number that ends with one or more zeroes (0), meaning that they are multiples of 10, 100, 1000, and so onâ€, 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
Definitions aside, we love round number so much that we always expect great things to happen in the years with round numbers. Hereâ€™s wishing that this expectation comes true for you!