Our decimal system of notation was developed by the Arabs a long time ago, and it is impossible for us to conceive of a better system. It has stood the test of centuries, and it works. There are no unexplored areas, and the discovery of new relationships is not expected.
As a budding accountant, chasing errors in a trial balance was not a fascinating sport like chasing girls. It was tedious and boring. The only way for a bookkeeper to avoid it was to make no mistakes - and that standard was too high for most of us to maintain continuously. The penalty for one little slip was a night or two at the office, checking an interminable mass of postings. For this reason, any hint that may aid in tracking an error to its well concealed lair was received with gratitude.
One kind of error that taxed every bookkeeper's patience was the transposition of figures - easy to make and hard to find. And yet if the answer to the old familiar question "How much are you out?" was divisible by 9, it invariably meant that a couple of figures had been twisted and each put where the other ought to be. This was usually accepted as a fact without asking why. Of course, the reason is that one digit was moved into the next higher column, thus multiplying it by 10, and the other in the next lower column, thus dividing it by 10. As the error is the difference between these two amounts, it is 9 times one digit minus 9 times the other, which resulted in the bookkeeper's first theorem: All transposition errors are divisible by 9.
I've been in retirement for a couple of decades now, and the last transposition I encountered was on my 69th birthday when Padma positioned the numeric birthday candles on the cake back to front.
Ever since, Padma has dispensed with numeric birthday candles although she could have used them on this year's birthday cake without risk of transposition: 77 expressed as 77 is still 77, i.e. BLOODY OLD!
