Jan Reidt, age 13, of Pacific, Missouri, for her question:

What is the history of our number system?

History, we are told, began when our ancestors learned to write down human events as they occurred. Historians, however, agree that numbers were invented before letters, during the dim era of pre history. This seems logical because people needed to count items more urgently than they needed to write down their names. Various numerical systems were improved through the ages and our system took some of the best features from all of them.

We cannot be certain how numbers began because nobody knew how to report it. Perhaps a shepherd invented a way to tally his sheep as they returned to the fold. Perhaps he set aside a pile of stones, one by one as they passed by. Thousands of years ago, shepherds cut a notch for each sheep on a tally stick. Several other methods were used in ancient times to keep records of items, one by one.

Later, the early number experts figured items in groups of three, nine or some other number. Eventually, the basic unit of ten became somewhat more popular, perhaps because it matched human fingers and toes. In time, early scholars developed whole numerical systems based on their favorite units. The Babylonians favored a base of 60 and multiples of six. We inherited their system to measure angles and circles. The Egyptians, Greeks and Hindus based their systems on ten.

Various symbols were invented to write the numbers. The Egyptians used letters of their alphabet. We inherited this custom to name the stars of a constellation in order of their brilliance. However, all these early scholars failed to find a simple way to jump from one number group to the next. The Hindus used words for each power of ten, for example one "seta" was 100. The Romans used clumsy notations with "X's", "L's" and "C's".

Around 600 A.D., the Hindus invented the masterpiece of numbers    the vacant slot we call the zero. The Greeks adopted the brilliant idea and the Arabs learned about it a century or so later. With the help of the zero, it was a cinch to write 10,20, 100, 1,000 and so on. Some people still clung to the clumsy old Roman system. But gradually the civilized world adopted the Hindu Arabic system, with the handy little zero that made arithmetic so simple. The Spaniards brought it to the New World and it crossed the Atlantic with the first American settlers.

Our decimal system of ten has its roots in the dim past and it prevailed because it was the most workable. However, we also inherited an odd assortment of old systems for measuring weights and distances. These we expect to discard when the New World adopts the still more streamlined metric system. This neat idea was instigated by Napoleon, who instructed his mathematicians to invent an entire number system based on tens.