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The place value system uses only a finite number of symbols to write any number.

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In some number systems, there are different symbols for each power of 10. In a place value system, only a small number of symbols are used.

In the Ancient Egyptian number system, dating from about 3000 BC, there were symbols for units, symbols for 10s, and so on. The number 365 was written:

where | represents a unit, represents 10 and represents 100.

The Chinese system writes numbers much as we say them. We say “three hundred and sixty-five:” in other words, so many hundreds, so many tens, and so many units. The number 365 is written as shown below.

It represents 3 x 100 + 6 x 10 + 5.

In both these systems there is no limit to the number of symbols required. We need a different symbol for millions, another symbol for 10 millions, and so on. The modern system uses precisely 10 symbols: the digits 0 to 9.

The value of each digit is shown by its place in the number. In 365, for example, the digit 5 on the right represents 5, the digit 6 represents 60, as it is one place to the left, and the 3 represents 300. This system came to the West from India via the Arab countries and is known as the Indo–Arabic system.

The ancient Babylonian place value system was even more economical. It used only two symbols: for 1 and for 10. The place value system consisted of grouping numbers in powers of 60 rather than of 10. The following number

represents 3 x 60² + 21 x 60 + 43 = 12 103.