Jodie Reese, age 7, of Huntington, West Va., for her question:

HOW DOES OUR NUMERATION SYSTEM WORK?

Man developed a numeration system very early in history since he found it was very important to keep count. Egyptians, Greeks and Romans used a system of repeating basic symbols and adding their values. The Hindus followed the principle of place value which became the decimal numeral system, currently being used in most parts of the world.

Today our numeration system has only 10 basic numerals, which we call digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. With these 10 symbols, we can represent any number regardless of its size.

We call our numeration system the decimal system because it is based on 10. The word decimal comes from the Latin word decem, which means ten. Ten is the base or the scale of the decimal system.

You can use any number as a base in building a numeration system. The number of digits used is always equal to the base. In the decimal system, for example, or base 10, 10 digits are used. In the quinary system, or base 5, 5 digits are used. In the binary system, or base 2, we use 2 digits while 12 are used in the duodecimal system or base 12.

Here's something to make that description easier to understand:

In decimal counting, you use one digit numerals to count from 1 to 9. Then you use two digit numerals to count from 10 to 99. In two digit numerals, the digit on the left stands for the number of groups of ten. The digit on the right shows the number of ones.

Here's an example: with the number 17, there is one group of ten plus seven ones.

After 99 you use the three digit numerals. The first digit on the left stands for the number of hundreds (or groups of ten tens). Thus, the numeral 357 stands for 3 hundreds plus 5 tens plus 7 ones.

The value of each digit in a decimal numeral depends on its place, or position, in the numeral. The numeral 573 contains the same digits

as the numeral 735 but each represents a different number because, the digits are in different positions.

Hindu mathematicians of the 300s and 200s B.C. used a system based on 10 which the Arabs improved A.D. 700s. A translation of the systems by a Persian mathematician in the 800s brought about the Hindu Arabic numerals into Europe, which many mathematicians regard as one of the world's greatest inventions.

The greatness of the Hindu Arabic numeral system lies in the principle of place value and in its use of zero. These two ideas make it easy to represent numbers and to perform mathematical operations that would be difficult with any other kind of system.

The binary numeration system was developed in the 1600s by a German mathematician named Gottfried Leibnitz. A use for it was found in the 1940s when computers were developed.