# decimal system

The decimal system is a number system that works with the base 10. Multi- digit numbers are listed in order of precedence from left to right, with the number furthest to the left having the highest precedence. The one on the far right has the least valence.

Each digit of the decimal system has a nominal or numerical value and a place value. The numerical value corresponds to the real value, the place value determines the position of the digit within the number word. In the decimal system, the numerical value can only consist of the character set 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The place value, on the other hand, is determined by exponentiating the digit with the base number 10. Example: the decimal number 462 consists of the three numerical values 4, 6 and 2, and the place values `4*10^2`,`6*10^1`and `2*10^0`.

To avoid extensive decimal representations, one uses the exponential representation or the notation with prefixes. So 4.650.000 in exponential notation becomes `4,65*10^6` or in prefix notation 4,65 M.

Digits which are smaller than 1, or have corresponding proportions, are provided with decimal point. Thus the valence of the 10s system finds its continuation with the exponents `10^-1`(0,.), `10^-2` (0,0..), `10^-3`, (0,00..) and so on. Another notation for smaller or proportional numbers is the decimal fraction. There is a direct connection between it and the decimal point notation. For example, the decimal fraction 1/4 becomes 0.25 in decimal point notation.