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decimal system

The decimal system is a number system that uses a base of 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, and the one furthest to the right having the lowest precedence.

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 raising the digit to the power of the base number 10. Example: the decimal number 462 consists of the three numerical values 4, 6 and 2, and the place values 4 x 10exp2, 6 x 10exp1 and 2 x 10exp0.

Example of the digit and place value in a decimal system

Example of the digit and place value in a decimal system

To avoid extensive decimal representations, one uses the exponential representation or the notation with prefixes. Thus 4,650,000 in exponential notation becomes 4.65 x 10exp6 or in prefix notation 4.65 M.

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

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Englisch: decimal system
Updated at: 24.01.2017
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Translations: DE