decimal system


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decimal system

[Lat.,=of tenths], numeration system based on powers of 10. A number is written as a row of digits, with each position in the row corresponding to a certain power of 10. A decimal point in the row divides it into those powers of 10 equal to or greater than 0 and those less than 0, i.e., negative powers of 10. Positions farther to the left of the decimal point correspond to increasing positive powers of 10 and those farther to the right to increasing negative powers, i.e., to division by higher positive powers of 10. For example, 4,309=(4×103)+(3x102)+(0×101)+(9×100)=4,000+300+0+9, and 4.309=(4×100)+(3×10−1)+(0×10−2)+(9×10−3)=4+ 3-10+ 0-100+ 9-1000. It is believed that the decimal system is based on 10 because humans have 10 fingers and so became used to counting by 10s early in the course of civilization. The decimal system was introduced into Europe c.1300. It greatly simplified arithmetic and was a much-needed improvement over the Roman numerals, which did not use a positional system. A number written in the decimal system is called a decimal, although sometimes this term is used to refer only to a proper fractionfraction
[Lat.,=breaking], in arithmetic, an expression representing a part, or several equal parts, of a unit. Notation for Fractions

In writing a fraction, e.g.
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 written in this system and not to a mixed number. Decimals are added and subtracted in the same way as are integers (whole numbers) except that when these operations are written in columnar form the decimal points in the column entries and in the answer must all be placed one under another. In multiplying two decimals the operation is the same as for integers except that the number of decimal places in the product, i.e., digits to the right of the decimal point, is equal to the sum of the decimal places in the factors; e.g., the factor 7.24 to two decimal places and the factor 6.3 to one decimal place have the product 45.612 to three decimal places. In division, e.g., 12.8 ÷ 4.32, where there is a decimal point in the divisor (4.32), the point is shifted to the extreme right (i.e., to 432.) and the decimal point in the dividend (12.8) is shifted the same number of places to the right (to 1280), with one or more zeros added before the decimal to make this possible. The decimal point in the quotient is then placed above that in the dividend, zeros are added to the right of the decimal point in the dividend as needed, and the division proceeds the same as for integers. The decimal system is widely used in various systems employing numbers. The metric system of weights and measures, used in most of the world, is based on the decimal system, as are most systems of national currency.

Decimal System

 

the most widespread system of numeration. The base of the decimal system is the number 10, which forms a unit of the second order. The unit of the third order is 100 = 102. In general, the unit of each subsequent order is 10 times greater than the unit of the preceding order (it has been suggested that the selection of the number 10 as the base of the decimal system is connected with counting on one’s fingers).

The decimal system is based on the positional principle, that is, the same symbol (digit) has different values, depending on the position in which it is placed. Thus, in order to write all numbers, only the first ten numbers require special symbols. These symbols, which are designated by 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, are called digits. To write a number, one determines how many units of the highest order are contained in it: then in the remainder, one determines the number of units of the order, which is one unit smaller, and so forth. The resulting digits are written in a sequence: for example, 4 × 102 + 7 × 101 + 3 × 10° = 473. Operations on numbers are carried out according to the order, that is, independently for the numbers of each order. If in so doing one obtains a number greater than 10 (in addition and multiplication), one adds one or several units to the following, higher order. In division and subtraction, it is necessary to break the orders down into smaller orders.

decimal system

[′des·məl ‚sis·təm]
(mathematics)
A number system based on the number 10; in theory, each unit is 10 times the next smaller one.

decimal system

1. the number system in general use, having a base of ten, in which numbers are expressed by combinations of the ten digits 0 to 9
2. a system of measurement, such as the metric system, in which the multiple and submultiple units are related to a basic unit by powers of ten
References in periodicals archive ?
It's based on a decimal system to make calculations simple and is used by nearly all the world.
Intended primarily for the University of South Africa (Unisa) undergraduate student, this work proceeds from an explanation of the Dewey Decimal System (DDC) to an examination of the formats for providing references using the Harvard method.
Included in the inaccuracies are: the connection between Fibonnaci and the decimal system; the relationship between current yield and market interest rates; the identification of joint stocks with limited liability; the omission of James Dodson, Richard Price, and the Equitable from early history of insurance; the treatment of hedging; and confusion about the composition of subprime mortgage borrowers.
The decimal system of numbers is our constant companion as we strive to make sense of the world.
A fundamental flaw in the vast majority of articles on folksonomies and taxonomies is the almost universal use of the Dewey Decimal System (or Library of Congress Subject Headings) as the example taxonomy.
The result is Compiled by Mike Harris 1 The first group referred to the UK coins of the realm prior to the introduction of the decimal system. They were the farthing (1/4d), halfpenny (1/2d /ha'penny), penny (1d), threepenny piece (3d/joey), sixpence (6d/tanner), shilling (1s/bob), two shillings (2s0d/florin) and half-a-crown (2s/6d).
The Arabic numeral - an improvement on the original Hindu concept - and the Arab decimal system facilitated the course of science.
In their introduction to Between the Covers, Hammond and Heltzel state their organizing principle, with a nod to library classification: "Just as the Dewey Decimal System was invented to impose order on books, we've created a system of our own to guide and stimulate your reading ...
of 812.5 in the Dewey decimal system, where we would do it in the
He was named after the Dewey decimal system used to catalogue books and lived at the library until his death last November.
It is an interesting fact that the development of modern finance in the early 13th century should have required Europeans to adopt a combination of Indian and Arabic models, replacing the Roman numeric system of counting (i, ii, iii, iv, etc) with a decimal system. A young mathematician from Pisa called Fibonacci made this modification, working in Bejaia in Algeria on the idea of a decimal system.
1 : based on the number 10 : numbered or counting by tens <We use a decimal system of writing numbers.>