decimal system
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=(4×10^{3})+(3x10^{2})+(0×10^{1})+(9×10^{0})=4,000+300+0+9, and 4.309=(4×10^{0})+(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 muchneeded 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 fraction 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.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"decimal system." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
"decimal system." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (April 16, 2019). https://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/decimalsystem
"decimal system." The Columbia Encyclopedia, 6th ed.. . Retrieved April 16, 2019 from Encyclopedia.com: https://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/decimalsystem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
decimal system
decimal system Commonly used system of writing numbers using a base ten and the Arabic numerals 0 to 9. It is a positional number system, each position to the left representing an extra power of ten. Thus 6741 is (6 × 10^{3}) + (7 × 10^{2}) + (4 × 10^{1}) + (1 × 10^{0}): note that 10^{0} = 1. Decimal fractions are represented by negative powers of ten placed to the right of a decimal point.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"decimal system." World Encyclopedia. . Encyclopedia.com. 16 Apr. 2019 <https://www.encyclopedia.com>.
"decimal system." World Encyclopedia. . Encyclopedia.com. (April 16, 2019). https://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/decimalsystem
"decimal system." World Encyclopedia. . Retrieved April 16, 2019 from Encyclopedia.com: https://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/decimalsystem
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.