Decimal System. This name is applied to any system of weights, measures, money, &c., in which the standard unit is divided into tenths, hundredths, &c., for the denominations below it, and multiplied by 10, 100, &c., for those above it. The nature of this method of division will be best explained by an example from the French system, where it has been most rigidly carried out. The mètre (= 39.37 English inches nearly) is the unit of length, and the foundation of the whole system. For the higher denominations of length, the Greek words déca, hecto, kilo, and myria, are prefixed to signify multiplying by 10, 100, 1000, 10,000; so that décamètre = 10 mètres, kilomètre = 1000 mètres, &c. The Latin words déci, centi, milli, on the other hand, are used to express division by 10, 100, &c., and thus furnish names for the lower denominations; décimètre = of a mètre, centimètre = of a mètre, &c. Similarly with money; the franc being the unit, a décime is the tenth part of a franc; and a centime, the hundredth part.
In 1865 Belgium and Switzerland adopted the French decimal system of money, weights, and measures. Afterwards the Italian lira, the Greek drachmê, the Spanish peseta, and more recently the Roumanian lei, and the Servian dinar, were assimilated to the franc. Other countries, though retaining each its own special unit coin, divide it into 100 parts—viz. Germany, Austria, Russia, and the United States of America. The following have adopted the metrical system of weights and measures, though rejecting the franc: Germany, the Netherlands, Spain, Portugal, Norway, and Sweden. Engineers, too, have their own decimal systems of measurement.
The method of decimal gradation in weights and measures naturally suggests itself to the arithmetician, on account of the language of numbers, and the Arabic notation. Practical legislators, however, have pronounced the number ten to be most unsuitable as a basis, especially for the purposes of 'retail trade.' In France the prices 1.25, 4.25, 6.75, &c. are extremely common; yet if half a yard of cloth, for example, is bought at 1.25 the yard, the exact price cannot be paid, and the buyer therefore suffers. He is compelled to pay more than the proper value by reason of the limitations inseparable from the decimal system. The analogous price in English money is 1s. 3d., which allows not only half a yard to be sold at the exact price, but even a quarter of a yard. To estimate the loss undergone by the poorer classes in France on account of the imperfections inherent to their monetary system, the most ordinary case will suffice—e.g. if sugar is sold at 25 centimes a pound, then any one who buys half a pound must pay exactly 4 per cent. more than the proper price. The same serious drawback is inseparable from the monetary system of the United States, as compared with that of Great Britain. In such a case as that just quoted, the poor buyer in New York is defrauded still more than in Paris; whereas, in Edinburgh, London, or Dublin, the buyer will not only lose nothing by such a transaction, but can buy even a quarter of a pound at the proper price.
In 1821, after an able report drawn up by John Quincy Adams, the United States government rejected the metrical system as unsuited to practical life. The question of adopting the French scheme has also been repeatedly discussed in the House of Commons, but though many, in the interests of certain scientific pursuits and international transactions, advocated a change, there seems little probability of uprooting our existing method, with its excellent supply of binary factors, and the much greater ease with which it lends itself to mental arithmetic. Although proposed in 1795, the decimal system in France required repeated legislation before it could gain footing, and though it was made obligatory from January 1, 1840, the people still retain traces of the older and less arbitrary mode of computation, just as the shilling and sixpence still exist in the United States as terms of reference. The centesimal division of the right angle was also proposed at the French Revolution, but has long been abandoned, even in France. It was also used as a basis in dividing the thermometric scale (misnamed centigrade for hectograde), but Fahrenheit's is often preferred because there are more subdivisions, and because it avoids the use of negative numbers. The application of the system to the division of time was so unworkable as scarcely to tolerate even a trial. There, as elsewhere, the duodecimal mode, as compared with the decimal, is vastly and incontestably superior. For the decimal system in numerical notation, see NOTATION, NUMERALS; and for the system of measurements based on the mètre, see MÈTRE.