the art of computing by decimal fractions. See Arithmetic.

Circulating Decimals, called also recurring or repeating decimals, are those in which a figure or several figures are continually repeated. They are distinguished into single and multiple, and these again into pure and mixed.

A pure single circulate is that in which one figure only is repeated; as .222, &c. and is marked thus .2.

A pure multiple circulate is that in which several figures are continually repeated; as .232323, &c. marked .23; and .524524, &c. marked .524.

A mixed single circulate is that which consists of a terminate part and a single repeating figure; as 4.222, &c. or 4.2. And

A mixed multiple circulate is that which contains a terminate part with several repeating figures; as 45.524.

That part of the circulate which repeats is called the repetend; and the whole repetend, supposed to be infinitely continued, is equal to a vulgar fraction whose numerator is the repeating number or figures, and its denominator the same number of nines; so .2 is = ; and .23 is = ; and .524 is = .

Dr Wallis of Oxford was the first who distinctly considered or treated of infinite circulating decimals, as he himself informs us in his Treatise of Infinities.

Decimal Coinage, a system of monetary calculation advancing to infinity from a fixed standard of value, and performing its multiplications by any increasing progression of tens, and its divisions by a decreasing progression which is also decimal.

This system, whose superiority to all others now in use is universally acknowledged, was first organized and established by the Constituent Assembly of France in 1790. It forms a part of that vast decimal metrical system of weights and measures, which, since the close of the last century, has obtained in France, and is slowly spreading thence into the other countries of Europe and America. The subject was so widely and keenly agitated throughout Great Britain in the opening months of 1853, that the House of Commons appointed a committee to investigate the whole matter. The report of this committee was laid before the house on the 1st of August of that year. This document was introduced with a strong recommendation of the decimal system of coinage, and proposed that the basis of that system when introduced should be the present pound sterling. By the retention of the pound, the decimal system might be introduced with the least possible change. Its tenth part already exists in the shape of the florin or two-shilling piece, while an alteration of four per cent, in the value of the present farthing will serve to convert that coin into the lowest step of the decimal scale, which it is necessary to represent by means of an actual coin, viz., the part of a pound. To this lowest denomination it was proposed by the committee to give the name of mil, in order to mark its relation to the unit of value. The addition of a coin to be called a cent, of the value of ten mils, and equal to the hundredth part of a pound, or the tenth part of the florin, would serve to complete the list of coins necessary to represent the monies of account, which would accordingly be pounds, florins, cents, and mils. As to the coins by means of which the decimal system will be developed, it is proposed that some of those now in use be retained, and that new coins be substituted for others of them. The coins thus retained would be the present sovereign (1000 mils), the half-sovereign (500 mils), florin (100 mils), and shilling (50 mils, or 5 cents). The present sixpence, under the denomination of 25 mils, might be retained; and the crown piece, or a piece of 250 mils, of which few are in circulation, need not be withdrawn. On the other hand, it would be desirable to withdraw the half-crown, and the threepenny and fourpenny pieces, which are inconsistent with the decimal scale.