Addition and SUBTRACTION OF DECIMALS are performed in the same manner as with common numbers, care being taken to place the numbers under each other according to their several values; as, tens under tens, hundreds under hundreds, &c.
Multiplication of decimals is performed in precisely the same manner as with whole numbers, merely pointing off as many figures in the product as there are decimals in the multiplier and multiplicand put together.
Division of decimals. As the last, but pointing off as many figures in the quotient as the decimal places in the dividend exceed those of the divisor. If there are not figures enough in the quotient, the deficiency must be supplied by prefixing left-hand ciphers. Ciphers are also added to the right hand of the dividend, or to a remainder, where there are more figures in the divisor than in the dividend, by which the quotient may be carried on to any extent.
A vulgar fraction is reduced to a decimal by dividing the numerator (increased sufficiently with ciphers) by the denominator. Thus, 1⁄2 = ·5, 1⁄8 = ·125, &c.
The value of a decimal, of any denomination, is found by multiplying it by the number of parts in the next less denomination, and cutting off as many places to the right hand as there are decimals, and so on until the terms are exhausted. Thus, ·634 oz. is =
·634
8
——
5·072 drachms.
60
——
4·320
or, 5 dr. 41⁄3 gr. (nearly).
The constant use of decimals in the laboratory, in the surveys of the Excise, and in numerous chemical calculations, induces us to press the subject on the attention of operatives and others of neglected education. An attentive perusal of the above, and a few hours’ application, will make the matter familiar to them.
DECOC′TION. Syn. Decoct′um, L. An aqueous solution of the active principles of any substance obtained by boiling; also the process of preparing such solutions.
The effect of decoction in water differs greatly from that of infusion. At the temperature of 212° Fahr., the essential oils and aromatic principles of vegetables are dissipated or decomposed; while by infusion in hot water, in covered vessels, they remain for the most part uninjured. The solvent powers of boiling water are, however, much greater than those of hot water; and many vegetable principles scarcely acted on by the one are freely soluble in the other. This is the case with many of the alkaloids, on which the medicinal virtues of several vegetables depend. On the other hand, the solutions of many substances, though more readily made by boiling, are speedily weakened or rendered inert by ebullition, in consequence of the active principles being either volatilised along with the steam, or oxidised or decomposed by exposure to the atmosphere. This is particularly the case with substances abounding in extractive or astringent matter. When the medicinal properties of vegetables are volatile, or are injured by a strong heat, infusion should be had recourse to, in preference to boiling; but when a solution of the fixed constituents is alone sought, decoction is preferable.