DEC′IMALS

Syn. Decimal fractions. Fractions which have for their denominator 10, or some power of ten; as 100, 1000, .; the number of ciphers in the denominator being always equal to the number of figures in the numerator. Thus, ·2, ·25, ·125, respectively represent 2 ⁄ 10 , 25 ⁄ 100 , 125 ⁄ 1000 . The denominator of decimals is never written, the dot placed before the first figure of the numerator expre ing its value. Ciphers placed on the right hand of a decimal fraction do not alter its value; for ·5, ·50, ·500, are each equal to 1 ⁄ 2 ; but ciphers placed on the left hand of a decimal diminish its value in a tenfold proportion; thus, ·3, ·03, ·003, respectively answer to the common fractions 3 ⁄ 10 , 3 ⁄ 100 , and 3 ⁄ 1000 . Every figure on the left-hand side of the dot or decimal sign is a whole number. 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, . 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, . The value of a decimal, of any denomination, is found by multiplying it by the number of parts in the next le 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. 4 1 ⁄ 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 pre 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.