DEC 



DEC 



Tn division the work is the same as in 

 whole numbers, only in the quotient, se- 

 parate, with a point, so many figures to 

 the right hand for a decimal fraction, as 

 there are fractional places in the dividend, 

 more than in the divisor, because there 

 must be so many fractional places in the 

 divisor and quotient together, as there 

 are in the dividend. 



As division of decimal fractions is ex- 

 tremely difficult, especially with regard 

 to the value of the figures of the quotient, 

 we shall here give a general rule for as- 

 certaining their values, viz. 



Rule, place the first multiple of the 

 divisor under the dividend, as in opera- 

 tions of common division ; then will the 

 unit's place of this multiple stand under 

 such a place of the dividend, as the first 

 significant figure of the quotient is to be ; 

 that is, the first significant figure of the 

 quotient will be of the same name or 

 value with the figure of the dividend 

 which stands above the unit's place of 

 the multiple. 



This rule will hold in all cases. 1. 

 When the number of decimals are equal 

 in the divisor and dividend, the quotient 

 will be integers, or whole numbers : for 

 placing the first multiple of the divisor 

 under the dividend, according to the 

 rule. Ex. I. 



8.45)295.75(35 

 25.35 



4225 

 4225 



The unit's place 5, is found to stand 

 under 9, the place of tens in the divi- 

 dend ; so that 3, the first figure of the 

 quotient, must be tens also, and 5, the 

 next figure, units. 2. When the number 

 of decimals in the dividend exceed those 

 in the divisor, as, Ex. 2. 



24.3)780.516(32.12 

 72.9 



Where 2, the unit's place of the mul- 

 tiple of the divisor, stands under 8, the 

 place of tens of the dividend ; whence 3, 

 the first figure of the quotient, must be 

 tens also ; and 2, the next figure, units ; 

 so that the remaining figures, 12, must 

 be decimals. This is done, more shortly, 

 by making as many figures of the quo- 

 tient decimals, as there are more deci- 

 mal places in the dividend than in the di- 



visor. 3. When there are not so many 

 decimal places in the dividend, as there 

 are in the divisor, cyphers must be added 

 to the right hand of the dividend, to make 

 them equal : thus, to divide 192.1 by 

 7.684, as in Ex. 3. 



7.684)192.100(25 

 15.368 



38420 

 38420 



Add two cyphers to make the deci- 

 mals equal ; and, by the above rule, the 

 quotient 25 will be found to be integers, 

 as 5, the place of units, stands under 9, 

 the place of tens. 4. If after division 

 there are not so many figures in the quo- 

 tient as there ought to be decimal parts, 

 supply this defect by prefixing cyphers 

 to the quotient found : thus, in Ex. 4. 



957)7.2540(. 00758 nearly. 

 6.699 



.5550 

 4785 



.7650 

 7650 



The quotient by division is found to be 

 758; and, by the above rule, the first 

 figure, 7, ought to stand in the decimal 

 place of thousandths, which it is rtiade to 

 do by prefixing two cyphers, 



Vulgar fractions are reduced to deci- 

 mals of the same value, by dividing the 

 numerator by the denominator. 



_,. 1 10 .. , 3 3.00 ,_ r 

 Thu Sj -= y =.5,and _= =.75, 



_ 2 2.000000, 8cc. _. . 

 and Y~ j =.285714, nearly. 



DECIMAL scales are those which are de- 

 cimally divided. 



DECIMATE, in military affairs, is to 

 choose, by lot, one out of ten, either by 

 way of punishment, or for the purpose 

 of being employed upon some public 

 work. 



DECIPHERING, the art of finding the 

 alphabet of a cypher. See CIPHEH, and 

 DIPLOMATIC CHARACTERS. 



DECK of a ship, is a planked floor from 

 stem to stern, upon which the guns lie, 

 and where the men walk to and fro. 

 Great ships have three decks, first, se- 



