DEC 



DEC 



the common cherry ; and the ilex, or 

 ever-green oak, on the oak. 



DECIMAL arithmetic, the art of com- 

 puting by deci;nal fractions. 



DtciMAL/rocrt'on, that whose denomi- 

 nator is always 1, with one or more cy- 

 phers: thus an unit may be imagined to 

 be equally divided into 10 parts, and each 

 of these into lOmore; so that by a continual 

 decimal subdivision the unit may be sup- 

 posed to be divided into 10, 100, 1000, 

 &c. equal parts, called tenth, hundredth, 

 thousandth part of an unit. In decimal 

 fractions, the figures of the numerator 

 are only expressed, the denominator be- 

 ing omitted, because it is known to be al- 

 ways an unit with so many cyphers as there 

 are places in the numerator. A decimal 

 fraction is distinguished from an integer 

 with a point prefixed, as .2 for 2 , .34 

 for^, .567 for.j.56^, &c. The same 

 is observed in mixed numbers, as 678.9 

 for 678 s 67.89 for 67 ^, 6.789 for 



Cyphers at the right hand of a decimal 

 fraction alter not its value ; for .5 or .50 

 or .5000 is each of them of the same value, 

 equal to , or J : but cyphers at the left 

 hand, in a decimal fraction, decrease the 

 value in a tenfold proportion ; for .05 is 



As the denominator of a decimal is al- 

 ways one of the mumbers 10, 100, 1000, 

 &c. the inconvenience of writing these de- 

 nominators down may be saved, by plac- 

 ing a proper distinction before the figures 

 of the numerator only to distinguish them 

 from integers, for the value of each place 

 of figures will be known in decimals, as 

 well as in integers, by their distance from 

 the 1st, or unit's place of integers, hav- 

 ing similar names at equal distances, as 

 appears by the following scale of places, 

 both in decimals and integers: 



Sec. 6666666 



Decimal fractions are easily reduced 

 into a common denominator, by making, 

 or even supposing, all of them to consist 

 of the same number of places ; so .3, .45, 



.067, .0089, may be written thus, .3000, 

 .4500, .0670, .0089 ; all which consisting 

 of four places, their common denomina- 

 tor is an unit with four cyphers, namely, 

 10000. 



Addition and subtraction of decimals 

 are the same as in whole numbers, when 

 the places of the same denomination are 

 set under one another, as in the following 

 examples : 



To 34.25 

 Add 3.026 



Sum 37.276 



From 16.5 

 Subtract .125 



Hem. 16375 



In multiplication the work is the same 

 as in whole numbers, only in the product ; 

 separate, with a point, so many figures 

 to the right hand as there are fractional 

 places both in the multiplicand and mul- 

 tiplier ; then all the figures on the left 

 hand of the point make the whole num- 

 ber, and those on the ri^ht a decimal frac- 

 tion. 



It is to be noted, that if there be not so 

 many figures in the product, as ought 

 to be separated by the preceding rule, 

 then place cyphers at the left, to com- 

 plete the number, as may be seen in 

 Ex. 5. 



Ex. 1. Mult. 456 

 by 21.3 



Ex. 2. Mult. 45.6 

 by 21.3 



Product 971 28 



Product 9712.8 



Ex. 3. Multiply 456 



by 0.213 



Product 97.128 



Ex. 4. Multiply 45.6 

 by 0.213 



Product 9.7128 



Ex. 5. Multiply 0.0456 

 by 213 



Product 00097128 



