DEC 



DEC 



green, on the common cherry; and the 

 ilex, or ever-green oak, on the oak. 



DECIMAL arithmetic, the art of com- 

 puting by decimal fractions. 



DECIMAL fraction, that whose denomi- 

 nator is always 1, with one or more cy- 

 phers : thus an unit may be imagined to 

 be equally divided into JO parts, and each 

 of these into 10 more ; so that by a conti- 

 nual decimal subdivision the unit may be 

 supposed to be divided into 10, 100, 1000, 

 &c. equal parts, called tenth, hundredth, 

 thousandth part of an unit. In decimal 

 tractions, 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 .*_, .34 

 for ^ y .567 for ^fc &c. The same 

 is observed in mixed numbers, as 678.9 

 for 678^, 67.89 for 67 T j!L, 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 *p or : but cyphers at the left 

 hand, in a decimal fraction, decrease the 

 value in a tenfold proportion ; for .05 is 



.067, .0089, maybe 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 : 



As the denominator of a decimal is al- 

 ways one of the numbers 10, 100, 1000, 

 &c. the inconvenience of writing these 

 denominators down may be saved, by 

 placing a proper distinction before the 

 figures of the numerator only to distin- 

 guish them from integers, for the value of 

 each place of figures will be known in de- 

 cimals, as well as in integers, by their dis- 

 tance from the 1st, or unit's place of inte- 

 gers, having similar names at equal dis- 

 tances, as appears by the following scale 

 of places, both in decimals and integers : 



&c. 6 6 6 6 6 6 6 6 6 6 6 6 6, 8cc. 



To 34.25 

 Add 3.026 



Sum 37.276 



From 16.5 

 Subtract .125 



Rem. 16.375 



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 right 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 213 



1368 

 456 

 912 



Product 971 2.8 



Ex. 2. Mult. 45.6 

 by 21.3 



Product 971.28 





456 

 0.213 



Ex. 3. Multiply 



Product 97.128 



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*T3 GO t/5 CO , i 



Decimal fractions are easily reduced 

 into a common denominator, by making, 

 or even supposing, all of them to consist 

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



Ex. 4. Multiply 

 by 



45.6 

 0.213 



Product 97.128 



Ex. 5. Multiply 0.0456 

 by 0.213 



Product 0.0097128 



