[ 6a I 



into 3, the produdt will be the cubic root of 28, which is 

 therefore 3,0365889718758. 



But fince each of thefe eight terms calculated above is 

 imperfetSt, being lefs than the truth, the fum of them may 

 be different from the truth. Two or three of the laft 

 figures muft be omitted, and then we can be fure that the 

 reft are true *. 



If 



* What figures are to be omitted, in order that the remaining decimal may be 

 true, is to be determined by finding out the greater and lefs limits of the decimal, 

 and as far as thefe agree, fo far we may be certain that the decimal is accu- 

 rate. Now as a decimal firft arifes, it is lefs than the truth, becaufe certain 

 figures are omitted ; this therefore we may confider as the lefs limit ; and if 

 to the lafl figure we add an unit, we ftiall have the greater limit. But in th^ 

 addition, multiplication, fubtra£tion and divlfion of decimals, the limits of the 

 fum, produft, difference, and quotient may be determined by the following 

 rules : 



1. Ill addition, the limits of the fum are had by adding together the greater 

 limits of the quantities to be added, for the greater limit of the fum ; and the 

 lefs limits together for the lefs limit of the fum. 



Thus, if the greater and lefs limits of one of the quantities be 123,5 ^""^ 

 123,2; and the greater and lefs limits of the other be 43,2 and 43,1; then 

 will 166,7 and 166,3 ^^ '^^ greater and lefs limits of the fum. 



2. In multiplication, the limits of the product are had by multiplying toge- 

 ther the greater limits of the fa£tor», for the greater limit of the pvoduft ; and 

 the lefs limits together, for the lefs limit of the produdt. 



Thusj if the limits of one quantity be 10,502 and 10,5, and the limits of 

 the otlier be '?,2i6 and 3,215; then the limits of the produd will be 33,774432 



aii^ 33>7S75- 



3. In fubtra^tion, the greater limit of the lefs quantity is to be fubtrafted 



from the lefs limit of the greater, itrr the lefs limit of the difference; and the 



lefs limit of the lefs from the greater limit of the greater, for the greater limit 



of the diSerencc. 



Thus, 



