ADDITION OF CIRCULATING DECIMALS. 99 



2. Let -j^ be the fraction proposetf. 



3. Let ~ be the fraction proposed. 



4. Let ~^^ be the fractioa proposed. 



5. Let -g-y'^^: be the fraction proposed. 



Addition of Circulating Decimals. 



RULE.* 



1. Make the repetends similar and conterminous, and 

 find their sum as in common addition. 



2. Divide this sum by as many nines as there are places 

 in the repetend, and the remainder is the repetend of the 

 sum \ which must be set under the ligures added, with 

 cyphers on the left hand, when it has not so many 

 places as the repetends. 



3. Carry the quotient of this division to the next col- 

 umn, and proceed with the rest as in finite decimals. 



EXAMPLES. 



I. Let 3-6+78-3476-f 735-3+375+-27+i87-4be add- 

 ed together. 



Dissimilar. Similar and conterminous. 



3'6 = y6666666 



78-3476 = 78-3476476 



735*3 ^ 735*3333333 

 375* = 375-0000000 



•27 = 0-2727272 



187-4 = 187-4444444 



1 3 80-0648 1 93 the sum. 

 In this question, the sum of the repetends is 2648 191, 

 which, divided by 999999, gives 2 to carry, and the re- 

 mainder is 648193. 2. Let 



* These rules are both evident from v/hat has been said in re- 

 duction. 



