5v6 ARITHMETIC. 



2. Multipl jT the nines in the said denominator by the 

 finite part, and add the repeating decimal to the product, 

 for the numerator. 



3. If the repetend begin in some integral place, the 

 finite value of the circulati?ig part must be added to the 

 finite part. 



r X A M P L E s. 



1. What is the viilgar fraction equivalent to '138 ? 



9X i3 + 8iri25:r: numerator, and pccii: the de- 

 nominator; .*. •I38n~-|r=:j^^ the answer. 



2. What is the least vulgar fraction equivalent to '53 ? 



Ans.VV 



3. What is the least vulgar fraction equal to '5925 ? 



Ans. ii. 



4. What is the least vulgar fraction equal to 'ooS'^py 133.'* 



5. What is the finite number equivalent to 31*62 ? 



Ans. 3 if k 



CASE III. 



To mak€ any number of dissimilar repetcnds shnlJar and con-^ 

 termifiouso 



RULE.* 



Change them into other repetends, which shall each? 

 consist of as many figures as the least common multiple of 



the 



tens, It is § of -s^r:^, and so the vulgar fraction c:'i6 is to4* 

 •^=:/^-|-^=rf|-, and is ,the same as by the rule. 



* Any given repetend whatever, whether single- compound, pure 

 or mixed, may be transformed into another repetend, that shall 



contist 



