REDUCTION O.F CIRCULATING DECIMALS. 97 



the several numbers of places, found in all the repetends, 

 •>ntains units. 



EXAMPLES. 



i. Dissimilar. Made similar and contei^ninous* 



9-814 •= 9-81481481 



i*_5; =r 1-50000000 



87-26 = ■ 87-26(566666 



•083 = -08333333 



124-09 = 124-09090909 



2. Make -3, '27 and '045 similar and conterminous. 



3. Make '321, '8262, '05 and '0902 similar and con- 

 terminous. 



4. iviake *52i7, 3*643 and 17*123 similar and conter«» 

 niinous. 



CASE IV. 

 To Jim! whether the decimal fraction^ equal to a given vulgar 

 one, be finite or infinite^ and cf hoiv many places the repe" 

 tend will consist, 



RULE.* 



I. Reduce the given fraction to its least terms, and di- 

 vide tlie denominator by 2j 5 or i o, as often as possible. 



' 2. If 



consist of an equal or greater number of figures at pleasure : thus 



4 maybe transformed to -44, or '444, or -44, &c. Also •57 = 



*5757='5757=!l"575 J ^nd so on; which is too evident to need 

 uny further demonstration. 



* In dividing I 'ooqo, &c. by any prime number whatever, ex- 

 cept 2 or 5, tlie figures in the quotient will begin to repeat over 

 »2ain as soon as the remainder is t. And since 9999, &c. is less 



than 

 N 



