M ARITHMETIC. 



EXAMPLES, 



Red nee ^^ to a decimal. 



4)5*000000 



6)1-250000 



i 



_ '208333, &c. 



2. Required the equivalent decimal expressions for 4-^ 

 and f. ^ Ans. '25, -5 and -75. 



3. What is the decimal of -^ ? Ans. '375. 



4. What is the decimal of ^V ' Ans. '04. 



5. What is the decimal of _A_ ? Ans. •015625, 



6. Express —-'-^^ decimally. Ans. '071577, &c. 



CASE IT. 



'Tc reduce nin. 



nhers of different defwminatiom to their equivalent 

 decimal values. 

 R U L E.f 



1. Write the given numbers perpendicularly under eacK 

 other for dividends, proceeding orderly from the least to 

 the greatest. 



2. Opposite to each dividend, on the left hand, place 

 such a number for a divisor, as will bring it tp the next 

 superior name, and draw a line between them. 



3. Begin 



it will be, as the denominator of one is to its numerator, so is the 

 denominator of the other to its numerator ; therefore 13 : 7 : : 1000, 



- 7X1000, &C. 70000, &C. o /: .u r 



&c. : ' 1 =: I r = '53846, the numerator of 



the decimal required ; and is tKe same as by the rule, 



f The reason of the rule may be explained from the first ex- 

 ample ; thus, three farthings is ^j- of a penny, which brought to a 

 decimal is '75 ; consequently g^d. may be expressed 9*75d. but 

 9*75 is -lo-^ of a penny ri-riV^- of a shilling, which brought to a 

 decimal is '8125 ; and therefore 15s. g^d. may be expressed 

 15-81255. In like manner 15-8 125s. is VAVV of a shillings 

 i-kl-h^l- of a pound ==, by bringing it to a decimal, '790625]. as 

 by the rule. 



