Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/483

 R I T H M E T I K. ■ 401 number amount to 2.5;,- and afford a deduction of 1 far- nominator is 9 for the repeating figure, or' 9 for every thing complete. Hence, by inl'pe&ion, we have fre- figure of the circle ; and then, if occafion require, requently 1 farthing more than by the common method ; duce this fraction to its lowed terms. but.the two methods will agree, or give the fame anfwer, Thus, = and ./ = f. if, from the figures to be turned into farthings, we fub- Again, .27,=fJ=A, and -7*4285, =£^£4.= $.. tradt their 25th part, efteeming the remainder farthings and decimal parts of a farthing. , Case III. When the given decimal is a mixt repeatThus, .718 1. = 145. 4 d. 2 f. by infpedlion ; but by er, or a mixt circulate. the common method, and by infpeftion corrected, the Rule. From the mixt repeater, or mixt circulate, anfwer comes out 1 farthing lefs, as follows. fubtradt the finite part, and the remainder is the numerator. of the vulgar fradtion ; the denominator is 9 for Common method. Ipfpettion corrected. the repeating figure,, or 9 for every figure of the circle, L. If 25 : 1 :: 18 : .72. with as many ciphers annexetl as there are figures in the .718 that is, 25)i8.o(.72 finite part. 20 17 5 Thus, .0^ = ^ = ^, and .16=: £.£ = 4-, and .083and 18 14.360 ■* 9 o’5‘ 6 o TT* .72 The reafon of the rule may be (hewn thus : Efleem the finite part of the lafl: example integer, and then the be etan (o) 17.28 mixt number lua^ t0 g‘veD circulate. Again, reduce this mixt number to an improper d. /. fradtion, viz. multiply the integer 3 by the denominator f. 1.28 And 17.28 = 4 1.28 999999, and to the produdt add the numerator, as diTo conclude, inllead of dividing by 25, we may mul- redted in reduction of vulgar fradtions. tiply by .04 ; and then the exadt value of any decimal Multiply the integer 3 into 999999 of a pound Sterling may be found as follows. by the method of multiplying any num- 3000000 From the primes and'feconds fet off the {hillings; ber by 9, 99, 999, ire. taught in mul3 multiply the remainder by 4, fetting the produdt two tiplication of integers, and to the proplaces to the right; fubtradt the produdt from the firfi: dudt add the numerator, and the fum 2999997 remainder ; and from the fecond remainder point off fo {hall be the numerator of the improper 571428 many places to the right as there are figures in the firft fradtion, as in the margin, remainder. The number on the left of the point is far3571425 num. things, and the figures on the right are a decimal of ; Now it is evident that the fame numerator will be found, if, in the upper 3571428 farthing. line, inftead of the fij^phers, you place 3 Example 2. Example 1. the figures3 of the circll,1 and from them d.f. • d.f.' v fubtradt 3571425 3, the finite part. .76911.: -15 4 2.336 To the numerator thus found. the denominatornum.is .718!.== 14 4 1.28 999999 ; and fo the vulgar fradtion is VWssW1' But 1 Rem. 191 eiieemed 3 an integer ; whereas, in fadl, it is -rau’ J 72 = 18X4 764=191X4 v/e and fo our vulgar fradtion will be ido times greater than it ought to be : to corredt this error, we mult multiply 2 Rem. 17.28 2 Rem. .18.336 denominator by 10O, which is done by annexing two Prob. V. To reduce a decimal to its primitive vul- the ciphers4 to it;as bandt etheru etrue fradtion comes out to be gar fradtion. A 6 sW$ s <5**>this rule y bis ofl great - importance, and will ofCase I. When the given decimal* finite. Rule. Divide both numerator and denominator of Becaufe occur in pradtice, we {hall here fubjoin another exthe given decimal by their greateft common meafure; ten ample. the quot is the vulgar fraction required. Thus, .875=-j%y5=£. For 875)1000(1 Reduce .041^ to a vulgar fradtion. 875 vw 41 Greateft common meafure 125)875(7 875 Num. 375 And i2 5)T^y(4. (o) Den. 9000 Case II. When the given decimal is a pure repeat- In this manner too may any mixt number, confining er, or a pure circulate. of an integer with a repeater or circulate, be reduced to Rule. Make the repeating figure, or the figures of an improper vulgar fradtien ; but no ciphers are to be anthe circle, the numerator of the vulgar fradtion ; the de- nexed.to the denominator for the figures of the integer/ Vol. I. No. 17. 3 . 5I Ex. Ks-
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