Page:Encyclopædia Britannica, first edition - Volume I, A-B.pdf/482

 ARITHMETIC K. fra&ion of the integer, and then reduce the vulgar frac- Pros. IV. To reduce adecimal to value. Rule. Multiply the given decimal by the number of tion to a decimal. Ex. x. Reduce 9 pence to the decimal of a Hulling. parts -of the next inferior denomination contained in an unit of the integer; and from the product point off fo J. s. 9=t and i2)9.o(.75 of a Hulling. many figures to the right hand as there are places in the given decimal. On the left hand of the point are parts, 84 Here the fraflion A=l ; and and on the right a decimal of one of thefe parts ; which the denominator 4 = 2X2 gives 60 decimal mufl: be reduced in the fame manner to the next inferior denomination, and from that to the next, and a finite decimal of two places. 60 fo on to the loweft ; the feveral figures on the left of the points are parts ; and if there be ftill fome figure or (°) of a pound. figures Ex. 2. Reduce 9 pence to the decimal on the right, they are a decimal of the loweft of the parts. d.== L. Exavi'le 2. 9 -xh? 240)9.oo(.0375 of a pound. Example 1. 7 20 Reduce .875 1. to value. Reduce .76911. to value. The fradtion ■ L. s. d. f. L. s. d. and the denominator 80= 1 800 .7691 = ij 4 2 .875=17 ^ 10X2X2X2 gives a finite 1 680 decimal of four places. / 1206 s. 15.3820 1200 d. 4.584 ~) Ex. 3. Reduce 16 s. 6 d. to the decimal of a pound. /. d. L. f. 2.336 16 6 = 24o)i98.o(.825 L. 12 1920 The reafon of pointirig the prodhd, as the rule dire<fts, is plain. For, in Ex. 1. as 1000 : 875 :: 20 : 17; 198 600 that is, as the decimal denominator to the decimal nu4 80 merator, fo the vulgar denominator to. the vulgar nuThe fradion 4^|. = merator. and the denominator 40=10X2 1 200 In Ex. 1. the full value of the decimal comes out in X2 gives a finite decimal of three 1 200 parts, the decimal being quite exhaufted ; but in Ex. 2. places. befides the parts, there is a decimal of a farthing, viz. (°) Prob. III. To reduce the remainder of a divifion to .336Thef. decimal of a pound Sterling may be reduced to a decimal. value by infpeftion, in the following manner. Rule. The remainder being the numerator, and the Double the figure in the place of primes for fhillings ; divifor the denominator of a vulgar fraction, after placing and if the figure in the place of feconds be 5, or exceed the decimal point on the right of the integral part of the 5, reckon 1 (hilling more ; and rejeding 5 in the fecond quot, annex ciphers to the remainder ; then continue the place, the figures in the fecond and third places are fo divifion til! o remain, or till the quot repeat or circulate, many farthings, abating 1 for every 25. or till you think proper to limit the decimal; and the L. /. d. f. number on the right of the point is a decimal of the inExamp. i. .718 = 14 4 2 teger exprefted in the quot. 2. .759 =1521 3. .894 = 17 10 3 Example 1. Example 2. Divide 513I. among 36men. Divide 176 s. among 24 In Example 1. the figure 7 doubled gives 14s.; the two following figures 18 are farthings, equal to 4d. 2 f. L. boys. In Example 2. the figure 7 doubled gives 14 s. and 5 ■'')si3(M-25 in the place of feconds gives 1 (hilling more, in all 15s.; 36 and the other figure 9 is farthings, vtz. 2 d 1 f. In Example 3. the figure 8 in the place of primes, i53 and 5 in the place of feconds, give 17s.; the remaining 144 figures 44, abating j, are farthings, viz. 10 dv. 3 f. When the figures in the fecond and third place to be Rem. 90 converted into farthings are 25, the anfwer, by infpec72 tion, comes out exad, viz. 24 f. or 6 d. ; but in all other cafes, the anfwer, by infpedion, is too great, no 180 allowance or corredion being made till the convertible 180 number.
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