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 407 A R I T H M E T I C K. circulate, to the produdl of the right-hand figure We fliall next torn the decimals of the former exam- plicand circle add the carriage from the left, then proceed ple into approximates, and then the operation will be as asof inthemultiplication of integers ; but before you add the follows. particular produdts, make them conterminous, and then By the rule. Common way at large. add as in addition of circulates. 25.8525.85— The produft commonly circulates; and then its circle 42-97+ +79-24 is fimilar to the circle of the multiplicand, as in Ex. 1. and 2.; but the produdt fometimes repeats, as in Ex. 5.; 180-95 103400 or it may turn out finite, as in Ex. 6. 2326 5170 Here it is obvious, that in multiplying .481 Ex. 1. 5170 2326 by 7, the carriage from the left would be 3 ; .481, 10340 180 fo fay, 7X1 = 7, and 3 of carriage, make 10, 7, &c. The product circulates, and its circle IIIO.77 45 Prod. 1110.76+ .370, is fimilar to .481, the circle of the mul- 3-370, It remains to be obferved, that the want of carriage tiplicand. from the fight hand may fometifnes affedt more columns Ex. 2. Ex 3. Ex. 4. on the left than one, and thereby occafion more uncertain 7.5x8, 7-5i8, 7-5)8, figures in the produdt than that on the right hand. The .05 .005 bell fecurity on this head is, never to limit the produdl •5 to fewer than four or five decimal places. To conclude, when decimals to be multiplied are long, you may frequently perform the operation more In the above three examples the products are mixt eafily in vulgar fractions, and then reduce the produdt to circulates, the three figures on the right being the circle, a decimal. and the figures on the left the finite parts. Rule II. If the multiplier be finite, and the multiIV. If the multiplier be interminate, reduce plicand repeat, in multiplying carry at 9 on the right it toRule a vulgar fraftfon, as directed in reduction of decihand ; and before you add, prolong the repetends of the Prob. V.; then multiply the given multiplicand by particular products, till their right-hand figures Hand di- mals, numerator, (working as in integers, if the multiplireftly under one another ; and in adding, carry at 9 on the cand be finite ; or as dire<5ted in Rule 2. if it repeat; or the right hand. The produdt repeats, as i Ex. 1. 2. ; or turns asproduct, prefcribed Rule 3. if it circulate) ; and divide the by theindenominator,. out finite, as in Ex. 6. px Here there are fix cafes -, for the multiplier may repeat Ex. 2. 2542V circulate,multiplicand. and may multiply a finite, a repeating, or ^ Q ' orcirculating Case I. When a repeating multiplier multiplies, a fi-t28.341^ nite multiplicand. Examp. Multiply 638.25.by .4 = ^ 638.25. 4 9)2553-00(283.(1 produft fought: Note, IT die multiplier has ciphers on the right, inffead of annexing ciphers to the produft, reiterate its right-hand figure' fo many times as there are ciphers. Ex. x. Ex. 2. 79.6 874-3'900 5° 3983.3 786900.0 ole III-. If the multiplier be finke, and the raulti-

n 72 33 27 60 54 Case II. When both factors repeat,Examp.