| XXX | (410) | XXX |
470
A R I T H M E T I C K. Ex. 12. Ear. 3. Ear. 4. 35)32.095(.9i7 3^5)76.75(23.615+ 35)3-2O9S(-09i7 650 3i5 * * 3'5 ' ■ 117J 59 59 35 35 975 2000 245 245 1950 245 255 Ear. 5. 0 20 6. I 500 35)-32°9*(.00917 35)* 3 i- 3i5"95('0°09 7 325 1750 59 . 59 _ 1625 35 35 125 245 245 In Ex. n . An integer divides an integer; and the In all the245 varieties, the figure 245 o iti the dividend dividend being lefs than the divifor, annex a cipher to it; ftands over theabove of the firft produft: and in Var. 1. again, after the dividend is exhaufted, annex a cipher the figure o is units in the place of tens, and 5, to the'remainder^ and continue the divifion till you find the firft figure of the quot, is tens; in Var.accordingly 2. the figure the quot circulates. the place of units, and fo 9 is units ; in Var. 3, In Ex. 12. A mixt number divides a mixt number : otheis infigure o is in the place of primes, and fo 9 is and after the dividend is exhaufted, by annexing ciphers &c. to the remainder, continue the divifion till the quot has primes, Here obferve that 9, the firft fignificant figure of the three decimal places; and as there is hill a remainder, it in all the above varieties, as well as in the variemight be carried further ; but three decimal places being quot, ties that follow, muft always be confidered, in multiin molt cafes, fufiiciently accurate, here you may limit it; plying the divifor, as an integer; and, in pointing the fo the quot is approximate. no decimal place is to be allowed for it. In divifion of decimals, the place of the firft figure of firftWeprodudl, ftiall now keep the dividend an integer, and give the quot may likewife be known from the firft dividual, to the divifor. much after the fame manner as in divifton of integers, decimal places Ear. 1. Ear. 2. by the following 3-5)32095(9170 -35)3I2°9S(9I7oo II. General Rule. 3I-5" 3- 5 ‘ ’ The place of the firft figure of the quot is the fame 59 ■with the place of that figure in the dividend which ftands 59 35 35 over the units of the firft product; Thus, in the example of integers in 35)32095(917, 245 245 the margin, the figure o, that ftands o- 315 245 245 ver 5, the units of the produft of 9.x 35, is in the place of hundreds; 59 and therefore 9, the firft figure of the 35 Var. 3. Var. 4. quot, is likewife hundreds ; and fo the 32095(9170000 quot is 917 integers. “035) 32095(917000 .0035) 0.0315-245 °-3 *5 245 To illuftrate the rule, we ftiall give decimal places to 59 59 the dividend of the above example; and thereby exhibit 35 35 the varieties that will occur in pointing the quot. 245 245Variety 1. Ear. 2. 245245 35)3209,5(91.7 • 35)320.95(9,17 J 315; • 35 * In Var. 1. lay, 9X3.5=31.5; and the unit 1 Handing under the. place of thoufands, the figure 9 is alfo 59 59 thoufands ; and as o at laft remains, annex a cipher for 3.5 35 the decimal .5- in'the divifor ;. then dividing, you ggt o 245'to the quot; and becaufe 9 ftands in the place of thou245 fands, the quot is wholly integers. 245 245 la Ex. it. n.)8( m)8.o(.72 77 30 22
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