7. Add together .7426, .846, 7.612, 5 5 and 12.0875. 8. Add 753.0375- 246 38246- -9724.28352. 67482.063750724.00003718- -and 378,2375 toge ther. W CHAP. IV. MULTIPLICATION of DECIMALS. HETHER the given Numbers be mixt Numbers or pure Decimals, multiply them as if they were all pure whole Numbers and when the product is found, Point off so many Decimal parts or places, as there are in both the Multiplicand and Multiplier, accounted together, N. B. It will sometimes fall out that in multiplying decimals by decimals there will not be so many figures in the product, as the rule requires decimal places; in that case supply the defect by prefixing as many cyphers as places are wanting, To multiply by 10, 100, 1000, &c. remove the separating point as many places to the right hand as the multiplier hath cyphers. To multiply finite or approximate decimals, so that the product shall consist of no more than a determinate number of places. Rule Under that place in the multiplicand, thought necessary to be retained in the product, write the units place of the multiplier, and invert the order of all its other places; that is, write the decimals on the left, and the integers (if any) on the right; in multiplying, omit those places in the multiplicand which stand to the right of the figure mul tiplied by, and let the right hand place of every line stand under each other. In each line let the lowest place be encreased by the carriage which would arise from the omitted places, carrying 1 from 5 to 15, 2 from 15 to 25, 3 from 25 to 35, &c. instead of carrying 1 for every 10; and the sum of these lines will give a product generally exact. Examples. Multiply 384.672158 by 36.8345. Now seeing there would be ten decimal places in the product whereof the greatest part are unnecessary: there fere to keep only four decimal places in the product. 384.672158 5438.63 115401647 23080329 3077377 115402 15387 1923 14169.2065 15. Multiply 3.141592 by 52.7438, so as to have only four decimal places in the product? CHAP. V. Answ. 165.6995. DIVISION of DECIMALS. ECIMALS and mixt Numbers are in effect divided as DECIMALS and mixt Nhall be set forth in the sundry cases following: L. General I. General Rule for pointing the Quotient. The places of decimal parts in the divisor and quotient, counted together, must be always equal to those of the dividend, therefore point off in the quotient as many figures as are the excess of decimal places in the dividend above those in the divisor. Case 1. When the places of decimals in the dividend and divisor are equal, the quotient will be an unmixed whole number. [1] Examples. [3] [2] .0078).4368( .7563)59062.4922 Case 2. When the places of decimals in the dividend are most, cut off the excess for decimal parts in the quotient. [4] 24.3)780.516( [6] .534) 30438( [5] Case 3. When there are not so many places of decimals in the dividend as the divisor, annex cyphers to the divi dend to make them equal; then will the quotient be an unmixed whole number. Case 4. If after the division is finished, there are not as many figures in the quotient, as there ought to be decimal places, (by the general rule) supply the defect by prolixing as many cyphers as there are places wanting. N 3 [7] [7].957)7.25406( [9] .43).13975( [8].525).0007875( [11].00875)38.075( Note. When decimals or whole numbers are to be divi. ded by 10, 100, 1000, &c. viz. unity with cyphers, it is -performed by removing the separatrix in the dividend so many places towards the left hand, as there are cyphers in the divisor. When the divisor doth not measure the dividend, we may approach as near the truth as we please by annexing cyphers continually, to the dividend, or the remainder: but six or seven places of decimals are generally esteemed sufficient, for the quotient differs from the truth by less than Tooooo of a unit. [12] .6252)14250( [14] 52.125)2.34( [13] 48.25)374,86( [15].056)82( Division may be contracted as follows: Rule. Let each remainder be a new dividend, and for each such new dividend point off one figure from the right band of the divisor, observing at each multiplication to have respect to the increase of the figures so cut off, as in multiplication. Examples. |