Let the divisor be conceived to stand under the containing left hand figures of the dividend, and the first figure of the quotient will possess the same place of integers or decimals, as that in the dividend which corresponds to the units place of the divisor. When there are many figures in the divisor the operation may be contracted, thus ; Find what place of integers, or decimals, the first figure of the quotient will possess; and consider how many quotient figures will serve the present purpose; then take the same number of the left hand of the divisor, and as many of the dividend as will contain them (less than ten times) rejecting the rest; then, instead of bringing figures down from the dividend, separate one from the right of the divisor, as often as necessary, till the whole be exhausted; remembering to carry from the right hand figures of the divisor as in contracted multiplication. When there are not so many figures in the divisor, divide as usual, till there be as many of the quotient figures found as the divisor is short of the intended quotient; then use the contraction. EXAMPLES. Divide 2508,92806 by 92,41035 92,41035)2508,91806(27,1498+facit. 18482070 Contracted so as to have three decimal places in the quotient 92,4103,5)2508,92806(27,149+facit. 1848207 & Divide ,00178600398 by ,00463 9 Divide 2508,928065051 by 92,41035, places of decimals in the quotient. 10 Divide ,00357200796 by ,771492 11 Divide 87,076326 by 9,365407, and places of decimals in the quotient. 10, ,385746 so as to have 4 facit 27,1498 facit,00463 let there be 7 facit 9,2976552 12 Divide 174,152652 by 18,730814, and let there be 3 Annex as many ciphers to the numerator as may be necessary, which divide by the denominator. Note. Note. The quotient must consist of as many decimal places, as there are ciphers annexed. If a compound fraction be given, reduce it first to a single 8 What is the equivalent decimal for ? 9 What is the decimal of? ,1923+ ,45614+ 7, 38, 7 57 36 10 What are the equivalent decimals for, and 14 ? 256 answer ,55,,95, ,375, 875, 0546875 CASE 2. To reduce any sum, or quantity, to the decimal of a given denomination; RULE. First. Divide the given sum, &c. in its lowest mentioned denomination, by the number of like parts in the proposed integer; the quotient will be the decimal required. Or, Secondly. Write the given numbers orderly from the least to the greatest in a perpendicular column, and divide each of them by such a number as will reduce it to the next name, annexing the quotient to the succeeding number; the last quotient will be the required decimal. EXAMPLES. EXAMPLES. 1 Reduce 15s 8d. to the decimal of a pound; also, 3qrs. 12lb. 6oz. 14,592dr. to that of an C.wt. s. d. qrs. 15 8=754960)754,00(,78541661.+facit. 20 0=960 6721) facit,861 C.wt. facit,375 2 Reduce 7s 6d. to the decimal of a pound. ,0375 facit,5385416+ 5 Reduce 24 grains to the decimal of a lb. facit ,0041666+ 6 Reduce 14 drams, to the decimal of a lb. avoirdupois. facit ,0546875 facit,225 7 Reduce 4C. 2qr. to the decimal of a ton. 8 Reduce 76 yards to the decimal of a mile. facit ,04318+ 9 Reduce 3gr. 2na. to the decimal of a yard. facit,875 10 Reduce 4 perches to the decimal of an acre. facit,025 11 Reduce 1 pint to the decimal of a gallon. ,125 12 Reduce 7 minutes to the decimal of a day. 13 Reduce 3 C.wt. 2qr. 14lb. to an C.wt. facit,00480+ 3,625 C.wt. 7,6875yds. 13,3575A. 3,42857+mo. CASE CASE 3. To reduce a decimal fraction to its value; Multiply it by the known parts of the integer. Note. To find the value of any decimal of a by inspection; double the first figure after the point for shillings, adding one, if the second be 5 or upwards; the second, if less than 5, or its excess above 5, call tens, and the third units of farthings, abating one when above 12, and two if above 36. EXAMPLES. 1 What is the value of .7854166 of a pound? 2 What is the value of ,76 of a pound? answer 15s. 2d. 1,6qr. 3 What is the value of ,625 of a shilling? answer 7d. 4 What is the value of ,8322916 of a answer 16s. 7d 5 What is the value of ,861 of an C.wt. ? answer 3qr. 12lb. 6oz. 14.592dr. 6 What is the value of ,7 of a lb. troy? 7 What is the value of ,761 of a day? answer 8oz. 8dwt. answer 18hr. 15m. 50,4sec. 8 What is the value of ,71 of 4oz. troy? answer 20z. 16dwt. 19,2gr. 9 What is the value of ,67 of a league ? answer 2M. 3pls. 1yd. 3in. 1,8b.c. 10 What is the value of ,4712 of an ell English? answer 2gr. 1,424na. 11 What |