Case 6. If a compound repetend be found in your divisor, or in both your divisor and dividend. RULE. Proceed as in the last case with your divisor and dividend, only remove them each so many places towards the right-hand, as they have places in the repetend of the divisor; but if the divisor be a compound repetend, without any terminate figures, divide by it as a terminate number; first subtracting the dividend from itself, as above directed. EXAMPLES. (19) Divide 147,47683 by 8,467. (20) Divide 4176,4266268 by 37,26974. LI. REDUCTION of DECIMALS. Case 1. To reduce a vulgar fraction to a decimal. RULE. Add ciphers to the numerator, and divide by the denominator: the quotient will be the decimal fraction required. Case 2. To reduce coins, weights, measures, &c. into decimals. RULE I. Reduce the given money, weights, &c. into the lowest denomination mentioned, for a dividend: then reduce the inte ger into the same denomination for a divisor: the result will be the decimal required. RULE II. Write the given denominations, or parts, orderly under each other, the inferior or least parts being uppermost; let these be the dividends. Against each part on the left-hand write the number thereof contained in one of its superior; let these be the divisors. Then begin with the lowest denomination, with ciphers added, making a dot between the ciphers and the figure; and divide, writing the quotient of each divisor as decimal parts on the right-hand of the dividend next below it; and let this mixed number be divided by its divisor, and so on, till all be finished; and the last quotient will be the decimal required. RULE III. To reduce shillings, pence, and farthings. If the number of shillings be even, take half for the first place of decimals, and let the second and third places be filled up with the farthings contained in the remaining pence and farthings, always remembering to add 1 when they are 25: if 40, add 2. But if the number of shillings be odd, multiply them by 5, and proceed with the pence and farthings as before. EXAMPLES. (8) Reduce 17s. 6d. to the decimal of a £. (9) Reduce 6s. 9d. to the decimal of á £. (10) Reduce 9s. to the decimal of a guinea. (11) Reduce 14s. 6d. to the decimal of a moidore. (12) Reduce 18s. 4 d. to the decimal of a £. (13) Reduce of a penny to the decimal of a £. (14) Reduce H dwts. to the decimal of a lb. Troy. (15) Reduce 10 drams to the decimal of a lb. avoirdupois. (16) Reduce 3 qrs. 14 lb. to the decimal of a cwt. (17) Reduce 6 inches to the decimal of a yard. (18) Reduce 6 furlongs to the decimal of a league, (19) Reduce 18 galls. 2 qrts. of wine to the decimal of a hhd. (20) Reduce 3 qrts. 1 pt. of ale to the decimal of a barrel. (21) Reduce 8 perches to the decimal of an acre. (22) Reduce 4 bushels 2 pecks to the decimal of a chaldron. (23) Reduce 12 minutes to the decimal of an hour. (24) Reduce 12 days to the decimal of a Julian year. By this rule the following decimal tables are made. |