2. Reduce 1, 2, 3, 4, and so on to 19 shillings, to decimals. Shillings. 1 •85, •9, 95. Answers. 55, 6, .65, 7, 75, Here, when the shillings are even, half the number, with a point prefixed, is their decimal expression; but if the number be odd, annex a cypher to the shillings, and then halving them, you will have their decimal expression. 3. *Reduce 1, 2, 3, and so on to 11 pence, to the decimals of a shilling. 4. Reduce 1, 2, 3, &c. to 11 pence, to the decimals of a pound. 7 2 Answers. 00416, 0083+, 6 Pence. Answers. 025, 02916+, 0333+, 0375, 0416+, 04583+. 5. Reduce 1, 2 and 3 farthings to the decimals of a penny. 1qr.=25d. 2qr.='5d. and 3qr75d. Answers. 6. Reduce 1, 2 and 3 farthings to the decimals of a shilling. Answers. 1qr.02083+s. 2qrs.04166+s. 3qrs.0625s. 7. Reduce 1, 2 and 3 farthings to the decimals of a pound. Ans. 1qr.0010416+ £. 2qrs.002083+ £. 3qrs.003125 £. 8. Reduce 13s. 51d. to the decimal of a pound. Ans. 6729+. 9. Reduce 7Cwt. 3qrs. 171b. 10oz. 12dr. to the decimal of a ton. Ans. 39538+. 10. Reduce 10oz. 13pwt. 9gr. to the decimal of a pound Troy. Ans. 8890625. Ans. 9375. 11. Reduce 3qrs. 3n. to the decimal of a yard. 12. Reduce 5fur. 12po. to the decimal of a mile. Ans. 6625. 13. Keduce 55m. 37sec. to the decimal of a day. CASE III. Aus. 03862+. To find the decimal of any number of shillings, pence and farthings, by inspection. I. Write half the greatest even number of shillings for the first decimal figure. * The answers to this question are the same as the decimal parts of a foot. The invention of the rule is as follows: As shillings are so many 20ths of a pound, half of them must be so many tenths, and consequently take the place of tenths in the decimals; but when they are odd, their half will always consist of two figures, the first of which will be half the even number, next less, and the second a 5: Again, farthings are so many 960ths of a pound, and had it happened that 1000, instead of 960, had made a pound, it is plain any II. Let the farthings in the given pence and farthings possess the second and third places: observing to increase the second place or place of hundredths, by 5 if the shillings be odd, and the third place by 1, when the farthings exceed 12, and by 2 when they exceed 36. EXAMPLES, 1. Find the decimal of 13s. 93d. by inspection. Add 6.. of 12s. 5 for the odd shilling. 2 for the excess of 36. 691 decimal required. 2. Find, by inspection, the decimal expressions of 18s. 31d. and 17s. 81d. Ans. £.914 and £-885. 4. Value the following sums, by inspection, and find their total, viz. 15s. 3d.+8s. 114d.+10s. 61d.+1s. 8d.+jd. +23d. CASE. IV. Ans. £1.834 the total. To find the value of any given decimal in the terms of the integer. RULE. 1. Multiply the decimal by the number of parts in the next less denomination, and cut off so many places for a remainder, to the right hand, as there are places in the given decimal. 1. Multiply the remainder by the next inferiour denomination, and cut off a remainder as before. III. Proceed in this manner through all the parts of the integer, and the several denominations, standing on the left hand, make the answer. This case is the reverse of Case II. and the reason of the rule is hence obvious. EXAMPLES. 1. Find the value of 73968 of a pound. 20 14.79360 9.52320 4 2.09280 Ans. 14s. 94d. 24 number of farthings would have made so many thousandths, and might have taken their place in the decimal accordingly. But 960 increased by part, of itself, is 1000, consequently any number of farthings, increased by their part, will be an exact decimal expression for them: Whence, if the number of farthings be more than 12, part is greater than qr. and, therefore I must be added; and when the number of farthings is more than 36, part is greater than qr, for which 2 must be added, Ans. 8.148d. or £1. Ans. 19s. 113d. 2. What is the value of 679 of a shilling? Ans. 2qrs. 13lb. 1oz. 10, dr. 5. What is the value of 8593 of a lb. Troy? To find the value of any decimal of a pound by inspection. RULE.* Double the first figure, or place of tenths, for shillings, and if the second figure be 5, or more than 5, reckon another shilling; then, after the 5 is deducted, call the figures in the second and third places so many farthings, abating 1 when they are above 12, and 2 when above 36, and the result will be the answer. Note. When the Decimal has but 2 figures, if any thing remain after the shillings are taken out, a cypher must be annexed to the right hand, or supposed to be so. EXAMPLES. 1. Find the value of 876£ by inspection. And 16s. 1s. double of 8. for the 5 in the second place, which is to be taken 61d. 26 farthings remain to be added. d. for the excess of 12. 17s. 61d. the Ans. 2. Find, by inspection, the value of 49 £. double of 4. for the 5 in the place of hundredths. [out of 7. 40 farthings, a 0 being annexed to the remaining 4. d. for the excess of 36. 9s. 94d. the Answer. 3. Find the value of 097£ by Inspection. Ans. 1s. 112d. 4. Value the following decimals by Inspection, and find their sum, viz. ·785£ + ·537£ + ·916£ † ·74£ + ·5£ + ·25£ + ·09£008.£. Ans. £3 16s. 6d. As this rule is the reverse of the rule, Case III. the reason is apparent from the demonstration of that rule. To find the value of goods in Federal Money.-Multiply the price and quantity together; point off in the product, for denominations lower than dollars, as many places as there are in the given price; or, if there be decimal places in the quantity also, according to the rule for multiplication of decimals. This is really multiplication of decimals, the dollar being considered the unit. EXAMPLES. 1. Find the cost of 823 yards, at $1.29c. a yard. 823x$1.29c. $1061.67c. Ans. 2. Find the value of 56yds. 2qrs. at $3.11c. per yard. 56yds. 2qrs.56·5; and 56.5x3.11 $175.71c. 5m. Ans. 3. What must pay for 64yds. at $5.50c. per yard' Ans. $33.68c. 7m. ·5. 4. Bought 7 yds. at 34 cents per yard: what did I pay for theAns. $2.6214c. whole? |