XIII. To reduce different Denominations to one and the Decimal of one. RULE-Beginning with the lowest denomination, divide by that number of the lowest denomination which makes a unit of the next higher. Annex the quotient to the next higher denomination, and proceed as before, until you have reduced the given denominations to the decimal of the required one. 1. Reduce £6 11 s. 11 d. 3 qrs. to shillings and decimal of a shilling. I multiplied £6 by 20 s. to bring the pounds into shillings, and to these shillings I added 11 s. I then divided 3 qrs. by 4 d. to reduce the farthings to the decimal of a penny. I annexed this decimal of a penny to 11 d. and divided by 12 d. to reduce them to the decimal of a shilling. This decimal of a shilling I annexed to shillings. 2. Reduce £8 11 s. 8 d. 3 d. to pounds and decimal of a pound. 3. Reduce 4 cwt. 3 qrs. 16 lb. 8 oz. to cwt. and the deci mal of a cwt. Ans. 4,915 4. Reduce 13 hours, 40 minutes, and 35 seconds, to the decimal of a year.. Ans. ,001560161§§. 5. Reduce 19 s. 9 d. to the decimal of a pound.. Ans. ,9875. 6. Reduce 99. 13° 25′ to the decimal of a circle. Ans. ,787 7. Reduce 8 cord feet, 7 feet board measure, 5 primes, 6 inches, to the decimal of a cord. · Ans. 1,00455568249, 8. Reduce 15 yrs. 19 d. 11 h. 37 m. 45 s. to years, and the decimal of a year. Ans. 15,053598894. 9. Reduce 475047465 seconds to years and the decimal Ans. 15,053399132of a year. XIV. To reduce the Decimal of a higher Denomination to Units of a lower Denomination. RULE.-Multiply the given decimal by that number of the next lower denomination which makes a unit of the given denomination, and point off your decimals from the right hand of the product. 1. Reduce 4,915 cwt. to units of a lower denomina-lings and pence. 2. Reduce £,9875 to shil tion. 4,915 3,660 25 3300 1320 16,500 16 3000 500 8,000 Ans. 4 cwt. 3 qrs. 16 lb. 8 oz. Ans. 19 s. 9 d. 3. Reduce £,6625 to shil lings and pence. Ans. 13 s. 3 d. 4. Reduce £,6875 to shil lings and pence. Ans. 13 s. 9 d. 5. Reduce £,7 to shilAns. 14 s. lings. 6. Reduce £,015625 to pence and farthings. Ans. 3 d. 3 qrs. 7. Reduce ,875 of a tun of wine to pipes, hogsheads, gallons, and quarts. Ans. 1p. 1 hhd. 31 gal. 2 qt. XV. Decimals. The first figure at the left hand of the decimal point is a unit, and the first figure at the right hand of the same point is tenths. Thus 1,1 represent one and one tenth. It is plain that the unit figure may represent any thing you may please to name, money, weight, measure, &c. But whatever denomination you give to the unit, the first figure at the right of the decimal point stands for one tenth of the unit of that denomination. If the unit stand for one dollar, then the ,1 represents a tenth part of a dollar. If the unit stand for one pound, then the,1 represents one tenth of a pound. Cents and mills are decimal parts of a dollar. Ounces and drams may be reduced to the decimal of a pound; quarts and pints to the decimal of a bushel; hours and minutes to the decimal of a day; inches to the decimal of a foot. In one word, every unit has the same parts in a decimal form, that a dollar has. Therefore, every thing ciphers like money. If,25 are a fourth part of a dollar, in reckoning money, the same expression may represent a fourth part of any unit of any other denomination. $,125 represent one eighth of a dollar. But,125 represent one eighth of any unit. To make the scholar familiar with decimal parts, several pages are filled with Tables. .11 Dollar. Dollar. Dollar. Cents. +25= 4,03125 Cents. N. Y.. 31-3 d. 4 = 16 = 32,0625 61-6 d. 4° = 18 = 2,09375 98-9 d. ===,125 =123-1 s. 13=26 ==,15625=15-1 s. 3 d. * = &==,1875 1831 s. 6 d.472 = f = √2,21875-214=1 s. 9 d. 16=32,25 =252 s. = 6 2·35= 48,28125-281-2 s. 3 d. 16 16 4:25 = 8,5 = }}=,53125=534=4 s. 3 d. |