380. Reduction of a Compound Number to the Decimal of a Higher Denomination. rod. Ex.-Reduce 2 yd. 2 ft. 8.94 in. to the decimal of a We may reduce the given number to the common fraction of a rod, and this common fraction to a decimal: 2 yd. 2 ft. 8.94 in. = 104.94 in. : 12) 8.94 .745 ft. 3) 2.745 .915 yd. But there is a shorter method than this. Beginning at the inches, and dividing them by 12, to reduce them to feet (as in Ex. 2, Art. 374), we find that 8.94 inches equal .745 ft. Annexing this decimal to the 2 ft. given, we have reduced the given number to 2 yd. 2.745 ft. Dividing the feet by 3, to reduce them to yards, we find that 2.745 feet equal .915 yd.; and, annexing this decimal to the 2 yd. given, we have reduced the given number to 2.915 yards. Dividing the yards by 5.5, to reduce them to rods, we find that 2.915 yards equal .53 of a rod-the decimal required. 5.5) 2.915 (.53 rd. 275 165 165 Ans. .53 rd. We have here reduced 2 yd. 2 ft. 8.94 in. to .53 of a rod. In Ex. 4, Art. 376, we reduced .53 of a rod to 2 yd. 2 ft. 8.94 in. The two processes, therefore, may be used to prove each other. RULE. To reduce a compound number to the decimal of a higher denomination, divide the number of the lowest denomination given by the number required of this denomination to make 1 of the next higher, and annex the decimal quotient to the number given of that next higher. Treat this result in the same way, and proceed thus till the required denomination is reached. 381.-EXAMPLES FOR PRACTICE. Reduce the following: prove Ex. 2, 3, 4, and 11. 1. 15 da. 23 h. 18 min. 9 sec. to the decimal of a leapyear; of a common year. First ans. .04363644+lp.-yr. 2. 17 cwt. 15 lb. 12 oz. 10 dr. to the decimal of a ton. 3. 1 qt. 3 gi. to the decimal of a gallon. Ans. .34375 gal. 4. 3 pk. 6 qt. 1.4 pt. to the decimal of a bushel. 5. 1 lb. Troy to the decimal of 1 lb. avoir. 1 lb. avoirdupois = 7000 gr. Reduce to grains-a common denomination, of the same value in both weights. 1 lb. Troy 5760 gr. = 57607000.82285714 Ans. 6. 1 oz. avoirdupois to the decimal of 1 oz. Troy. Ans. .9114583 oz. 7. 3 diamond carats to the decimal of an ounce Troy. 8. £1 d. to the decimal of a guinea. Ans. .982142857 guin. 9. $1.25 to the decimal of an eagle. 10. 210 A. 3 R. 20 sq. rd. 24 sq. yd. 1 sq. ft. 115 sq. in. to the decimal of a sq. mile. Ans. .3295 sq. mi. 11. 13 ch. 181. 3.168 in. to the decimal of a mile. 12. A surface 2 chains 25 links square to the decimal of an acre. Ans. .50625 A. 13. 20 cu. ft. 432 cu. in. to the decimal of a cubic yd. 14. 0.3 f 12 m48 to the decimal of a gallon; to the common fraction of a gallon. Reduce the common fraction to a decimal; does this decimal agree with the one first obtained? 15. 7s. 10d. 2 far. to the decimal of a pound; to farthings; to the common fraction of a guinea; to the decimal of a guinea. Last ans. .375 guin. 16. 1 mi. 3 fur. 20 rd. 4 yd. 1 ft. 2 in. to the decimal of a league. Ans. .48 league. 17. An angle of 41° 13′ 12′′ to the decimal of a right Ans. .458 of a right angle. angle. 382.-EXERCISE ON THE METRIC SYSTEM. 1. Write 1 myriametre 9 hectometres 7 metres 6 decimetres, 3 centimetres, as metres and the decimal of a metre, and read as such. Ans. 10907.63 metres. 2. Write the above as kilometres; as decimetres; as Ans. 10.90763 kilometres, etc. decametres. 3. Write 2 decalitres 9 decilitres as litres. 4. Write 1 quintal 1 myriagram 3 kilograms 2 hectograms 4 decagrams 5 grams as kilograms. 5. Read 246819 centimetres as a compound number. Ans. 2 kilometres 4 hectometres, etc. 6. Read 9753124 decigrams as grams. 7. Express 3 millilitres as the decimal of a litre; as the common fraction of a kilolitre. Ans. 100000 kilol. 8. How many centiares in a square measuring 3 metres on each side? 9. How many hectares in 2300000 centiares? In 4750 ares? 10. How many steres of wood in a pile, 50 metres long, 1.1 metres wide, and 2 metres high? Ans. 110 steres. 11. What price per kilogram equals 25 c. per pound avoirdupois ? Ans. 55 c. + How many 12. How many grams equal 1 scruple? equal 1 oz. Troy? How many equal 1 lb. avoir. ? 13. Reduce 1 tonneau 7 quintals to grams. 14. What price per stere equals $10 a cord? 15. If a locomotive travels a kilometre in 45 seconds, what rate is that per hour? 16. Read 4.1763 myriametres as metres; as kilometres; reduce them to centimetres. 17. If land is worth $100 an acre, how much is it worth per hectare? Ans. $247.114. 18. Bought 50 kilograms of lard, at 75 centimes per kilogram. What was the cost in francs, etc.? 19. How many hectolitres of apples, at $2.25 a hectolitre, should be given for 3 decasteres 5 steres of wood, at $1.50 per stere? Ans. 231 hectol. 20. How many kilometres in a mile ? 21. At $2.50 per kilolitre, what is the freight on a box, 4 metres long, 1 metre wide, and .5 of a metre high? 22. About how many litres make a gallon? About how many steres make a cord? Which is greater, 45 kilograms or 1 cwt.? 5 metres or 1 rod ? 23. How many steres of wood can be piled in a bin, 4 metres long, 3 metres wide, and 2 metres high? 24. A druggist, having kilog. of quinine, makes up 200 pills containing 2 decigrams of quinine each. How many more of these pills might he have made out of the quinine on hand? 25. A person invests $10000 in land, at $125 a hectare. How many lots of 4 ares each can he make out of his purchase? 26. A farmer, having 4 hectometres of wire fence, uses a portion of it to enclose a field 50 metres square. How many decametres has he left? Ans. 20 decam. 27. What is the profit on 75 hectolitres of potatoes, bought at 7 francs a hectolitre, and retailed at 1 franc a decalitre ? 28. Reduce of a kilometre to metres; to the fraction of a myriametre. First ans. 125 metres. 29. Reduce 5 grams 4 centigrams to the decimal of a tonneau; to the fraction of a kilogram. 30. Reduce .325 of a hectolitre to the decimal of a kilolitre; to decilitres. CHAPTER XIV. ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION, OF COMPOUND NUMBERS. 383. Compound numbers may be added, subtracted, multiplied, and divided. These operations are performed on the numbers of each denomination separately just as on simple numbers. In addition and multiplication, results that are reducible to a higher denomination must be reduced; and in subtraction and division, reduction descending is often necessary. Similar reductions are made in performing these operations on simple numbers, as will be shown. Addition of Compound Numbers. 384. Ex.-Find the sum of 20 sq. rd. 5 sq. ft. 91 sq. in., 1R. 5 sq. rd. 27 sq. yd., and 3 R. 2 sq. rd. 3 sq. yd. 6 sq. ft. 53 sq. in. For convenience we write numbers of the same denomination in the same column, and to avoid errors mark the denominations above. Beginning to add at the right, we find the sum of the square inches to be 144. But 144 sq. in. = 1 sq. ft. and add 1 sq. ft. to the next column. Write 0 under the square inches, |