REMARK 1.-The GRAMME is the weight of a cubic centimetre of pure water at the temperature of 39.2° Fahrenheit. This weight is 15.4323487 grains. The new United States half-dime weighs 5 grammes. REMARK 2.-1 Avoirdupois Pound is 7000 grains. 1. In 1 quintal how many pounds? Ans. 220.46 lb. 2. In 1 M. g. how many pounds? Ans. 22 lb., nearly. 3. In 1 D. g. how many drams? Ans. 5.64 dr. 4. How many nickel half-dimes can be made of g. of the metal? Ans. 5400 half-dimes. 27 K. 5. Write 1234567.890 grammes in terms of every name in the table. Ans. 1.23456789 T.; 12.3456789 Q.; 123.456789 M. g., etc., to 1234567890 m. g. 6. In $3.25 how many cents? Ans. 325 cts. Ans. 705 c. 8. In m.4.25 how many centimetres? Ans. 425 c. m. 9. In 1. 12.09 how many centilitres? Ans. 1209 c. 1. 10. In g. 13.75 how many centigrammes? Ans. 1375 c. g. 11. The Ohio River is about 1000 miles long. How many K. m. is it in length? Ans. 1609 K. m. 12. Mont Blanc is 15668 feet high. What is the height in metres? Ans. 4775.6 m. 13. Mt. Everett is 29100 feet high. What is the height in metres? Ans. 8869.68 m. 14. If cloth sells at $4.50 per yard, what should be the price per metre? Ans. $4.92 PERCENTAGE. 99. PERCENTAGE embraces those operations in which numbers are compared with 100. (1) The contraction PER CENT. is generally used for the word hundredth, or hundredths. Thus: 1 per cent. of 78 is the same as saying 1 hundredth of 78; 5 per cent. of 75 is 5 hundredths of 75. (2) The RATE per cent. is the number of hundredths. Thus: In the expression 5 per cent. of 75, 5 is the rate per cent. 100. To represent decimally any given rate per cent., write the given rate as so many hundredths. EXAMPLES. 1. Represent 1 per cent. decimally; 2 per cent.; 3 Ans. .01; .02; .03; .05 per cent.; 5 per cent. 2. Represent 10 per cent. decimally; 15 per cent.; Ans. .10; .15; .20; .25 per cent.; 50 per cent.; Ans. .30; .50; 75; .90 per cent.; 130 per cent.; 4. Represent decimally 125 150 per cent.; 100 per cent. Ans. 1.25, 1.30; 1.50; 1.00 5. Represent per cent. decimally; per cent.; 11⁄2 per cent.; 2 per cent. Ans. .005; .0025; .015; .025 101. To find the per cent. (or percentage) of a number at a given rate. EXAMPLES. 1. Find 2 per cent. of $50; 7 per cent of 500 lb. of coffee; 25 per cent. of 64 bushels of wheat. (1) PROBLEM.-What are 2 hundredths of 50? of 50 is 1. (3) RESULT.-Hence, 2 per cent. of $50 is $1.00 RULE. Multiply the given number by the RATE per cent. written as a decimal, and place the decimal point in the product so as to cause as many figures to stand on its right as there are figures on the right of the point in both multiplicand and multiplier. REMARK. In the application of this rule it is of very great convenience to familiarize the following equivalents: .061; 121}; .16}=}; .25=1; .33}=} .50 = 1; .37=}; .62)=}; .75=2; .663= Hence, to multiply a number by .331, divide by 3; to multiply by .12, divide by 8, etc. 2. Find 1 per cent. of $1.00; $1.50; $2.00; $2.50; $3.00; $3.50; $10.00. Ans. $0.01; $0.015, etc. 3. Find 2 per cent. of $5.00; $15.00; $20.00; $30.00; $50.00; $75.00; $100.00. Ans. $0.10; $0.30, etc. 4. Find 3 per cent. of 35 lb. of tea; 75 lb; 100 lb.; 150 lb.; 200 lb.; 500 lb.; 1000 lb. Ans. 12 lb.; 21 lb., etc. 5. Find 4 per cent. of 500 galions of molasses; 750 gal.; 900 gal.; 1250 gal. Ans. 20 gal.; 30 gal., etc. 6. Find 5 per cent. of 100 barrels of apples; 240 bbl.; 780 bbl.; 374 bbl. Ans. 5 bbl.; 12 bbl, etc. 7. Find 6 per cent. of $100; $120; $145, $150; $300; $700; $5000. Ans. $6; $7.20, etc. 8. Find 7 per cent. of 196 lb. of flour; 392 lb.; 588 lb.; 784 lb. Ans. 13.72 lb. =138 lb., etc. 9. Find 8 per cent. of $25000; $50000; $100000; $60000; $95000. Ans. $2000, etc. 10. Find 17 per cent. of 200 marbles; 19 per cent. of 5400 apples; 27 per cent. of 1300 peaches. Ans. 34 marbles, etc. 11. Find 6 per cent. of $320; $480; $640; $800; Ans. $20; $30, etc. $960; $1120. 320÷16=20. 12. Find 12 per cent. of 1200 yards of calico; 64 yd.; 1248 yd.; 72 yd. 1200-8-150. Ans. 150 yd.; 8 yd., etc. Ans. 16 peaches, etc. 13. Find 163 per cent. of 96 peaches; 102 peaches; 1962 peaches. 14. Find 25 per cent. of 1.24 francs; 3.36 fr.; 5.44 fr.; 7.96 fr. Ans. 31 centimes, etc. 1.24÷÷÷4=.31 15. Find 33 per cent. of 117 yards; 100 yards; 500 yards; 720 yards. 117-3=39. Ans. 39 yd.; 331 yd., etc. 16. Find 100 per cent. of $50; 34 lb.; 27 yd.; 500 fr.; 9000 lb. Ans. $50; 34 lb., etc. 17. Find 106 per cent. of $80; 1123 per cent. of 960 lb.; 125 per cent of 24 yd. 80×1-85. Ans. $85; 1080 lb., etc. 18. A merchant buys calico at 15 cts. per yard, and wishes to clear 33 per cent. in retailing it. For how much must he sell the calico per yard? Ans. 20 cts. 19. I buy corn at 40 cts. per bushel, and wish to clear 5 per cent. in its sale. What must I ask per bushel? Ans. 42 cts. 20. The cost of goods is 20 cts. per yard, rate per cent. of PROFIT 25. What is the selling price? Ans. 25 cts. 21. Cost price $1.50, rate per cent. of profit 331. What is the selling price? Ans. $2.00 22. I buy 50 barrels of potatoes at $2.50 per barrel, and find them so much damaged that I am willing to lose 20 per cent. on the cost. What is the selling price per barrel? What do I lose per barrel? How much Last Ans. $25. do I lose in all? 23. Cost price $1.40, rate per cent. of Loss 14. What is the selling price? Ans. $1.20 24. A butcher buys a fat ox weighing 640 lb. at 61 cts. per pound. What amount of money will he receive if he retails the meat in market at an advance of 663 per cent. on the wholesale price, allowing a loss of 150 lb. for hide and wastage? If he sells the hide for $5.00, what does he clear in the transaction? Ans. 16.041 |