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NOTE.

-

The given denominate number may also be reduced to a fraction of the required denomination (Art. 170), and then this fraction to a decimal (Art. 187). Thus, 2s. 6d.

=

30 240

= .125£.

EXAMPLES FOR PRACTICE.

2. Reduce 15s. 6d. to the fraction of a pound.

Ans. .775.

3. Reduce 5cwt. 2qr. 14lb. to the decimal of a ton.

Ans. 282.

Ans. .96.

Ans. .775.

4. Reduce 3qr. 21lb. to the decimal of a cwt. 5. Reduce 6fur. 8rd. to the decimal of a mile. 6. Reduce 3R. 19p. 167ft. 72in. to the decimal of an acre. Ans. .872595+.

189. To find the value of a decimal in whole numbers of a lower denomination.

Ex. 1. What is the value of .9875 of a pound? Ans. 19s. 9d.

OPERATION.

.9875

20

There will be 20 times as many ten thousandths of a shilling as of a pound; therefore, we multiply the decimal, .9875, by 20, and reduce the improper fraction to a mixed number by pointing off four figures on the right, which is dividing by its denominator, 10000. The figures on the left of the point are shillings, and those on the right decimals of a shilling. The decimal

1 9.7 5 0 0 12 9.0 0 0 0 .7500 we multiply by 12, and, pointing off as before, obtain 9d., which, taken with the 19s., gives 19s. 9d. for the answer. RULE.-Multiply the decimal by that number which will reduce it to the next lower denomination, and point off as in multiplication of decimals.

Then, multiply the decimal part of the product, and point off as before. Continue in like manner till the decimal is reduced to the denominations required.

The several whole numbers of the successive products will be the

answer.

EXAMPLES FOR PRACTICE.

2. What is the value of .628125 of a pound?

3. What is the value of .778125 of a ton?

Ans. 12s. 6d.

Ans. 15cwt. 2qr. 6lb. 4oz.

4. What is the value of .75 of an ell English?

5. What is the value of .965625 of a mile?

Ans. 3qr. 3na.

Ans. 7fur. 29rd.

189. What is the rule for finding the value of a decimal in whole numbers of a lower denomination?

6. What is the value of .94375 of an acre?

Ans. 3R. 31p.

7. What is the value of .815625 of a pound Troy?

Ans. 9oz. 15pwt. 18gr.

8. What is the value of .5555 of a pound apothecaries' weight? Ans. 63 53 09 1917gr.

MISCELLANEOUS EXERCISES.

1. What is the value of 15cwt. 3qr. 14lb. of coffee at $9.50 per cwt.? Ans. $150.95. 2. What cost 17T. 18cwt. 1qr. 7lb. of potash at $53.80 per Ans. $963.88+.

ton? 3. What cost 37A. 3R. 16p. of land at $75.16 per acre? Ans. $2844.80+.

4. What cost 15yd. 3qr. 2na. of cloth at $3.75 per yard? Ans. $59.53+.

5. What cost 153 cords of wood at $ 4.62 per cord?

Ans. $71.10+.

6. What cost the construction of 17m. 6fur. 36rd. of railroad Ans. $67263.03+.

at $3765.60 per mile? 7. What cost 27hhd. 21gal. of temperance wine at $15.371 per hogshead? Ans. $420.24+. 8. What are the contents of a pile of wood, 18ft. 9in. long, 4ft. 6in. wide, and 7ft. 3in. high? Ans. 611ft. 1242in.

9. What are the contents of a board 12ft. 6in. long, and 2ft. 9in. wide?

10. Bought a cask of vinegar containing $0.37 per gallon; what was the amount?

Ans. 34ft. 54in. 25gal. 3qt. 1pt. at Ans. $9.70+.

11. Bought a farm containing 144A. 3R. 30p. at $97.62 per

acre; what was the cost of the farm?

12. Sold Joseph Pearson 3T. 18cwt.

Ans. $14149.52+.

21lb. of salt hay at

$9.37 per ton. He having paid me $20.25, what remains

due?

Ans. $16.41+.

13. If of a cord of wood cost $5.50, what cost one cord? What cost 7 cords? Ans. $48.71+. 14. If 42 yards of cloth cost $ 12ğ, what cost 173 yards? Ans. $46.18+.

15. The ship Constantine cost $35000; of it was sold to Captain Sampson for $9000; of the remainder to T. Lamb for $9200, and the balance to another person at a profit of $500; what was gained in the sale of the whole ship? Ans. $1200.

PERCENTAGE.

190. PERCENTAGE and Per Cent. are terms derived from per centum, meaning by the hundred.

Percentage is an allowance, at a certain rate, by the hundred.

The Rate per cent. is the rate of allowance by the hundred; as 1 per cent., or 1 hundredth.

The Basis of percentage is the number on which the percentage is reckoned.

Rates per cent. being hundredths may be expressed in the same manner as hundredths in decimal fractions. Thus, 5 per cent is written .05; 25 per cent., .25, &c.

When the rate per cent. is more than 100 per cent. it is expressed decimally as a mixed number. Thus, 103 per cent., equal to 183, is written 1.03.

When the rate per cent. is less than 1 per cent., or less than one hundredth, it may be often conveniently expressed as a complex decimal (Art. 180, Note). Thus, of 1 per cent. may be written .005, or .001; 12 per cent., .122, or .12}, &c.

NOTE.-The sign % is often used, in business, instead of the words per cent.

EXAMPLES.

Write decimally 2 per cent.; 3 per cent.; 5 per cent.; 6 per cent.; 7 per cent.; 8 per cent.; 10 per cent.; 12 per cent.; 15 per cent.; 25 per cent.; 30 per cent.; 40 per cent.; 50 per cent.; 60 per cent.; 75 per cent.; 100 per cent.; 105 per cent.; 115 per cent.; 61 per cent.; 8 per cent.; 20 per cent.; 1 per cent.?of 1 per cent.; of 1 per cent.; of 1 per cent.; of 1 per cent.

191. To find the percentage of any quantity.

Ex. 1. Bought a house for $625, and sold it at 6 advance; what did I gain by the sale?

of

per cent. Ans. $37.50.

190. From what are the terms percentage and per cent. derived, and what the meaning? Define percentage. How is the rate written when more than 100? How when less than 1? If the per cent. is a fraction, or contains a fraction, what is the fraction, if expressed decimally?

OPERATION.

Sum,

$625

Rate per cent.,

Per cent., or gain,

.06 $37.50

Since the rate is 6 per cent. or 18.06, we multiply the $625 by the decimal expression .06, and point off as in multiplication of decimal fractions.

RULE. Multiply the given quantity or number by the rate per cent., expressed as a decimal, and point off the product as in multiplication of decimal fractions. (Art. 185.)

NOTE. If the per cent. contains a fraction that cannot be expressed in an exact decimal, or, if thus expressed, would require several figures, it is more convenient to multiply by it as a complex decimal.

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10. Sent to Liverpool 5000 bushels of wheat, which cost me $1.25 per bushel; but 25 per cent. of the wheat was thrown overboard in a storm, and the remainder was sold at $2 per bushel; what was gained on the wheat? Ans. $1250.

11. T. Page received a legacy of $8000; he gave 19 per cent. of it to his wife, 37 per cent. of the remainder to his sons, and $2000 to his daughters; what sum had he remaining?

Ans. $2082.40.

12. My tailor informs me it will take 10 square yards of\ cloth to make me a full suit of clothes. The cloth I am about to purchase is 14 yards wide, and on sponging it will shrink 5 per cent. in width and 5 per cent. in length. How many yards of the above cloth must I purchase for my 66 new suit"? Ans. 6yd. 1qr. 177na.

13. A man having $ 10000, lost 15 per cent. of it in speculation; what sum had he remaining? Ans. $8500.

191. Explain the operation for finding the percentage of any quantity. The reason for the process? The rule?

SIMPLE INTEREST.

192. Interest is an allowance made for the use of money, or for value received.

The Rate per cent. is the sum paid for the use of $100, 100 cents, 100 £, &c., for any given time, but usually for one year. The Principal is the sum on which the interest is computed. The Amount is the interest and principal added together. Legal Interest is the rate per cent. established by law. Usury is a higher rate per cent. than is allowed by law.

The legal rate per cent. varies in the different States and in different countries.

In Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New Jersey, Pennsylvania, Delaware, Maryland, Virginia, North Carolina, Tennessee, Kentucky, Ohio, Indiana, Illinois, Iowa, Missouri, Arkansas, Mississippi, Florida, District of Columbia, and on debts or judgments in favor of the United States, it is 6 per cent.

In New York, Michigan, Wisconsin, Minnesota, Georgia, and South Carolina, it is 7 per cent.

In Alabama and Texas, it is 8 per cent.

In California, it is 10 per cent.

In Louisiana, it is 5 per cent.

In Canada, Nova Scotia, and Ireland, it is 6 per cent.

In England and France, it is 5 per cent.

NOTE. The legal rate, as above, in some of the States, is only that which the law allows, when no particular rate is mentioned. By special agreement between parties, in Ohio, Indiana, Michigan, Illinois, Iowa, and Arkansas, interest can be taken as high as 10 per cent.; in Florida and Louisiana, as high as 8 per cent.; in Texas and Wisconsin, as high as 12 per cent.; and in California, any per cent. In New Jersey, by a special law, 7 per cent. may be taken in the city of Paterson, and in the counties of Essex, Hudson, and Bergen.

193. To find the interest of $1 at 6 per cent. for any given time.

Since the interest of $1 is 6 cents, or T of the principal, for 1 year, or 12 months, for 1 month it will be of 6 cents, or

192. What is interest? What is rate per cent.? What is the principal? What is the amount? What is legal interest? What is usury? What is the legal rate per cent. in the different States? In Canada, Nova Scotia, and Ireland? In England and France ?

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