11. What is the product of 9.688 by .24? Ans. 2.6642. 12. What will 56 pounds of coffee cost, at .37 of a dollar per pound?

13. If a box must have a capacity of 24.958 cubic feet to contain a ton of anthracite coal, what must be the capacity of a box that will contain 4.5 tons?

14. What is the weight of 128 cubic feet of common soil, if the weight of a cubic foot is 137.125 pounds?

Ans. 17552 pounds.

SECTION XXVII.

DIVISION OF DECIMALS.

253.-Ex. 1. In 9 tenths of a dollar how many times 3 tenths?

2. How many times 3 tenths is? Is .9?

3. In 42 hundredths of a dollar how many times 6 hundredths of a dollar?

4. How many times is .8 contained in .48? .3 in .06? 5. What is 6 10? .6 10? .6÷.6? .06

.6?

WRITTEN EXERCISES.

254.-Ex. 1. Divide 1.345 by 5.

5)1.345

SOLUTION.-1.345 is 1345 thousandths; of 1345 thou.269 sandths is 269 thousandths, or .269.

2. Divide 1.46 by .25.

25)146.00(5.84

125

210

200

100
100

SOLUTION.-.25 is the same as 2, or 1 X 25. First, divide 1.46 by To, by multiplying by 100, which is done by removing the decimal point in the dividend two orders to the right, making the dividend 146. 146 divided by 25 is 5, with 21 ones remaining. 21 ones are 210 tenths, which divided by 25 is 8 tenths, with 10 tenths remaining. 10 tenths are 100 hundredths, which, divided by 25, is 4 hundredths. Hence, 1.46 divided by .255.84. Or,

Multiplying both the divisor and dividend by 100, the denominator of the divisor, making the divisor a whole number, and then dividing, we have the quotient 5.84, as before.

By the first explanation it appears that in decimals, as in common fractions (Art. 206),

Dividing by a fraction is performed by multiplying by its denominator and dividing the result by its numerator.

By that process in the division of decimals,

The number of decimal orders in the quotient is made as many as there are in the dividend, less the number in the divisor.

3. Divide .5964 by .35.

4. Divide .2601 by 51.

Ans. 1.704.

Ans. .0051.

255. Rules for Division of Decimals.—1. If the divisor is an integer, divide as in integers, and point off as many decimal orders in the quotient as there are decimal orders in the dividend.

2. If the divisor is a decimal, make it an integer by moving the decimal point to the right, and move the decimal point in the dividend as many orders to the right, and then divide. Or,

3. If the divisor is a decimal, multiply the dividend by its denominator and divide the result by the numerator.

When the divisor is 10, 100, etc., the division may be performed simply by removing the decimal point in the dividend as many orders to the left as there are ciphers in the divisor.

5. 325.72 by 958.

Ans. .34.10. 172.8 by .0144.

11. What is the value of 21.17.0073?

12. What is the value of .01562525? Ans. .000625. 13. What is the value of 2.15565 1.05?

14. What is the quotient of 3.672 by .81? Ans. 4.533+.

When, as in the last problem, the division will not terminate, the sign + may be annexed, to indicate that the quotient is not complete. The quotient is then called an approximate quotient.

15. What is the approximate quotient of 45.5 divided by 2100? Ans. .0216+. 16. If you should travel 787.5 miles in 210 hours, at what rate per hour would you travel?

17. If .0001 is a dividend and 1.25 a divisor, what is the quotient?

Ans. .00008. 18. Divide three thousand one hundred twenty-five millionths, by one hundred twenty-five thousandths.

19. If 375 bushels of potatoes be worth as much as 7.5 tons of hay, how many bushels are worth as much as 1 ton?

Ans. 50. 20. A tract of land containing 125.4 acres was sold for 7586.7 dollars; what was the price per acre?

21. How many casks, each containing 31.5 gallons, can be filled from a vat containing 368.25 gallons?

Ans. 11; and 21.75 gallons remain. 22. If 16.284 cubic feet of fire-bricks weigh one ton, how many loads, of a ton each, will a pile of such bricks, containing 333.822 cubic feet, make?

Ans. 20; and 8.142 cubic feet remain.

TEST QUESTIONS.

256.-1. What kind of decimals can be ADDED or SUBTRACTED? What is the rule for addition or subtraction of decimals? What does the decimal point in the result of addition or subtraction mark?

2. In what simple way may the value of a decimal expression be MULTIPLIED by 10? Why does the removal of the decimal point in an expression one order to the right make the value expressed tenfold? What are the rules for multiplication of decimals?

3. In what simple way may the value of a decimal expression be DIVIDED by 10? Why does the removal of the decimal point in an expression, one order to the left, make the value expressed one tenth as large? What are the rules for division of decimals? When is a quotient called an approximate quotient?

UNITED STATES

257. Money is a measure

of value used as a medium of

trade.

BRONZE

258. Coin, or Specie, is metal stamped, and authorized by government to be used

as money.

259. Paper Money consists of Notes,

issued by banks and by the Treasury

of the United States, as substitutes for coin. Treasury Notes of less face-value than one dollar are called Fractional Currency.

260. Currency is the Coin and Notes in circulation as money.

Bullion is uncoined gold or silver. An Alloy is a baser metal mixed with a finer.

The gold and silver coins of the United States are .900 fine, or 9 parts pure metal and 1 part alloy.

261. United States Money is the currency of the United States.

262. The Coins of the United States are made of gold, silver, nickel and bronze.

The Gold Coins are a $1 piece, which at the standard weight of 25.8 grains is the unit of value; a quarter eagle, or $23 piece; a $3 piece; a half-eagle, or $5 piece; an eagle, or $10 piece; a double-eagle, or $20 piece; which coins are legal tender in all payments.

The Silver Coins are the dime, quarter-dollar and half-dollar, which coins are legal tender in all payments not exceeding $5. Also a trade dollar, for commercial uses, which is issued only to depositors of bullion at the Mint, and will not be used for home circulation.

The weight of the half dollar is 192.9 grains, or 12 grams, and of the trade dollar 420 grains; and, as the fineness of both is the same, the intrinsic value of the trade dollar is somewhat greater than that of two silver half-dollars.

The Nickel Coins are a five-cent piece and a three-cent piece, which coins are legal tender in all payments not exceeding 25 cents: The weight of the nickel 5-cent piece is 5 grams, or 77.16 grains.

The Bronze Coin is a one-cent piece, which coin is legal tender in all payments not exceeding 25 cents.

Of

263. Canada Money, or the money of the Dominion of Canada, consists, like United States money, of dollars and cents. this money, 100 cents are 1 dollar.

The Canada coins are the twenty-cent, ten-cent and five-cent pieces, made of silver, and the cent, made of bronze.

264. The Dollar is the principal unit of United States money. Dimes, cents and mills may be written respectively as tenths, hundredths and thousandths of dollars.

265. Dimes, or tenths of cents, are commonly regarded as a number of cents.

Thus, 15 dollars 3 dimes 6 cents 7 mills are written $15.367, and read. fifteen dollars thirty-six cents seven mills.

266. Any decimal of a dollar less than a cent may be read as a decimal of a cent.

Thus, $42.5025 may be read forty-two dollars fifty and twenty-five hundredths cents.