1. If the number of figures in the quotient be less than the excess of the decimal places in the dividend over those in the divisor, the deficiency must be supplied by prefixing ciphers.

2. If there be a remainder after dividing the dividend, annex ciphers, and continue the division; the ciphers annexed are decimals of the dividend.

3. The dividend must always contain at least as many decimal places as the divisor, before commencing the division.

4. In most business transactions, the division is considered sufficiently exact when the quotient is carried to 4 decimal places, unless great accuracy is required. 5. To divide by 10, 100, 1000, etc., remove the decimal point as many places to the left as there are ciphers on the right hand of the divisor.

9. Divide 3 by 3; divide 3 by .3; 3 by .03; 30 by .03.

16. Divide fifteen, and eight hundred seventy-five thou

sandths, by twenty-five ten-thousandths.

17. Divide 365 by 100.

18. Divide 785.4 by 1000.

Ans. 6350.

Ans. .7854.

Ans. 1000000.

19. Divide one thousand by one thousandth.

When are ciphers prefixed to the quotient? If there be a remainder, how proceed? If the dividend have less decimal places than the divisor, how proceed? How divide by 10, 100, 1000, etc.?

PROMISCUOUS EXAMPLES.

1. Add six hundred, and twenty-five thousandths; four tenths; seven, and sixty-two ten-thousandths; three, and fifty-eight millionths; ninety-two, and seven hundredths. Ans. 702.501258.

2. What is the sum of 81.003 + 5000.4 + 5.0008 + 73.87563 +1000+25 +3.000548 + .0315 ?

3. From eighty-seven take eighty-seven thousandths.

4. What is the difference between nine million and nine millionths? Ans. 8999999.999991.

5. Multiply .365 by .15.

Ans. .05475.

6. Multiply three thousandths by four hundredths.

7. If one acre produce 42.57 bushels of corn, how many

bushels will 18.73 acres produce?

8. Divide .125 by 8000.

9. Divide .7744 by .1936.

10. Divide 27.1 by 100000.

Ans. 797.3361.

11. If 6.35 acres produce 70.6755 bushels of wheat, what

does one acre produce?

Ans. .000015625.

Ans. .000271.

Ans. 11.13 bushels.

Ans. .

Ans. 267.

Ans. .016.

Ans. .5.

12. Reduce .625 to a common fraction.

13. Express 26.875 by an integer and a common fraction.

16. How many times will .5 of 1.75 be contained in .25 of 171?

Ans. 5. 17. What will be the cost of 3§ bales of cloth, each bale containing 36.75 yards, at .85 dollars per yard?

18. Traveling at the rate of 43 miles an hour, how many hours will a man require to travel 56.925 miles?

Ans. 12 hours.

DECIMAL CURRENCY.

156. Coin is money stamped, and has a given value established by law.

157. Currency is coin, bank bills, treasury notes, etc., in circulation as a medium of trade.

158. A Decimal Currency is a currency whose denominations increase and decrease in a tenfold ratio.

The currency of the United States is decimal currency, and is sometimes called Federal Money; it was adopted by Congress in 1786.

The Coin of the United States consists of gold, silver, nickel, and bronze.

The Gold Coins are the double-eagle, eagle, half-eagle, quarter-eagle, three-dollar and one-dollar pieces.

The Silver Coins are the dollar, half-dollar, quarter-dollar, the twenty-cent, and ten-cent pieces.

The Nickel Coins are the five-cent and three-cent pieces. The Bronze Coins are the one-cent pieces.

1. The mill is a denomination used only in computations; it is not a coin. 2. The trade-dollar is designed solely for commerce, and not for currency. Its weight is 420 grains. The weight of the currency dollar of 1878 is 412 grains.

3. The character $ is supposed to be a contraction of U. S. (United States), the U being placed upon the S.

What is coin? Currency? Decimal currency? Federal money? What are the gold coins of U. S.? Silver? Copper? What are the denominations of U. S. currency? What is the sign of dollars? From what derived?

159. The gold dollar is the unit of United States money; dimes, cents, and mills are fractions of a dollar, and are separated from the dollar by the decimal point; thus, two dollars one dime two cents five mills, are written $2.125.

By examining the table, we see that the dime is a tenth part of the unit, or dollar; the cent a tenth part of the dime or a hundredth part of the dollar; and the mill a tenth part of the cent, a hundredth part of the dime, or a thousandth part of the dollar. Hence the denominations of decimal currency increase and decrease the same as decimal fractions, and are expressed according to the same decimal system of notation; and they may be added, subtracted, multiplied, and divided in the same manner as decimals.

Dimes are not read as dimes, but the two places of dimes and cents are appropriated to cents; thus, 1 dollar 3 dimes 2 cents, or $1.32, are read one dollar thirty-two cents; hence, When the number of cents is less than 10, we write a cipher before it in the place of dimes.

The half cent is frequently written as 5 mills; thus, 24 cents, written $.245.

160. Business men frequently write cents as common fractions of a dollar; thus, three dollars thirteen cents are written $3, and read, three and thirteen hundredths dollars. In business transactions, when the final result of a computation contains 5 mills or more, they are called one cent, and when less than 5, they are rejected.

EXAMPLES FOR PRACTICE.

1. Write four dollars five cents. 2. Write two dollars nine cents.

Ans. $4.05.

3. Write ten dollars ten cents.

4. Write eight dollars seven mills.

Ans. $8.007.

What is the unit of U. S. currency? What is the general law of increase and decrease? In practice, how many decimal places are given to cents? In business transactions, how are cents frequently written? What is done if the mills exceed 5? If less than 5?

5. Write sixty-four cents.

6. Write three cents two mills.

Ans. $0.64.

7. Write one hundred dollars one cent one mill.

8. Read $7.93; $8.02; $6.542.

9. Read $5.272; $100.025; $17.005.

10. Read $16.205; $215.081; $1000.011; $4.002.

REDUCTION.

161. By examining the table of Decimal Currency, we see that 10 mills make one cent, and 100 cents, or 1000 mills, make one dollar; hence,

To change dollars to cents, multiply by 100; that is, annex two ciphers.

To change dollars to mills, annex three ciphers.

To change cents to mills, annex one cipher.

To change dollars and cents to cents, or dollars, cents, and mills to mills, remove

the decimal point and the sign, $.

5. Change $63.045 to mills.

Ans. 63045 mills.

6. Change 16 cents to mills.

7. Reduce $3.008 to mills.

8. In 89 cents how many mills?

162. Conversely,

To change cents to dollars, divide by 100; that is, point off two figures from the right.

To change mills to dollars, point off three figures.

To change mills to cents, point off one figure.

How are dollars changed to cents? to mills? How are cents changed to mills? How are cents changed to dollars? Mills to dollars? to cents?