WRITTEN EXERCISES.

259. To Multiply Decimals.

1. Multiply .29 by .7.

ANALYSIS.—Multiplying the decimals as integers the product is 203; but as the multiplicand has two decimal figures and the multiplier one, the product must have three. (Art. 258.) Hence, the

.29

.7

.203, Ans.

and from

RULE.-Multiply the numbers as integers, the right of the product point off as many figures for decimals as there are decimal places in both factors.

NOTE.-If the product has not as many figures as there are decimals in both factors, supply the deficiency by prefixing ciphers.

17. What cost 465 pounds of coffee, at 31 cts. a pound?

18. Find the cost of 608 pounds of tea, at 87 cts. a pound. 19. Find the cost of 563.5 tons of hay, at $6.75 a ton.

260. When the Multiplier is 10, 100, 1000, etc.

20. Multiply 4.506 by 100.

ANALYSIS.-Moving a figure one place to the left multiplies its value by 10 (Art. 34, 2°), hence, moving the decimal point one place to the right multiplies the number by 10, moving it two places, multiplies the number by 100, etc. Hence, the

OPERATION.

4.506

100

Ans. 450.600

RULE.-Move the decimal point in the multiplicand as many places to the right as there are ciphers in the multiplier. (Art. 91.)

21. Mult. 46.3842 by 1000. 22. Mult. 6.42302 by 1000.

23. Mult. 25.46 by 1000.

24. Mult. 3.004 by 1000,

261.

DIVISION OF DECIMALS.

DEVELOPMENT OF PRINCIPLES.

1. What is the quotient of .8 divided by .2 ? ANALYSIS.-.8 and .2 . Now foo = 4, Ans.

2. What is the quotient of .06 divided by .03?

3. When tenths are divided by tenths, and hundredths by hundredths, what is the quotient? Why?

Ans. Because they have common denominators. (Art. 224, 2°.) 4. The product of two numbers is 3.2 and one of the factors is 4; how do you find the other factor? (Art. 114.)

5. Of what is division the reverse? (Art. 101.) 6. What corresponds to the product? To the factors? 7. What is the product of .06 by .4? How many decimal figures has it?

8. If .024 is divided by .4, what is the quotient? How many decimal figures has it? Why?

Ans. Since division is the reverse of multiplication, the dividend must have as many decimal figures as the divisor and quotient.

9. How many decimal figures are there in the product of any two factors?

10. When tenths are divided by units, how many decimal figures in the quotient? Hundredths by units? By tenths? Thousandths by hundredths?

11. If the dividend has five decimal places, and the divisor three, how many decimal places will there be in the quotient? 262. From these examples we derive the following

PRINCIPLES.

1o. When the decimal places in the divisor and dividend are equal, the quotient is a whole number.

2o. The number of decimal places in the divisor and quotient must equal those in the dividend.

WRITTEN EXERCISES.

263. To Divide Decimals.

1. What is the quotient of .98 divided by .7? SOLUTION.-We divide as in whole numbers, and point off as many figures for decimals in the quotient as the decimal places in the dividend exceed those in the divisor, which is one. Hence, the

OPERATION.

.7).98

Ans. 1.4

RULE.-Divide as in whole numbers, and from the right of the quotient point off as many figures for decimals, as the decimal places in the dividend exceed those in the divisor.

If the quotient does not contain figures enough, supply the deficiency by prefixing ciphers.

NOTES.-1. When there are more decimals in the divisor than in the dividend, make them equal by annexing ciphers to the latter before dividing. (Ex. 3.)

2. After all the figures of the dividend are divided, if there is a remainder, ciphers may be annexed to it as decimals, and the division continued at pleasure.

3. For ordinary purposes, it will be sufficiently exact to carry the quo tient to four or five places of decimals; but when great accuracy is required, it must be carried farther.

When there is a remainder at the close of the operation, the sign + should be annexed to the quotient to show that it is not complete.

19. If 1.7 yd. of cloth will make a coat, how many coats will 81.6 yds. make?

20. How much broadcloth, at $5.675 a yard., can be bought for $45,40?

to

21. If a stage goes 8.25 miles an hour, how long will it take 125 miles?

go

22. If a barrel of beef is worth $14.25, how many barrels can be bought for $798?

23. If a steamer goes 215.6 miles per day, how long will it take to go 1000 miles?

264. When the Divisor is 10, 100, 1000, etc.

24. Divide 324.56 by 100.

ANALYSIS.-As each removal of a figure one place to the right diminishes its value ten times, moving a decimal point one place to the left divides the number by ten, two places to the left divides it by 100, etc. Hence, the

OPERATION.

100) 324.56

Ans. 3.2456

RULE.-Remove the decimal point in the dividend as many places to the left, as there are ciphers in the divisor. (Art. 34, 3°.)

Perform the following divisions as indicated:

232. What is a Decimal Fraction?. Why called Decimals? 234. How are they expressed? 235. What is the denominator of a decimal? 237. How determine the value of a decimal figure?

236. In writing and reading decimals, what should be made the starting point? 240. How write decimals? How read them?

244. What is the effect of removing the decimal point one place to the left? One place to the right? 244. What is the effect of annexing a cipher to a decimal or removing one from its right?

245. How reduce decimals to a common denominator? 247. How reduce decimals to common fractions? 249. Common fractions to decimals! 254. How are decimals added? 256. How subtracted?

How point off the product?

259. How are decimals multiplied? 263. How divided? How point off the quotient.

265. Coins are pieces of metal stamped at the Mint, authorized by Government to be used as money at fixed values.

266. Money is the measure of value.

267. Currency is the money employed in trade. It consists of coins, bank bills, bonds, bills of exchange, etc.

268. A Decimal Currency is one whose orders or denominations increase and decrease by the scale of tens.