Written Exercises.

339. Example.— Multiply 9.8 by .06.

SOLUTION.

9.8

.06

.588

EXPLANATION. — Begin with the lowest order of the multiplier, and multiply each order of the multiplicand separately, as in integers.

6 hundredths times 8 tenths are 48 thousandths, or 4 hundredths 8 thousandths; write 8 thousandths, etc.

6 hundredths times 9 ones are 54 hundredths; 54 hundredths and 4 hundredths are 58 hundredths, or 5 tenths 8 hundredths, etc. Prefix the decimal point, giving .588, the product required. Or, since tenths multiplied by hundredths produce thousandths, the product must contain three decimal places, or as many decimal places as are in both factors, giving .588, the product required.

340. Rule for Multiplication of Decimals. Multiply as if the numbers were integers, and from the right hand of the product point off as many figures for decimals as there are decimal places in both factors.

Note 1. - If there are not so many figures in the product as there are decimal places in both factors, supply the deficiency by prefixing ciphers.

2. To multiply by 10, 100, 1000, etc., remove the decimal point in the multiplicand as many places to the right as there are ciphers in the multiplier.

6. 25 times $2.25; 56 times 8.175; 875 times .008.

7. .5 of $9.75; .18 of 5.25 tons; .75 of 100.235.

8. 91.82 × .135; .7364 × 50; .0012 × .12; .009 × .008. 9. 900.125 miles x 81; 70.0876 miles x 8.5.

10. Multiply 5 million and 5 millionths by 5 and 5 millionths; by five thousand five hundred-thousandths.

11. If the multiplicand is four hundred seventy-five hundred-thousandths, and the multiplier is four hundred and seventy-five hundred-thousandths, what is the product?

12. What is the product of .7 x .07 x .007? 700 × 70 x .7? 100.01 x .01 x .001? 10000 x .0001 × 1.0001? 13. If a bushel of wheat weighs 60.75 pounds, what is the weight of 10 sacks, each containing 3 bushels?

14. If a horse can eat 1.3125 bushels of corn in a week, how many bushels are needed for 15 horses for 13 weeks? 15. Find the sum of .004 of $5000+ $.025 × 25000. 16. Multiply 2000 by .002. To their product add their From their difference take their product.

sum.

17. A grocer bought a barrel of flour, 196 pounds, at $.041⁄2 a pound, and retailed it at $.05 a pound. What did he gain?

18. If a merchant buys a case of silk containing 16 pieces, at $53.25 a piece, and pays $1.25 for the box, what is the whole cost? What is gained by selling at $53.371⁄2 a piece?

4. How many times are 2 tenths contained in 8 tenths?

5

5. Divide by 180; 180 by 1800 ; .6 by .06; .08 by .008. 6. What is the quotient of 2.4 divided by 8?

341. Analysis. — In 1 are 10 tenths, and in 2 are two times 10 tenths, which are 20 tenths; 20 tenths and 4 tenths are 24 tenths; of 24 tenths is 3 tenths. Hence, etc.

7. Divide 3 by .6; .3 by 6; .03 by .6; .006 by .03.

8. The product of two factors is .015, and one of the factors is .5. What is the other factor?

9. The dividend is the product of what two factors? The dividend contains as many decimal places as what two factors?

10. Of what order is the quotient, if ones are divided by ones? Tenths by ones? Tenths by tenths? Hundredths by ones? Hundredths by tenths? Thousandths by tenths? 342. Principle.

The number of decimal figures in the quotient equals the number of decimal places in the dividend, less the number of decimal places in the divisor.

SOLUTION. 9)3.015 .335

EXPLANATION.-3.015 equals 3015 thousandths; and of 3015 thousandths is 335 thousandths, or .335, the quotient required. Or,

Divide as in division of integers; and since the dividend contains three decimal places, and the divisor has no decimal places, the quotient must have three decimal places.

344. Example 2.- Divide .625 by 2.5.

SOLUTION.

2.5).625(.25

50

125

125

EXPLANATION. - Divide as in division of common fractions (301).

.625 625 and 2.5= 25; and .625 ÷ 2.5

625

1000

1000'

=

the quotient required. Or,

Divide as in division of integers; and since the dividend contains three decimal places, and the divisor one decimal place, the quotient must have two decimal places.

345. Rule for Division of Decimals.

Divide as if the numbers were integers, and from the right hand of the quotient point off as many figures for decimals as

the number of decimal places in the dividend exceeds the number of decimal places in the divisor.

Note 1. — If the number of figures in the quotient is less than the difference between the number of decimal places in the dividend and the number in the divisor, supply the deficiency by prefixing ciphers.

2. If the dividend has not so many decimal places as the divisor, make the number equal by annexing decimal ciphers before commencing to divide.

3. If there is a remainder after all the figures in the dividend are used, the division may be continued by annexing ciphers, each cipher annexed adding one to the number of decimal places in the dividend. Four or five decimals in the quotient are generally enough.

4. To divide by 10, 100, 1000, etc., remove the decimal point in the dividend as many places to the left as there are ciphers in the divisor (157).

Problems.

(4)

9)72.9(31)7.29(25).625( 75)9.375(38)467.4

(6)

(3)

(7)

(5)

(8)

3.5)4.725 miles (2.73) 8.8998 tons (3.28)$6018.80(

Find the value of―

9. .6755; 81.25 ÷ 25; 82÷ 16; .0496 ÷ 18. 10. .025 2.5; .0025.25; 25.25; 25 ÷ .0025. 11. .05 100; .007 2000; 700.0002; 1÷.00001. 12. $300.75 25; $500÷.625; 1760 yards.44 yards. 13. Divide one by one hundredth; one hundredth by one thousand; one hundred-thousandth by one hundredth.

14. What is the quotient of two thousand five millionths divided by four hundred one? By 401 hundred-thousandths? 15. If the dividend is 990 and the divisor is 2.475, what is the quotient? If the divisor is .0495?

16. What is the divisor if the quotient is .3243, and the dividend is 3243? If the dividend is 32.43?

17. If 144 bushels of wheat cost $316.80, what is the price of 1 bushel? If 75 bushels cost $159.375?

18. How many bins, each holding 100.25 bushels, are needed to contain 2005 bushels of wheat? 802 bushels? 19. How many bottles are needed to hold 21.5 gallons of cologne, if each bottle contains .03125 of a pint?

20. (500 x .05).005; 1-(.006 600 x 1000) = ? 21. From the quotient of 300 by .003 take their difference. 22. Divide 10 thousandths by 10 thousand, and multiply the product by the difference between 5 tens and 5 tenths.

23. Divide 6 thousand by 6 thousandths, and multiply the quotient by 400 times 25 ten-thousandths.

24. If 8 yards of silk cost $18.0625, how much will 133 yards cost? 20.5 yards? 50.05 yards?

25. In four days a merchant's sales were $12.75, $800.50, $75.37, and $1500.251. What were his average daily sales?

UNITED STATES MONEY.

346. United States money is the legal money, or currency, of the United States.

348. The Dollar is the principal unit of United States

money.

Notation and Numeration of United States

Money.

349. Dollars are written as integers, with the dollar sign ($) prefixed.