MULTIPLICATION.

145. Each removal of the decimal point one order toward the right multiplies by 10.

For, cach figure is made by the removal to denote units of an order next higher; hence the value expressed is made ten'fold (Art. 33).

Thus, .08 X 10.8; .8 X 108; .306 X 100 = 30.6.

146. Each removal of the decimal point one order toward the left divides by 10.

For, each figure is made by the removal to denote units of an order next lower; hence, the value expressed is made one tenth as much as it was.

Thus, 6.5 10.65; .65 ÷ 10 = .065; 73.4100 .734

One or both of the Factors Decimals. 147. 1. Multiply 3.16 by .4.

OPERATION.

3.16
4

3.16 multiplied by 4 gives 12.64; but as the multiplier is .4, the product must be only a tenth as large, and 12.64 divided by 10, by removing the decimal point one order to the left, Ans. 1.264 gives 1.264. Therefore, the product of 3.16 by

.

.4 is 1.264.

Rule.-Multiply as in integers, and point off as many figures for decimals in the product as there are in both multiplicand and multiplier, supplying the deficiency, if any, by prefixing ciphers; or,

What effect has the removal of a decimal point one order towar the right? One order toward the left? Explain the operation Recite the Rule.

If the multiplier is a decimal, multiply by its numerator, and divide by its denominator.

When the multiplier is 10, 100, 1000, etc., remove the point to the right as many orders as there are ciphers on the right of the multiplier.

17. What cost .65 of an acre of land, at $84 an acre?

Ans. $54.60.

18. Multiply 12 hundredths by 8 thousandths. 19. What cost 18.75 barrels of flour, at $6.75 a barrel?

20. Find the value of .1 X .1 X .1.

Ans. $126.5625.

Ans. .001. Ans. .000602.

Ans. $2.28125.

21. Find the value of .0002 X 3.01. 22. What cost 18.25 yards of cambric, at $0.125 a

yard?

23. When $14.56 is the cost of a load of coal, what is the cost of 2.25 loads?

Ans. $32.76.

How do you multiply by 10, 100, 1000, etc.?

24. Multiply thirty-six units and forty-eight hundredths, by four hundred seventy-five thousandth.

DIVISION.

148. Since the dividend is equal to the product of the divisor and quotient, it must have as many decimal figures as there are in both divisor and quotient. Hence,

The quotient must have as many decimal figures as the number of decimal figures in the dividend exceeds that in the divisor.

149. 1. Divide 1.264 by .4.

OPERATION.

.4)1.264

Ans. 3.16

1.264 divided by 4 gives .316; but, as the divisor is .4, the quotient must be ten times as large, and .316 multiplied by 10, by removing the decimal point one order to the right, gives 3.16. Therefore, the quotient of 1.264 divided by .4 is 3.16.

2. Divide .00115 by .05.

OPERATION.

05).00115

.023

.00115 divided by 5 gives .00023; but, as the divisor is .05, the quotient must be one hundred times as large, and .00023 multiplied by 100, by removing the point two orders to the right, gives .023. Therefore,

the quotient of .00115 divided by .05 is .023.

Rule. Divide as in integers, and point off as many figures for decimals in the quotient as the number of decimal figures in the dividend exceeds that in the divisor, supplying the deficiency, if any, by prefixing ciphers; or,

What is the dividend equal to? How many decimal figures must the quotient have? Explain the operation. Recite the Rule.

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

When the divisor is 10, 100, 1000, etc., remove the point to the left as many orders as there are ciphers in the divisor.

150. When the number of decimal figures in the divisor exceeds that in the dividend, annex to the dividend as many ciphers for decimals, at least, as will make the number of decimal figures in both equal.

Here, in Example 14, the division does not terminate. In such cases, after carrying it to a sufficient exactness, denote the incompleteness by annexing the sign.

How do you proceed when the divisor is 10, 100, 1000, etc.? How do you proceed when the number of decimal figures in the divisor exceeds that in the dividend?

15. Divide 2.117 by .0073.

16. Divide 8 by .002.

17. Divide 7.43 by .0079.

18. Divide 89 by .003.

Ans. 290.

Ans. 4000.

Ans. 940.5063+.

Ans. 29666.66+.

19. Find the quotient of 80.3 divided by .22.

20. Find the quotient of 80.3 divided by 2.2.

Ans. 36.5.

21. If 3.5 acres produce 142.1 bushels of corn, what is the yield per acre? Ans. 40.6 bu. 22. How many yards of cotton cloth, at .125 dol lars per yard, can be bought for $46.95?

Ans. 375.6 yd. 23. At .75 dollars a day, how many days must a boy work to earn $141? Ans. 188 days.

24. If you can walk 12.5 miles in one day, how many days will it take you to walk 102.5?

25. Bought 30 pounds of butter for $5.85; how much was that a pound?

Ans. $0.195.

26. Divide one hundredth by one ten-thousandth.

Ans. 100.

REVIEW.

1. Add seven hundred forty-three thousandths, seven hundredths, five units and sixteen ten-thousandths.

Ans. 5.8146.

2. Add eighty-seven units and twenty-nine hundredths, seventy-three units and forty-seven thousandths, three thousand five units and one hundred six ten-thousandths,

REVIEW. What is a Unit? (1.) What is the Unit of a Fraction? Ans. The unit or single thing divided into equal parts.