NOTE. As the multiplier contains three decimal places and the multiplicand four, the product has 3 + 4 or seven places as is

seen.

59. RULE. Place multiplier under multiplicand without paying attention to decimal points. Multiply as in whole numbers, and point off as many places in the product as there are in both multiplicand and multiplier, prefixing ciphers if necessary.

(11) A U. S. gallon of water weighs 8.355 pounds. What

is the weight of 17.3 gallons?

Ans. 144.5415 lbs.

(12) A steamship sailed at an average speed of 325.75 miles per day. If another steamer sailed from the same port at the same time at the rate of 395.35 miles per day, how far apart were they in 5.75 days? Ans. 400.2 miles (13) A cubic foot of water weighs 62.5 pounds. How much will 177.35 cubic feet of water weigh? Ans. 11084.375 lbs. (14) The stroke of an engine is 3.117 feet. It makes 107 revolutions per minute. Over what total distance will the crosshead travel in 4.5 minutes? Ans. 3001.671 ft.

NOTE. There are two strokes for each revolution.

DIVISION OF DECIMALS.

60. In division of decimals we pay no attention to the decimal point until after obtaining all the figures of the quotient. We first make sure that there are as many decimal places in the dividend as there are in the divisor. This we accomplish by annexing ciphers to the dividend until it has as many decimal places as the divisor, unless the dividend has as many as, or more decimal places than the divisor, in which case the operation is unnecessary. We then divide exactly as with whole numbers. Finally, subtract the number of decimal places in the divisor from the number of decimal places in the dividend, and point off the resulting number of places in our quotient. The following are illustrations of the process.

NOTE. As there are no decimal places in the divisor and three in the dividend, we have nothing to subtract from three, so that the number of decimal places in the quotient is three.

Divide .196 by .004.

.004).196(49

16

36

NOTE.

36

0

We have here the same number of decimal places in both dividend and divisor. For this reason there are no places to be pointed off in the quotient and hence it is a whole number. Divide 794 by .25.

.25)794.00 (3176

75

44

25

190

175

150

150

0

NOTE. We here add two ciphers to the dividend so as to have the same number of decimals in dividend and divisor. Then dividing we obtain a whole number.

Let us observe this example a little further. The divisor, .25, equals or 1. If we divide by the result is the same as

5

0

when we multiply by 4.

Multiplying 794 by 4 we obtain 3176.

Divide .0027 by 1.35.

1.35).00270(.002

270

0

NOTE. In dividing, as usual, we consider the figures as whole numbers. Now, 135 is not contained in 27. We have seen that to add a cipher does not change the value of a decimal. We add a cipher to the dividend. Then we have 270 as a dividend and the divisor 1.35 is contained twice. Since we have added a cipher to the dividend it has five decimal places. The divisor has two. Hence the quotient must have 5 -2 or three decimal places. In order to have three decimal places we prefix two ciphers to the quotient 2 and place the decimal point in front of them.

We may use this method in dividing the smaller of two numbers by the larger.

Divide 35 by 125.

125)35.00(.28

250

1000

1000

0

NOTE. In order to divide 35 by 125 we have annexed two ciphers. We then get an answer and no remainder. By annexing the two ciphers we get two decimal places. Therefore, as there are two decimal places in the dividend and none in divisor we have two decimal places in the quotient (.28).

Let us perform the division another way.

This further illustrates the relations of the two methods.

RULE. Proceed as in division of whole numbers, but point off in the quotient as many decimal places as the number of decimal places in the dividend exceeds the number of decimal places in the divisor, prefixing ciphers to the quotient when necessary.

NOTE. In division it is usually best to carry on the division to three or four decimal places by annexing a sufficient number of ciphers to the dividend, and then, if there is a remainder, to signify the fact by the sign +