Explanation. Since the denominator contains only the prime factor 2 it may be reduced to an exactly equivalent decimal. It is found necessary to add four ciphers to the dividend and, therefore, there will be four decimal places in the answer.

65. Decimal Equivalents of the Fractions of an Inch. It is often necessary to find the decimal equivalent of a given fraction of an inch. It is convenient to have a table giving these values. Such a table is shown on page 68, but all of the values are not filled in, for the reason that the student is expected to fill in the missing ones as part of the problem assignment of this lesson.

SUMMARY OF CHAPTER VI

33. To add decimals, write the numbers so that the decimal points are in a vertical line, add as with whole numbers and place the decimal point in the result directly under the other decimal points. (Sec. 58.)

34. To subtract decimals, write the minuend and subtrahend so that the decimal points are in a vertical line, subtract as with whole numbers and place the decimal point in the result directly under the other decimal points. (Sec. 59.)

35. To multiply decimals, proceed as though multiplying whole numbers and point off as many places in the product as there are places in both the multiplicand and multiplier. (Sec. 60.)

36. To divide decimals, proceed as though dividing whole numbers, adding ciphers to the right of the decimal point in the dividend if necessary. Point off as many places in the quotient as the difference of the number of places in the dividend less the number of places in the divisor. (Sec. 61.)

37. To change a decimal fraction to a common fraction, supply the denominator 1, followed by as many ciphers as there are figures to the right of the decimal point, and reduce the resulting common fraction to its lowest terms. (Sec. 63.)

38. To change a common fraction to a decimal fraction, place a decimal point after the numerator and add as many ciphers after it as are needed. Then divide the numerator by the denominator and point off as many places in the quotient as there are ciphers added in the dividend. (Sec. 64.)

PROBLEMS

86. Write the following decimals in figures: Sixty-five thousandths, two hundred twenty-five thousandths, fifty-two and two hundredths, five hundred ninety-six and two-tenths, one half of one-thousandth, seven hundred sixty-five and five one-thousandths.

87. Read the following decimals and write them out in words: 622.215, .075, .2865, 1.024, 100.005.

88. Add up the following decimals an check the result by adding down:

91. Divide 4.2 by 3.25 and express the result to three decimal places.

92. Divide 9.035 by 13 and express the result to three decimal places.

93. Reduce the following common fractions of an inch to decimal equivalents: ", 12", }" and 15". These are the values which are missing in the table on page 68 and the student should supply these results in that table.

94. Change the following decimals to common fractions and

1311

711

, 16

reduce the result to lowest terms: (a) .0221, (6) .0638, (c) .6862, (d) .8255.

95. How many times is the length .0725' contained into 16.862'?

96. A carpenter agrees to build a fence 120 ft. long for $45.50. The cost of the lumber is 21.8¢ per lineal foot; the labor cost 7.2¢ per lineal foot and the hardware cost 1€ per lineal foot. What was the actual cost of the fence and what was the profit?

97. California redwood weighs 26.23 pounds per cubic foot. How much will 15 cu.ft. weigh?

98. A circle is 3.1416 times as far around as across it. Find the number of feet around a circle which is 3.1667' across.

a

99. One cubic foot of water weighs 62.5 pounds. Find the part of a cubic foot occupied by one pound of water and express the result in a decimal.

100. If it costs $125 per day to run a gang and a concrete mixer laying 23 cu.yds. of concrete paving material, what is the cost per cubic yard?

CHAPTER VII

THE USE OF RULES. PULLEY SIZES. WIDTH OF BELTS.

FORMULAS. SHORT METHODS OF MULTIPLICA-
TION AND DIVISION

66. Rules. The practical carpenter is often obliged to use a rule in working out some of his problems. Such rules are of two kinds; those which have a rational mathematical basis and those which are the result of experience. Both of these kinds are valuable so long as they are true. Some of the rules are exact and others merely give an approximate result. You must be sure that you know whether a rule is reliable or not before you use it. It pays to be on the lookout for good, reliable rules which will give the desired result with but little work.

67. Rule for Pulley Sizes. The mill-man frequently has to find the speed of a saw, grindstone or belt-pulley. The following rule is a good one to use in a case of that kind.

To find the number of revolutions of a driven pulley in a given time, multiply the diameter of the driving pulley by its number of revolutions in the given time and divide by the diameter of the driven pulley.

Example. A pulley on the main shaft 48" in diameter drives a pulley 26'' in diameter on the counter shaft. The main shaft makes 65 revolutions per minute (r.p.m.). How many r.p.m. does the counter shaft make?