divisions to be uncovered on the barrel and the remainder will give the number of divisions that the thimble should be turned from zero. Example: Calculate the setting for in. (= .4375 or .437}). First unscrew the micrometer until the 4 is uncovered on the barrel. Then divide the remainder .0375 by .025. This gives 1 and leaves a remainder of .0125. The thimble should, therefore, be unscrewed one full turn or 1 division beyond 4 on the barrel, plus 12.5 divisions on the thimble. PROBLEMS 71. Write the following as decimals: One and twenty-five one-hundredths. Three hundred seventy-five one-thousandths. Three hundred and seventy-five one-thousandths. Seven hundred sixty-five and five one-thousandths. 72. Read the following decimals and write them out in words: .075 .137 100.037 .12 1.09375 73. Find the sum of .2143, 783.5, 138.72, and 10.0041. 74. From 241.70 take 215.875. 75. a. Find the product of 78.8763 .462. b. Multiply 21.3 by .071. 76. a. Divide 187.2421 by 123.42. b. Divide 25 by .0025. 1 16 77. Reduce in. to a decimal and compare with the table. 17 32 78. Reduce in. to a decimal and compare with the table. 1 24 79. Calculate the decimal equivalent of in. 80. Write .8125 as a common fraction and reduce it to the lowest terms. 81. If an alloy is .67 copper and .33 zinc, how many pounds of each metal would there be in a casting weighing 75 lb.? 82. A steam pump delivers 2.35 gallons of water per stroke and runs 48 strokes per minute; how many gallons will it deliver in one hour? 83. The diameter of No. 8 B. W. G. wire is .165 in. and of No. 12 wire is .109 in. What is the difference in diameter of the two wires? What do the letters B. W. G. stand for? 84. A machinist whose rate is 27.5 cents per hour puts in a full day of 10 hours and also 3 hours overtime. If he is paid "time and a half" for overtime, how much should he be paid altogether? 3 4 85. The depth of a thread on a in. bolt with U. S. Standard threads is .065 in. What is the diameter at the bottom of the threads? 86. I want 5000 ft. of in. ☐ (square) steel bars. I find from a table that this size weighs 1.914 lb. per foot of length. How many pounds must I order and what will it cost at $1.85 per 100 lb.? 2 87. Explain how you would set a micrometer for in. over 1000 8 7 in. 88. A 28-tooth 7-pitch gear has an outside diameter of 4.286 in. The diameter at the bottom of the teeth is 3.67 in. How deep are the teeth cut? 89. A 2 in. pipe has an actual inside diameter of 2.067 in. The metal of the pipe is .154 in. thick. What is the outside diameter of the pipe? 90. Read the micrometer shown below in Fig. 7. 44. Explanation.-Percentage is merely another kind of fractions or, rather, a particular kind of decimal fractions, of which the denominator is always 100. Instead of writing the denominator, we use the term "per cent" to indicate that the denominator is 100. When we speak of 6 per cent" we mean To or.06. These all mean the same thing; namely, six parts out of one hundred. Instead of writing out the words "per cent” we more often use the sign % after the number, as, for instance, 6%, which means "6 per cent." Since per cent means hundredths of a thing, then the whole of anything is 100% of itself, meaning 188, or the whole. If a man is getting 40 cents an hour and gets an increase of 10%, this increase will be 10% (or 1% or .10) of 40 cents and this is easily seen to be 4 cents, so his new rate is 44 cents. Another way of working this would be to say that his old rate is 100% of itself and his increase is 10% of the old rate, so that altogether he is to get 110% of the old rate. Now 110% is the same as 1.10 and 1.10X40-44 cents, the new rate. 00 Any decimal fraction may be easily changed to per cent. Here we first change the decimal to a common fraction having 100 for a denominator. Then we drop this denominator and use, instead, the per cent sign (%) written after the numerator. This sign indicates, in this case, 87.5 parts out of 100, or 87.5 The change from a decimal to percentage can be made without changing to a common fraction as was just done. Having a decimal, move the decimal point two places to the right and write per cent after the new number. .625=62.5% .06=6% 1.10=110% If it is desired to use a certain number of per cent in calculations, it is usually expressed as a decimal first and then the calculations are made. For example, when figuring the interest on $1250 at the rate of 6%, we would first change 6% to .06 and multiply $1250 by .06 which gives $75.00. $1250 .06 $75.00 A common fraction is reduced to per cent by first reducing it to a decimal and then changing the decimal to per cent. Example: The force in a shop is cut down from 85 men to 62. of the original number of men are retained? What per cent Therefore, the number of men retained is 72.9% or nearly 73% of the original number of men. If we want to reduce the fraction to per cent, we first get .125 and then, changing this decimal to per cent, we have .125 12.5%. Then of anything is the same as 121% of it, because 12% = 12.5 =}. The following table gives a number of different per cents with the corresponding decimals and common fractions: 45. The Uses of Percentage.-In shop work, the chief use of percentage is to express loss or gain in certain quantities or to state portions or quantities that are used or unused, good or bad, finished or unfinished, etc. Very often we hear expressions like: "two out of five of those castings are bad;" or "nine out of ten of those cutters should be replaced." If, in the first illustration, we wanted to talk on the basis of a hundred castings instead of five, we would say "40 per cent of those castings are bad," because "two out of five" is the same as , =10%, 40%. And in the second case: "90 per cent of those cutters should be replaced." Here, "nine out of ten" == 10%, 90%. If a piece of work is said to be 60% completed, it means that, if we divide the whole work on the job into 100 equal parts, we have already done 60 of these parts or 0% of the whole. 50 = 90 = If a shop is running with 50% of its full force, it means that For of the full force is working. If the full force of men is 1300, then the present force is 50% of 1300 .50X1300=650. If the full force were 700 men, then the 50% would be 350. = Another very common use of percentage is in stating the portions or quantities of the ingredients going to make up a whole. We often see formulas for brasses, bronzes, and other alloys in |