888 30. Three dealers in Babbitt metal bought 1,250 tons of Babbitt, and it was delivered so that one received of it, the second man received of it, and the third man received the remainder. How many tons did each dealer receive? Answer, 375 tons; 4683 tons; 406 tons. 31. Antifriction metal is composed of the following parts: of tin, of zinc, 15 of antimony. In a crank brass containing 87 pounds of Babbitt metal how many pounds of the above metals are contained? Answer, tin, 77,3 pounds; zinc, 3,2 pounds; antimony, 62 pounds. 32 125 219 32. There were 4,015 square feet of heating surface in a certain boiler and 126 square feet of grate surface. How many square feet of heating surface to 1 square foot of grate surface? Answer, 31 square feet. 33. In distributing a bale of waste weighing 100 pounds the storeroom keeper gave of it to the fire rooms, of it to the starboard engine room, of it to the port engine room, and of it to the auxiliary station. How many pounds did each station receive? Answer, 36, 18, 18, 28 pounds. REVIEW OF COMMON FRACTIONS. 1. A man bought a suit case for $63, 3 pair of stockings for $3 a pair, and a pair of shoes for $33; he gave the storekeeper a $20 bill. How much change did he receive? Answer, $8.87. 2. A man can finish a piece of work on a lathe in 12 days by working 8 hours a day. How many hours must he work each day in order to do the work in 8 days? Answer, 1133 hours. 3. What is the value of 630 manhole gaskets at $1 per dozen? Answer, $233. 4. In turning up a piece of work in a lathe it was necessary to remove of the weight of the stock. After it was finished the work weighed 39 pounds. What was the weight of the stock before being turned up? Answer, 62 pounds. 5. If 6 is subtracted from each of the terms of the fraction 4, will its value be decreased or increased, and how much? Answer, 165% (decreased). 3 6. A, B, and C each receive the same salary. During one year A saved of his salary, B saved of his, and C saved as much as A and B together. How much of his salary did C save? Answer, 123 280. 1 7. The storeroom keeper issued, 6, and and of a quantity of soap and then had 26 pounds left. How much did he have at first? Answer, 80 pounds. a 8. There were 100 gallons of oil in tank, worth 35 cents per gallon; of it was used in 1 day, 3 of it was used the next day. What was the value of the oil that remained? Answer, $2.91%. 9. Two ships in making a voyage made the following speed: The first ship steamed at the rate of 13 miles an hour for 5 hours, the second ship at the rate of 143 miles per hour for 4 hours. Which steamed the greater distance, and how much? Answer, the first ship, 14,407 miles. 1200 5 7 10. Three coal passers, A, B, and C, can empty a bunker of coal in 12 hours. A and B can by working together empty it in 18 hours. In how many hours can C alone empty it? Answer, 36 hours. 11. A tank which holds 280 gallons of water is empty. It has a supply pipe which will fill it in 10 hours and a discharge pipe which will empty it in 7 hours. If the supply pipe has been running into it for 4 hours, and then both pipes are opened, in what time will it be emptied? Answer, 9 hours. 12. A and B can overhaul an engine in 12 days. If A can only do three-fourths as much work as B, how long will it take each man to do the work alone? Answer, A, 28 days; B, 21 days. 13. A ship can make 14 miles per hour in still water. In making a trip down the river it was accelerated 3 miles per hour, and was retarded the same amount per hour in coming back up the river. It took 10 hours to make the trip down the river. How long will it take to come back up the river? Answer, 163 hours. DECIMALS. I. The orders of integers decrease from left to right in a tenfold. ratio. Thus, in the number 1,111, 1 thousand is ten times 1 hundred, 1 hundred is ten times 1 ten, and 1 ten is 10 times 1 unit. ORDERS OF DECIMALS. II. 1. The orders may be continued from the order of units toward the right by the same law of decrease. 2. Let the order of units be separated from the order that follows by a point (.). 3. Then in the number 1.111 First, since the 1 to the left of the point is 1 unit, the 1 to the right of the point is 1 tenth, for 1 unit is 10 times 1 tenth. Second, since the first order from the unit is 1 tenth, the second order from the unit is 1 hundredth, for is 10 times. Third, since the second order from the unit is 1 hundredth, the third order from the unit is 1 thousandth, for is 10 times 1000 Fourth, in like manner it may be shown that 1 in the fourth order to the right from the unit is 1 ten-thousandth; 1 in the fifth order to the right is 1 hundred-thousandth; 1 in the sixth order is 1 millionth, etc. NOTE. A number with figures other than 1 might be used as well for the purpose of illustration. 4. The position of the integral and decimal places relative to the unit may be illustrated in the following: 5. The first order on the left of the unit is tens, the first order on the right is tenths, the second order on the left is hundreds, the second order on the right is hundredths, etc. DEFINITIONS. III. 1. A decimal fraction or decimal is one or more tenths, hundredths, or thousandths, etc., written like the orders of integers. 2. A decimal point (.) is placed before the order tenths to distinguish the fraction. 3. Decimal orders increase from right to left and decrease from left to right, the same as the orders of integers. 4. The names of the orders of decimals are similar to the names of the corresponding orders of integers. IV. Conversion of the common fractions 10, 100, 1000, etc., to decimals. Hence: When the denominator is 10, there is one decimal order. 2. is written .01; there being no tenths, the cipher is written in the vacant order. Hence: When the denominator is 100, there are two decimal orders. 3. To 1000 is written .001; there being no tenths or hundredths, ciphers are written in the vacant orders. Hence: When the denominator is 1,000, there are three decimal orders. 4. In a like manner: 10000 is written .0001. 100000 is written .00001. 1000000 is written .000001. Hence: The number of orders in the decimal is always the same as the number of ciphers in the denominator of the common fraction. 5. 1 and are. Written, .11. 10, 100, 1000 are 111. Written, .111. 1000 1111 10, 100, 1000, 10000 are 100%. Written, .1111. Hence: Tenths and hundredths are read as hundredths; tenths, hundredths, and thousandths are read thousandths; tenths, hundredths, thousandths, and ten-thousandths are read ten-thousandths, etc. 6. The numerator of the decimal is the number it expresses, disregarding the decimal point. 7. If there are vacant orders before the numerator, ciphers are written in them. 8. The name of the right-hand order is the name of the decimal. TO WRITE DECIMALS. V. 1. Write two hundred and sixty-five thousandths. Number written: .265. Explanation: First write the numerator, 265, as an integer. The figure 5 must stand in the order thousandths, then the 6 must be hundredths, and the 2 must be tenths; the decimal point, therefore, is placed before the figure 2. 2. Write two hundred and sixty-five millionths. Number written: .000265. Explanation: Write the number 265 as an integer. The figure 5 must stand in the order millionths, then the 6 must stand in the order hundred-thousandths, 2 must be ten-thousandths, and ciphers must be written in the orders thousandths, hundredths, and tenths; the decimal point must be placed before 0 tenths. 3. Write two and sixty-five hundredths. Number written: 2.65. Explanation: Write the numerator, 265, as an integer. The figure 5 must stand in hundredths order, then 6 must stand in the order tenths; the decimal point, therefore, must be placed between the figures 2 and 6. 4. Write four hundred and ninety-eight and two hundred and sixtyfive millionths. Number written: 498.000265. Explanation: First write the decimal as in example 2; then write the integer, placing it at the left of the decimal point. RULE: Write the numerator as an integer. Place the decimal point so that the name of the right-hand order shall be the same as the name of the decimal. NOTE. When the decimal is a proper fraction it is sometimes necessary to prefix ciphers to the numerator. When the decimal is an improper fraction, the decimal point is placed between the two figures of the numerator. In a mixed number, the decimal point is placed after the units order of the integer. Write the following numbers: 5. Twenty-six hundredths. 6. Thirty-five hundredths. 7. Eighty-seven hundredths. 8. Four hundred and nineteen hundredths. 9. Five thousandths. 10. Fifty-four thousandths. 11. Three hundred and four thousandths. 12. Seven thousand two hundred and ninety-three thousandths. 13. Twenty-five and forty-seven thousandths. 14. Two hundred and five ten-thousandths. 15. Four thousand one hundred and twenty-five ten-thousandths. 16. Nine hundred-thousandths. 17. Nine hundred thousandths. 18. Six hundred and five hundred-thousandths. 19. Twenty thousand three hundred and four hundred-thousandths. 20. Seven millionths. 21. Two hundred and three millionths. 22. Three hundred thousand and four millionths. 23. Twenty-four ten-millionths. 24. Eighty thousand and six ten-millionths. 25. Two hundred millionths. 26. Two hundred-millionths. 27. Nine hundred and seven hundred-millionths. 28. Twenty million, twenty thousand and three hundred-millionths. 29. One million ten thousand and one hundred-millionths. 30. One million ten thousand and one hundred millionths. 31. One hundred and six and thirty-seven thousandths. 32. One hundred and one thousandth. 33. Two hundred and twenty-five thousandths. 34. Two hundred units and twenty-five thousandths. 35. Two thousand nine hundred and twenty-nine millionths. 36. Two thousand nine hundred units and twenty nine millionths. 37. One million and five billionths. 38. Two hundred and two billionths. 39. Two hundred units and two ten-billionths. 40. Sixty-five and six thousand and five millionths. 7 41. Change the following common fractions to decimals: fo, fo, 180, 100, 100, 100. 17 42. 87 41 53 100 100 100 1000 1000 1000⚫ 43. 1000, 101 1000 10000 VI. 1. Read .265. 100000, 5 03 1000000⚫ TO READ DECIMALS. Number read: Two hundred and sixty-five thousandths. Explanation: Disregarding the decimal point, the number is two hundred and sixty-five; this is the numerator of the decimal. The right-hand order of the decimal is thousandths; this is the name of the decimal. 2. Read .000265. Number read: Two hundred and sixty-five millionths. Explanation: Disregarding the decimal point, the number is two hundred and sixty-five; this is the numerator of the decimal. The right-hand order is millionths; this is the name of the decimal. 3. Read 2.65. Number read: Two hundred and sixty-five hundredths, or two and sixty-five hundredths. RULE: Disregarding the decimal point, read the number as an integer. Give the name of the right-hand order. NOTE. Before commencing to read the decimal, the right-hand order should be ascertained. A mixed number may be read either as an integer and a fraction or as an improper fraction. Read the following decimal numbers: 4. .029, .341, 2.327, 50.005, 184.173. 5. .0003, .625, .2374, .2006, .0104. 6. 3.0205, 810.2406, 10,720.0905. |