DRILL TABLE No. 5. (See Supplement, Art. 1.) 242. For supplementary practice in fractions. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 D 5 4 7 4 63 3 2 15 31 43 61 13 4 4 3 D 10 352–366. Divide B by C. 367-381. Divide D by A. 217-231. Take B from D. 232-246. Take B + C from D. 382-396. Multiply C by A by B. 442-456. C = 3 of what? 457-471. D= & of what? 472–486. A × C = { of what? 487-501. 4 x D is How do you find what part one number is of another? of what? What effect does multiplying the numerator of a fraction have upon the fraction? Why? In what other way could you produce the same effect, and why? What effect does dividing the numerator have upon a fraction? Why? In what other way could you produce the same effect, and why? SECTION X. DECIMAL FRACTIONS. 243. A decimal fraction is one or more of the decimal parts ox a unit, as 1 tenth, 2 hundredths, 25 thousandths, etc. NOTE.-Some elementary applications of Decimals were treated with integral numbers. (Art. 27–30, 44, 60, 89, 135.) In this section are given applications which require a knowledge of principles taught in common fractions. 244. To read and write decimals. The manner of reading and writing decimals is taught in Art. 29 and 30. The following table shows the correspondence between the names of decimals and integers : Name the orders of decimals from tenths to millionths; from millionths to tenths. Illustrate the manner of reading and writing decimals. How are integral numbers and decimals read when written together? Exercises in Reading and Writing Decimals. 245. Read or write in words the following: Write in figures the following: 25. 208 ten-thousandths. 26. 1, and 45 thousandths. 27. 18 ten-thousandths. 29. 648 millionths. 30. 6 thousand 48 millionths. 31. 41 hundred-thousandths. 28. 582 hundred-thousandths. 32. 8, and 4003 millionths. 33. 45, and 673 millionths. 34. 5 thousand, and 51 thousandths. 35. 6 hundred, and 48 millionths. 36. 10 million, and 75 ten-millionths. Write in decimal form 347 37.5; 54; 28100; 10500; 4180; 31000; 10000; 1004000 331 38. Write 15, and Ans. 4.5; 0.331. 100 135 4368, 3331 10 100 39. Write 18; 33; 188; 1888; Write the following in decimal form, each example as one number: 1000 40. 10, 180, and 10‰· 41., Too, and 18. 42. 100, 1000, and 1. 43. 10, 1000, 10800, and 180. 44. 18, 180, 10800, and 1000. 45. 50, 100, 1008000, and 10000. a. What is the denominator of the decimal 0.1? 0.25? 0.41? 4.0075 ? b. What are the numerators of the above decimals? REDUCTION OF DECIMALS. 246. To change decimals to lower denominations. Illustrative Example. Change 0.26 to thousandths; to millionths. WRITTEN WORK. 0.26 0.260 = 0.26 0.260000 = To express a decimal in a lower denomination, annex zeros to the given expression until the place of the required denomination is filled. Ans. 0.260; 0.260000. 46. Change 4 to tenths; to hundredths; to thousandths. 47. Change 0.7 to thousandths; to millionths. 48. Change 4.5 to hundredths; 9.27 to ten-thousandths. 49. Express 5, 32, and 465 each as tenths; as thousandths. 247. To change decimals to common fractions. Illustrative Example. Change 0.75, 0.875, and 0.371⁄2 each to common fractions in their simplest forms. 248. To change common fractions to decimal fractions. Illustrative Example. Change ğ to a decimal. WRITTEN WORK. 8)5.000 of 1 equals of 5 (Art. 180). 5 equals 50 tenths, 500 hundredths, or 5000 thousandths. of 5000 thousandths is 625 thousandths. Ans. 0.625. 249. From the preceding example may be derived the following Rule. To change a common fraction to a decimal fraction : Annex zeros to the numerator and divide it by the denominator. ADDITION AND SUBTRACTION OF DECIMALS. For addition and subtraction of decimals, see Arts. 44 and 60. 250. Illustrative Example. Change and to decimals and add them. WRITTEN WORK. = 0.375 = Changed to decimals, &= 0.375 and 0.45, the sum of which is 0.825. Ans. 0.825. Change the following to decimals, and add in lines and 5 64. ++? 70. 3+1+1=? 76. 7 + 10 + 10 =? ㄍㄨ 16 = ?+?+?=? 25 ? +? +?=? 4 ? + ? +? = ? 251. Illustrative Example. Change 6 and 4 to deci Neither nor can be completely expressed in decimal form; however far the division is carried, there will still be a remainder. Whenever the denominator contains factors other than 2 and 5, the division is interminable. Further explanations of such fractions will be found in the Supplement, Arts. 11-14. |