DRILL EXERCISES IN THE MULTIPLICATION OF DECIMALS It is of great importance to the practical accountant to be able to perform multiplication horizontally when one of the factors contains one, two, or even three digits. See § 64. Write down the products of the following without copying the examples: 14. 2.4 X 3.16 39. .6 X 60 41. .0006 X 600 63. 4.6 X .03036 64. .069 X .0128 65. .4888 X .012 66. 42.3 X .25 67. 9.3 X 48.7 68. 4.59 X .023 69. 106.8 X 1.5 70. 96.7 X .82 71. 39.2 X 9.6 72. 77.6 X 1.05 73. 5.2 X .163 MISCELLANEOUS WORK 1. During December, January, February, and March, a family paid bills as follows: Find the total expenses for all these items for each month and also find the total expenses by horizontal addition for the four months. 2. Following is a partial inventory. Copy on a suitable blank, extend, and foot the total values. 3. A man sold a house for $8400, thereby gaining of the purchase price. What was the purchase price? 4. The income from a certain business for two years was $18,500. Find the income for each year if that of the second year was less than that of the first year. 5. Multiply the sum of 3 and 7 by the difference between 18 and 73. CHAPTER XIII REDUCING FRACTIONS TO DECIMALS 158. Common Fractions and Decimals used Interchangeably. It is frequently necessary to change common fractions into decimals. Several examples of this are given in this chapter, and the student can easily find many more. Since a 159. Examples of Reduction of Fractions to Decimals. fraction may be regarded as an indicated division, it follows that it may be reduced to a decimal by carrying out the division. Thus, the decimal value of is found by dividing 3 by 8. Most fractions do not have an exact decimal equivalent. Thus, can be written approximately as .33, or .333, or .3333, etc., but there is no decimal which equals exactly. However, for any given fraction, it is possible to find a decimal which differs from it by as little as we please. Thus, 33 differs from by 30; .333 differs from by 3000; and .3333 differs from 3 by 30000· Example. Reduce to a decimal. .4286 7)3.0000 Carrying the division to four places of decimals, we get .4285 and a remainder 5. (The remainder is really .0005). Since 5 is more than one half of 7, it follows that .4286 is the nearest approximation to four places of decimals. This decimal differs from by less than 10000. Some 160. Combination of Decimal and Common Fractions. times numbers are expressed as combinations of common and decimal fractions. = Thus .33 or .333. The first is read "thirty-three and one third hundredths and the second, three hundred thirty-three and one third thousandths." Similarly = .163, or .1663, or .16663. 161. Important Decimal Equivalents of Common Fractions. — There are certain common fractions whose decimal equivalents should be memorized perfectly. These are: Based on these the decimal equivalents of many other fractions Give the decimal equivalents of the fractions below. Úse two decimal places and give the remainders, if any, as common fractions, Reduce each of the following fractions to a decimal. Give each result correct to four places of decimals. Use long division only 162. Reasons for Reducing Fractions to Decimals. Fractions are reduced to decimals for several reasons. If fractions like 11, 1, 5 9, 17, are to be added, the result may be found more readily by adding their decimal approximations. Thus, f 13 = .272727 = .466667 = .555556 This sum is certain to contain the nearest approximation to four places of decimals. That is, 1.7655 may be taken as the nearest approximation to four places. And 1.76554 is obviously the nearest approximation to five places. By the exercise of a little common sense, we can readily decide how far the decimals need to be carried to obtain a given degree of accuracy in the result. 1 = .470588 1.765538 163. Comparing Magnitudes of Fractions. Another reason why fractions are reduced to decimals is that the magnitudes of numbers can be compared more readily in that form. Example. One ball team has played 37 games and won 21, and another has played 59 games and won 32. Which has won the greater fraction of the games played? The first team has won of its games and the second of its games. It is not all obvious at a mere glance which is greater, or 3. On reducing these fractions to decimals we find .568 and = .542. = State of Wisconsin between the ages In 1911 the number of persons in the of 5 and 24 years inclusive was 972,500. tary schools; 35,914, secondary schools; and 11,827, higher schools. In the same year, the number of persons between those ages in the State of Montana was 142,800, while the numbers attending elementary, secondary, and higher schools respectively were 66,651, 3655, and 545. These numbers do not give any idea as to the comparative school attendance in these states. However, when we know that in Wisconsin .508, .037, and .012 are the fractions of the total number which attend each kind of school, while in Montana these fractions are .467, .026, and .0038, we can make comparisons at once. WRITTEN EXERCISE At a certain stage in the pennant race in the American League the number of games played and won respectively by the various teams were: Boston 73, 46; Chicago 74, 48; Cleveland 78, 41; Detroit 72, 36; New York 70, 36; Philadelphia 70, 25; St. Louis 76, 30; Washington 71, 30. Reduce the fraction of games won by each team to a three-place decimal and arrange the teams in the proper order. |