CHAPTER VI REVIEWING AND EXTENDING THE WORK IN DECIMALS EXPRESSING REMAINDERS IN DIVISION You have expressed remainders as common fractions in short division. You have also seen in Chapter IV how to express them as decimal fractions. In practice, remainders are never expressed as common fractions when the divisor is large. 1. In a school of 585 pupils $2075 was deposited in the school bank one month. Find the average amount deposited per pupil. 2. During 68 da. of a summer vacation, a boy earned $49. How much did the earnings average per day? 3. Mr. Jones sold a farm of 56 acres for $4000. Find the average price per acre. 4. Helen's brother earned $265 in 43 da. How much did that average per day? EXPRESSING REMAINDERS IN DIVISION 149 5. In a corn-raising contest in Alabama, a total of 98 acres was planted by the contestants. The total yield of all was 10,346 bu. Find the average yield. 6. A pig ate 312 lb. of feed to gain 36 lb. in weight. Find to hundredths the amount of feed that it took for every pound of increase in weight. 7. John took a 3-day automobile trip with his father. By taking out the time of all stops, they actually traveled 26 hours. The speedometer showed that they had traveled 513.8 miles. Find to hundredths of a mile their average speed. 26)513.80 Here but one zero had to be annexed in order to carry the result to hundredths. Why? When the divisor is a whole number, the decimal point in the quotient comes directly above the decimal point in the dividend, just as in dividing dollars and cents. Look at these and tell how many digits in the quotient before READING DECIMALS OF MORE THAN TWO PLACES The division may be carried beyond the second place to any place desired. To read decimals remember that The first place to the right of the decimal point is tenths' place; the second hundredths' place; the third thousandths' place; and the fourth place ten thousandths. REDUCING FRACTIONS TO DECIMALS 151 REDUCING FRACTIONS TO DECIMALS Unless the terms of a fraction are small, they are more easily added, subtracted, multiplied, or divided when expressed as decimals. 1. Multiply 14 by 38 after reducing to a decimal. .3125 16)5.0000 48 20 16 40 32 80 14.3125 38 114 5000 429 375 543.8750 5 A common fraction is reduced to a decimal by dividing the numerator by the denominator. So = .3125, read "3125 16 ten thousandths." However, the name of such decimals is seldom read. .3125 is more often read, "point, three, one, two, five." In reading this product, the zero is not named. It is read "875 thousandths" or "point, eight, seven, five." 14. Express 7 oz. as a decimal of a pound. Tell what simple common fraction the following decimals nearly equal, telling whether they are more or less than the fraction you name. REDUCING, ADDING, AND SUBTRACTING DECIMALS Just as fractions may be changed to larger terms without changing their value, so may decimals. .5 is 5 tenths, and .50 is 50 hundredths, which has the same value, for .50 is 5 tenths and no hundredths. Also .37 is not changed by annexing a zero, for .370 is still 37 hundredth and no thousandths. And, in general, Annexing zeros to a decimal does not change its value. Thus .4 = .40 .400; and 2.17 2.170 2.1700. = = = |