The use of the caret in division of decimals. Many teachers prefer to mark off by a caret as many decimal places from the right of the decimal point in the dividend as there are decimal places in the divisor, and divide as in integers, placing the decimal point directly below or above the caret in the dividend. Thus, .8)5.68.8)5.6,8 7.1 It is evident in the above problem that if both the dividend and divisor were changed so as to make the divisor a whole number, the decimal point in the dividend would be in the place occupied by the caret, and that the decimal point would be placed in the quotient immediately after the numbers to the left of the caret had been used in the process of division. The use of the caret determines the position of the decimal point in the quotient, and at the same time retains the identity of the problem. Thus, Mark off by a caret the same number of decimal places from the right of the decimal point in the dividend as there are decimal places in the divisor. Divide as in integers, placing the decimal point in the quotient immediately after all the numbers to the left of the caret have been used in the process of division. The division is frequently not exact. In such cases the sign + may be placed after the decimal to show that the division is not complete; thus, 1÷ 7 = .142 + Find the sum of the quotients: 38. Divide $.10 by $100. 39. If a stone cutter earns $3.75 a day, how many days I will it take him to earn $311.25 ? 40. If 4275 acres of land cost $1731.375, what is the price per acre? 41. At $. 22 a dozen, how many dozen eggs can be bought for $19.47? 42. If 16 stoves are sold for $292, what is the average price per stove? 43. Divide $.18 by $20. 44. If the wheel of a bicycle is 9.25 feet around, how many times does it turn in going a mile? 45. The product of two numbers is .9375. One of them is .75. What is the other? 46. There are 304 square yards in one square rod. How many square rods are there in a plot containing 559.625 square yards? 47. A merchant, in closing out his stock of goods, sold .371⁄2 of the stock the first month, .35 the second month, and the remainder, $5500 worth, the third month. What was the value of his stock of goods? Changing a common fraction to a decimal. Written Work Since = 45, to change a fraction to fraction to a decimal, consider it a problem in division of decimals. Thus, = 4+5=5)4.0 When the division does not terminate, the quotient may be Thus, 7)3.000__or as an shown as a complex decimal. = 0.4284 BUSINESS APPLICATIONS OF DECIMALS In all business transactions three things must be considered : (1) The quantity of the commodity bought or sold. (2) The price per unit at which it is bought or sold. (3) The total amount paid or received for the commodity. Quantity is measured by standard units established by custom or law; thus, the pound is a unit of weight; the foot or the yard, a unit of length; and the gallon or the barrel, a unit of liquid measurement. The price per unit is the amount of money paid or received for a standard unit of the commodity; thus, when butter is sold at 25 per pound, the standard unit is the pound and the price is 25 cents. 1. What standard is used in measuring grain? butter? eggs? milk? cloth? hay? oil? 2. What unit is used in measuring values in money? How many cents are there in $1? in $1? $1? $? 50% is what part of $1? 20 is what part of $1? 25? 10? 5¢? |