3. Pointing off two decimal places in a number affects its value how? Three places? Four places? 4. How many decimal places must we point off in a number to divide it by 10? by 1000? by 100? by 10000? 5. Divide 12,468 by 10; by 100; by 1000; by 10,000. 6. Divide 367.54 by 10; by 100; by 1000; by 10,000. 7. How may any integer be divided by 10? by 100? by 1000? 8. How may any decimal be divided by 10? by 100? by 1000? 6912 8.53632 853632 2.47 = 247 ÷ 100 3.456 × 2.47 = 3456 × 247 = 3456 × 247 ÷ 1000 ÷ 100 853632 + 1000 ÷ 100 = 8.53632 We divide 853,632 by 1000 and 100 by pointing off 3 + 2, or 5, decimal places. Summary To multiply decimals, multiply them as integers. Point off in the product as many decimal places as there are decimal places in both factors. If the number of figures in the product is less than the required number of decimal places, prefix ciphers. 1. One factor has three decimal places, the other four. How many has the product? 2. The product has four decimal places, the multiplicand How many has the multiplier? one. 3. The product has six decimal places, the multiplier three. How many has the multiplicand? 4. The product has four decimal places. What could be the number of decimal places in each of the factors? 64. Written 1. Divide 27.3587 by 4.7. 5.821 4.7 27.3587 235 385 376 98 94 47 47 The quotient and divisor are factors of what? When the product and one factor are known, how may the number of decimal places in the other factor be found? Summary To divide decimals, divide as with integers and point off in the quotient as many decimal places as there are in the dividend, minus the number of decimal places in the divisor. If the dividend contains fewer decimal places than the divisor, annex ciphers to make the required number. NOTE. It has been found helpful to make a dot, before dividing, as many places to the right of the decimal point in the dividend as there are decimal places in the divisor, and on a line with the tops of the figures, making the decimal point in the quotient directly over this dot, thus: 65. Find the quotients correct to three decimal places: An expression written within, or included by, any of these signs is to be treated as a single number. 67. The operations indicated within a sign of aggregation must be performed before those operations indicated outside the sign; e.g. 40 × (9 −6) ÷ [2 + 4] = 40 × 3 ÷ 6 = 20 68. When several successive operations are indicated without the use of signs of aggregation, the indicated multiplication and division must be performed before the indicated addition and subtraction; e.g. 70. Written Perform the operations indicated: 4. 2.03 x 607.015-59.6034 5. 487 +598 + {6.45 − (20.3 −14.35)} 6. 41.983 — .87 × 10.3 +.047 7. (41.983.87) × [10.3 + .047] 8. 2310÷[10 × .7] + 604 × 3.50 9. 378.34-58.7649.83 x 64.8-6.48 × 71. Indicate the operations and solve: 1. The difference between 496.37 and 288.037, multiplied by the quotient of 183.75 divided by 2.5. 2. A grocer bought a load of potatoes containing 48 bushels, at 65 cents a bushel, and sold them at 80 cents a bushel. What was his profit? 3. The product of three numbers is 18.902. Two of the numbers are .02 and 130. Find the other. 4. A machinist earns $1080 a year. In how He pays $180 a year for rent, $306 for food, and $369 for other expenses. many years, at that rate, can he save $900? 5. What number divided by 20.8 will give the quotient 85 and the remainder 11.7? 6. A city lot worth $1200 and three carriages at $190 each were given in exchange for 30 acres of land. At what price per acre was the land valued ? |