2. What is the value of: 1. 13.2 × 2.475. 2. .132 × 2.475. 5. .008 X 751.1. 39. 3 hundredths 20. 8.47 X 9.432. 21. .84 X 9.60. 27. 1561 × .625. 40. Four hundred thousand two hundred sixty-eight ten-millionths by two hundred sixty and two hundred seventy-five thousandths. THE DECIMAL POINT AS A MULTIPLIER. 1. .0004 X 10 = what? 10 what? 000.4 X 10 2. Since .0004 × 10 = 0.004 and 0.004 × 10 00.04, how does the decimal point become a multiplier? 3. To become a multiplier, does it move toward the right or the left? 4. Its removal one place to the right multiplies the number by what? Its removal two places multiplies by what? Three places? PRINCIPLE. Every removal of the point one place toward the right multiplies the number by ten. RULE. To multiply by a number consisting of 1 with ciphers annexed, remove the decimal point as many places towards the right as there are ciphers in the multiplier. EXERCISES. 1. Multiply .394 by 100. Process. 39.4 Explanation. Since the multiplier is one with two ciphers annexed, we remove the decimal point two places towards the right, and have 39 and 4 tenths as product. 1. 57 horses, at $86.375 each. 2. 200 barrels of flour, at $8.53 each. 4. 236 bushels of oats, at $.515 a bushel. 5. 363 bushels of clover seed, at $4.52 a bushel. 7. 280 barrels of apples, at $33 a barrel. 8. 100 cords of wood, at $5.47 a cord. 9. 305 acres of land, at $823 an acre. 2. A lady made the following purchases: 47 yards of sheeting, at $.141 per yard; 9 yards of ribbon, at $.451 per yard; 38 yards of silk, at $3.46 per yard. What did her purchases cost her? 3. Multiply six hundred twenty-five ten-millionths by three and eight thousandths. Since one factor of .54 is .6, what is the other factor? = Since .54.6 .9, how does the number of decimal places in the dividend compare with the number in the divisor and quotient? 2. .054.09 × .6. Assuming .054 to be a dividend and .09 to be a divisor, what is the quotient? Since the dividend has 3 decimal places and the divisor 2, how can you operate with 3 and 2 to find the number of places in the quotient? PRINCIPLE. The number of the decimal places in the quotient equals the number of places in the dividend minus the number in the divisor. EXERCISES. 1. Divide 82.32 by 2.1. Process. 392 39.2. Or, dividing without regard to the decimal point, we have 392 as quotient. Since the dividend has two decimal places and the divisor one, the quotient has one; hence the quotient sought is 39.2. RULE. Divide without regard to the decimal point, but finally point off from the right of the quotient as many figures for decimals as the number of decimal places in the dividend exceeds the number of those in the divisor. NOTES.-1. When the quotient does not contain as many figures for decimals as the rule requires, supply the deficiency by prefixing ciphers. 2. Before beginning to divide, it is best to make the number of decimal places in the dividend at least equal to the number of decimal places in the divisor. 3. When the process of division has used only as many decimal places of the dividend as equal the number of decimal places of the divisor, the quotient will be an integer. 4. .5964 by 35 (Note 1). 16. .003125 by .125. 5. 26.01 by 51. 6. .456 by .06. 17. .03759 by .01253. 18. .13 by .026 (2 and 3). 7. 4375 by .25 (Note 2). 19. .75 by .025. does the decimal point become a divisor? 3. To become a divisor, does the decimal point move towards the right or the left? 4. Its removal one place to the left divides the number by what? Its removal two places divides the number by what? Three places? PRINCIPLE. Every removal of the point one place toward the left divides the number by ten. RULE. To divide by a number consisting of 1 with ciphers annexed, remove the decimal point as many places toward the left as there are ciphers in the divisor. EXERCISES. 1. Divide 48.26 by 100. Process. .4826 Explanation. Since the divisor is 1 with two ciphers annexed, we remove the decimal point two places toward the left, and have .4826 as quotient. 2. Divide: 1. 534.79 by 100. 6. 4956.74 by 10,000. |