72. Reduce,, 3, 18, 74, 75, and 7 to decimals. 164. A decimal is a fraction, and, if its denominator is written, it will appear as a common fraction. 73. Reduce 0.48 to the form of a common fraction and then to its lowest terms. 74. Reduce 0.125 to its lowest terms. 0.48=4&= 1}, Ans. 100 75. Reduce 0.17 to the form of a common fraction. 77. Reduce 1.5, 3.75, 8.25, 9.125, and 2.0125. (For Circulating Decimals, see Appendix, page 340.) 165. QUESTIONS. 152-4. How are decimals numerated? 157. What are decimals? 158. Do the principles of Common Fractions apply to Decimals? 159. What is the denominator of a decimal? 161. Give the Rule for Multiplication of Decimals. Explain. If the number of figures in the product is less than the number of decimal places in both factors, what must be done? Pointing off in the product is really doing what? 162. Give the Rule for Division of Decimals. Explain. If there are not as many decimal places in the dividend as in the divisor, what must be done? If the number of places in the quotient is less than the excess of decimal places of the dividend over those of the divisor, what must be done? Pointing off in the quotient is really doing what? How can the rule for pointing off in Division of Decimals be explained by reference to the rule in Multiplication of Decimals? 163. Rule for reducing a Common Fraction to a Decimal? Explain. 164. How can Decimals be written as Common Fractions ? DECIMAL SYSTEM OF MONEY, WEIGHTS, AND MEASURES. 167. In this currency, the dollar is the unit, cents and mills being decimals of a dollar. Thus, $3.62 represents three dollars and sixty-two cents; $4.085 represents four dollars, eight cents, and five mills; etc. Figures at the right of the third decimal place represent parts of a mill; thus, $5.36275 dollars, 36 cents, 2 mills, and The terms eagle and dime are not much used. of a mill. Eagles and dollars are read together as dollars, and dimes and cents as cents; thus, $47.843 is read 47 dollars, 84 cents, 3 mills. Mills are often written and read as fractions of a cent; thus, $0.122, twelve cents and a half. 168. Reduction is the changing of a quantity to units of greater or less value without changing the value of the quantity expressed. 169. Dollars are reduced to cents by moving the decimal point two places to the right, and to mills by moving the decimal point three places to the right. Thus, $6=600 cents =6000 mills. 170. Cents are reduced to dollars by moving the decimal point two places to the left. Mills are reduced to dollars by moving the decimal point three places to the left. Thus, 3789 cents $37.89; and 3789 mills $3.789. 171. Oral Exercises. 1. Reduce $47 to cents. 2. Reduce $ 34.56 to cents. 3. Reduce $3.456 to mills. 4. Reduce $483 to cents; to mills. 5. Reduce $6.84 to cents; to mills. 6. Reduce $1.876 to mills. 7. Reduce 564 cents to dollars. 8. Reduce 3692 mills to dollars. 9. Reduce 87694 cents to dollars. 10. Reduce 76843 mills to dollars. = = Write the answers to these ten examples. 11. If to pay for a knife at $2, a pocket-book at $ 3, a lot of paper and envelopes at $1.25, I have only a ten-dollar bill, how much change ought I to receive back?. 12. If I had $ 75, and paid out of it three 10's, four 5's, two 2's, and 62 cents, how much should I have left? 172. When a decimal can be reduced to a common fraction with not more than one figure as its denominator, instead of multiplying by the decimal, it is often easier to use this common fraction as a multiplier. Thus, in United States currency, instead of multiplying by the number expressing the number of cents, in practice we often use the common fractions in the following 13. What cost 64 yards of cloth at $0.87 a yard? Solution. $0.87}=} of a dollar. If a yard is worth of a dollar, 64 yards would be worth 64 times of a dollar, or of 64 dollars, or $56, Ans. 173. Price is the assigned value of a unit of any article; cost is the assigned value of the whole, or of a number of units, of the quantity. 174. The rules given for operations in decimals apply to operations in United States Money. 14. Bought a hat for $4.50, a coat for $18.75, a vest for $5.25, and a pair of boots for $5; what did I pay for all? 15. If apples are worth $2.50 a barrel, what are 3 barrels worth? 16. When 8 cords of wood are worth $ 44, what is the value of 1 cord? 17. At $6 a ton how many tons of coal can I buy for $24? Solution. I can buy as many tons as $6 is contained times in $24; $24 $6=4; hence, I can buy 4 tons. 18. What cost 48 barrels of apples at $1.37 a barrel? Solution. $1.371 = $18. 48 barrels at $1 a barrel would cost $48. of a dollar more on each barrel would be of 48 dollars, or $18; $48 +$18-$66, Ans. 19. What cost 48 pounds of raisins at 12 cents a pound? 20. What cost 54 yards of calico at 163 cents a yard? 21. What cost 74 bushels of apples at 333 cents a bushel? 22. What cost 40 pairs of gloves at 50 cents a pair? 23. How many pounds of sugar at 12 cents a pound may be bought for 3 bushels of corn at 87 cents a bushel? (First find how many pounds for 1 bushel.) 175. Written Exercises. 24. Paid $87.50 for a horse, $145.25 for a pair of oxen, $14.25 for a wagon, and $ 45.75 for a cart; what did I pay for all? 25. A man who owed $699.60, paid $164.67; how much did he still owe? 26. Bought a farm for $ 3684.75, and stock and tools for the farm for $1476.25; how much more did I pay for the farm than for the stock and tools? 27. If 12 gentlemen have $7497.84 apiece, what sum have they all? 28. If 45 persons deposit $ 346.25 each in a savings-bank, how many dollars do they deposit? 29. Divide $69345.36 equally among 18 men. |
