NOTE 1. When the division does not terminate, or has been carried as far as is desirable, the remainder may be expressed as a common fraction and made a part of the result; or, the fraction may be rejected and an approximation expressed to the nearest decimal; or, the sign + may be used to mark the incompleteness of the division (Notes, Art. 144). NOTE 2. - When the divisor is an integer, the decimal point in the quotient must invariably be placed directly under or over that of the dividend. If it is desirable to divide without changing decimal points, it may be done, care being taken to give the quotient as many decimal places as those in the dividend exceed those in the divisor. 145. Divide 1.0665 by.00135. 150. Divide 555 by .0037. 146. Divide .08748 by 1.08. 151. Divide.0016016 by .00143. 152. Divide ninety-five and three tenths by two hundred sixty-four thousandths, to the nearest thousandth. 153. Divide one hundred eight and twenty-nine thousandths by seven and two tenths, to three decimal places. 154. If a man can walk three and seventy-five hundredths miles in an hour, in how many hours can he walk seven hundred eighty-seven and five-tenths miles? MISCELLANEOUS EXERCISES. 155. Write four hundred three ten-thousandths; four hundred, and three ten-thousandths. 156. Write and read: 0.00567; 2.13007; 1.00157. 87 162 157. Express as decimals: 10000 ; 100000; 1008000. 158. Find the mixed decimal equal to 43 + 18. 159. From 45 subtract 36.00073. 160. Find the least fraction which is to be added to the sum of 25.7, 8.389, and 23.056 to make the result an integer. 161. Find the difference between 6346 and .6346; 4.2 and .0042; .0000005 and .00005. 162. Simplify, and express the result in a decimal form, 3 +17 + 476 + 3.125. 163. Change .03125 to a common fraction in its smallest terms. 164. Change 4, 23, 17, .136, and .0408 to equivalent decimals having a common denominator, and find their sum. 165. If the year is considered 365.25 days, instead of 365.242264, how great will be the error in 1880 years? 166. The dividend is 7423.973, the quotient 12.130, and the remainder .413. What is the divisor? 167. Divide $7498.70 among A, B, and C, so that A shall have just $749.83 more than each of the others. 168. What is the value of 20004 + (20.104 × 5.07) (6.44.005)? 169. Add 23, 4, and 51.652, expressing the sum to the nearest thousandth. 170. A man willed his property to his three sons, - to the youngest he gave $968.49; to the second, 3.4 times as much as to the youngest; and to the eldest, 3.7 times as much as to the second. Required the value of his property. 171. If a train of cars moves at the rate of 30.25 miles an hour, find to the nearest ten-thousandth how many hours it will take to go 150.75 miles. 1 172. Reduce to its simplest form .01 .0009 .4 x .0005+.002 × .0125° 173. Dividing a certain sum by .027, the quotient is 6116, and the remainder .003. What is the dividend? 174. Bought wheat at $0.94 per bushel, to the amount of $59.22, and sold it for $ 70.56. What was made on a bushel ? 175. What is the cost of 60.5 tons of coal when 0.9 of a ton costs $6.66? 176. Find .3 of .0643 of $ 1728. 177. Divide (12.8.16) by (.128÷.0016). 178. What part of .84 is .012? 179. If .6875 of a gallon of wine costs $3.75, what will 40.25 gallons cost? 180. If of an acre costs $153, what will 46.78 acres cost? 181. If one pound costs $0.18%, how many pounds can be bought for $14.40? 182. If 35.84 cubic feet of water weigh a ton, what will be the weight of 2458.6 cubic feet? 183. If 48 is .08 of some number, what is .7 of it? 184. The product of three factors is 5.76; one of them is .024, another is .06; find the third. 185. How many times is the difference of (0.331) and (0.87) contained in their product? QUESTIONS. 137. What is a decimal fraction? 138. What is a decimal? 139. A mixed decimal ? 141. What is the denominator of a decimal? 142. What is the principle in relation to annexing or cutting off a cipher from the right of a decimal ? 143. How is a decimal reduced to a common fraction? 144. How is a common fraction reduced to a decimal ? 146. How do you multiply in decimals? 147. How do you divide in decimals? UNITED STATES MONEY. AMERIC RICA 149. Coins are pieces of metal stamped by authority of the government to circulate as money. 150. The principal Coins of the United States are: BRONZE, the cent; NICKEL, the five-cent; SILVER, --the dime, quarter-dollar, half-dollar, and dollar; GOLD, -the dollar, quarter-eagle, three-dollar, half-eagle, eagle, and double-eagle. 151. In ordinary business transactions, eagles, dimes, and mills are rarely mentioned, eagles being expressed as dollars, dimes as cents, and mills as a fraction of a cent. Thus, 3 eagles, 2 dollars, 5 dimes, 8 cents, 5 mills are written, $32.581 152. To change cents to mills, multiply by 10. Thus, To change dollars to cents, multiply by 100.- 45 cents = 450 mills; $5 = 500 cents, or 5000 mills. 153. To change mills to cents, divide by 10. Thus, To change cents to dollars, divide by 100. 850 mills $0.85; 365 cents = $3.65; 47000 mills = $47. = = 154. The dollar being the unit, of which cents are hundredths and mills are thousandths, it follows that All the rules for the processes in decimals are applicable to processes in United States money. ORAL EXERCISES. 1. How many mills in 7 cents? In 7 cents 4 mills? 2. How many cents in 70 mills? In 75 mills? 11. In changing cents to dollars, how many places to the left is the decimal point moved ? Change 6370 mills to dollars. |