lowing manner the eldest was to have a fourth part, and each of the other sons to have equal shares. What was the share of each son? 205. When the decimal places of the divisor exceed those of the dividend. When there are more decimal places in the divisor than in the dividend, annex as many ciphers to the dividend as are necessary to make its decimal places equal to those of the divisor; all the figures of the quotient will then be whole numbers. And always bear in mind that, the number of decimal places in the quotient, is equal to the excess of the number in the dividend over the number in the divisor. 6. Divide 6 by .6. By .06. By .006. By .2. By .3. By .003. By .5. By .005. By .000012. 206. When the division does not terminate. When it is necessary to continue the division further than the figures of the dividend will permit, we may annex ciphers to it, and consider them as decimal places 205. What do you do when the decimal places of the divisor es ceed those of the dividend? What will the quotient then be? ANALYSIS.-We see, that in this example, .06).20(3.333 + the division will never terminate. In such cases, the division should be carried to the third or fourth place, which will give the answer true enough for all practical purposes, and the sign + should then be written, to show that the division may still be continued. 18 20 18 20 18 2 Ans. 3.333 + 3. Divide 37.4 by 4.5. 4. Divide 586.4 by 375. 5. Divide 94.0369 by 81.032. 6. Divide 36.2678 by 2.25 207. United States Currency. If we regard 1 dollar as the unit of United States Currency, all the lower denominations,-dimes, cents, aud mills,--are decimals of the dollar. Hence, all the operations upon United States Money are the same as the corresponding operations on decimal fractions. 206. How do you continue the division after you have brought down all the figures of the dividend? When the division does not terminate, what sign do you place after the quotient? What does it show? 207. What is the unit of United States Currency? What parts of this unit are dimes? What parts are cents? Mills? CONTRACTIONS IN DIVISION. 208. CONTRACTIONS IN DIVISION OF DECIMALS, like that of whole numbers, are short methods of finding the quotients. CASE I. 209. To divide by 10, 100, &c. 1. Divide 479.256 by 10. OPERATION. 10)479.256 47.9256 ANALYSIS.-Removing the decimal point one place to the left, diminishes the value of the decimal ten times; two places, 100 times, &c.; therefore, to divide by 10, 100, 1000, &c., we remove the decimal point as many places to the left as there are ciphers in the divisor. Rule. Remove the decimal point as many places to the left as there are ciphers in the divisor. Examples. 1. Divide 3169.274 by 100; by 1000. 2. Divide 57135.62 by 1000; by 100; by 10. 3. Divide 67.5 by 100; by 1000; by 1000000. NOTE. If there are not as many figures at the left of the decimal point as there are O's in the divisór, prefix ciphers before writing the decimal point. 4. Divide 4.9 by 100; by 1000; by 10000. 5. Divide .30467 by 10; by 100; by 1000. 210. To divide so that the quotient may contain a given number of decimals. 208. What are contractions in division of decimals? 1 Divide 754.347385 by 61.34775, and find a quotient which shall contain three places of decimals. Rule. I Note the unit of the first quotient figure, and then note the number of figures which the quotient must contain: II. Select, from the left, as many figures of the divisor as you wish places in the quotient, and multiply the figures so selected by the first quotient figure, observing to carry for the figures cast off, as in the contraction of multiplication: III. Use each remainder as a new dividend, and in each following division omit one figure at the right of the divisor. ANALYSIS.-In this example the order of the first quotient figure is tens; hence, there are two places of whole numbers in the quotient; and as there are three decimal places required, there will be five places in all; hence, fire figures of the divisor must be used. In the operation, by the common method, the figures at the right of the vertical line, do not affect the quotient figures. 209. How do you divide by 10, 100, &c. ?-210. Explain the manner ût dividing, so that the quotient shall contain a given number oʻ decimal places. Examples. 1. Divide 59 by .74571345, and let the quotient contain four places of decimals. 2. Divide 17493.407704962 by 495.783269, and let the quotient contain four places of decimals 3. Divide 98.187437 by 8.4765618, and let the quotient contain seven places of decimals. 4. Divide 47194.379457 by 14.73495, and let the quotient contain as many decimal places as there will be integers in it. REDUCTION. 211. A DENOMINATE DECIMAL is one in which the unit of the fraction is denominate. Thus, .3 of a dollar, .7 of a shilling, 8 of a yard, &c., are denominate decimals, in which the units are, 1 dollar, 1 shilling, 1 yard. CASE I. 212. To change a common to a decimal fraction. THE VALUE of a fraction is the quotient of the numerator divided by the denominator (Art. 133). 1. Reduce to a decimal. ANALYSIS.-If we place a decimal point after the 7, and then write any number of O's after it, the value of the numerator will not be changed. If then, we divide by the denominator, the quotient will be the decimal number: Hence, OPERATION. 8) 7.000 .875 Rule.-Annex decimal ciphers to the numerator, and then divide by the denominator, pointing off as in division of decimals 211. What is a denominate decimal? |