How do you divide one decimal by another? How many decimal places must the quotient have? If the whole number of figures in the quotient is not as great as the number of decimals required, how do you proceed? EXAMPLES. 1. Divide 0.123428 by 11.8. OPERATION. 11.8)0.123428(0.01046. 118 542 472 708 708 In this example, the dividend contains 6 decimal places, and the divisor but 1; therefore, by the rule the quotient ought to contain 5, but as there are but 4 figures in the quotient, we make up the deficiency by prefixing a cipher before making the decimal point. 2. Divide 3.810688 by 1.12. Ans. 3.4024. Ans. 0.456. Ans. 1.1213. Ans. 9.8008. 38. When there are not as many decimal places in the dividend as in the divisor, we may by ART. 32 annex as many ciphers to the dividend as we please, if we do not change the place of the decimal point. When the number of decimal places are the same in both dividend and divisor, the quotient will be a whole number. When there are not as many decimal places in the dividend as in the divisor, how do you proceed? When the number of decimal places in the dividend is the same as in the divisor, what will the quotient be? 6. Divide 244.431 by 1.2345. In this example, before performing the division, we annex a cipher to the dividend so that it may have as many decimal places as the divisor has; we then perform this 39. When there is still a remainder, and we wish a more accurate quotient, we may continue to annex ciphers and to divide as far as we please, observing the rule for placing the decimal point. Where, in the quotient, we have written the sign + it is to indicate that the quotient is still larger than is written. It frequently happens, as in this example, that the work will never terminate. When there is still a remainder, how may we proceed to obtain a still more accurate value for the quotient? What does the sign + at the right of a quotient indicate? 13. Divide 7.85 by 3.43. 14. Divide 0.478 by 0.58. 15. Divide 0.9009 by 0.4051. Ans. 2.2886+. Ans. 0.824+. Ans. 2.223+. 40. We may, obviously, divide any decimal by 10, 100, 1000, &c., by removing the decimal point as many places to the left as there are ciphers in the divisor; when there are not so many figures to the left of the decimal point, we may prefix ciphers. How may we divide a decimal by 10, 100, 1000, &c.? When in the decimal number there are not as many figures on the left of the decimal point as there are ciphers in the divisor, how do you proceed? FEDERAL MONEY. 41. This is the currency of the United States. Its denomination., or names, are Eagles, Dollars, Dimes, Cents, and Mills. 42. The gold for coinage is not pure, but consists of 22 of pure gold, of silver, and of copper; or, as usually expressed, 22 carats of gold, 1 of silver, and 1 of copper. A carat being part of the whole. The standard for silver is 1489 of pure silver, to 179 of pure copper; which, in carats, is 21 of silver, and 59 Where is Federal money used? What are its denominations? Which are coined from gold? Which from silver? Which from copper Which one is never coined? What metals are mixed with gold for coining? In gold coins, what is the ratio of the copper and silver to the gold? What is a carat? What is the standard for silver coins? What is the ratio when estimated in carats? Is the copper for copper coins also alloyed? Repeat the table of Federal Money. 43. Since the different denominations succeed each other in a ten-fold ratio, as in whole numbers and decimals, it is plain that the preceding rules for decimals are applicable to this currency. Feder money ought never to be treated as denominate numbers, since it is by far the simplest and best way to consider its denominations the same as decimals. To make this more clear, we will give the following table of Federal money? F TABLE. Tenths of a dollar, or dimes. 4 4=$4444, 44 cents, 4 mills. 4 4 4 $444, 44 cents, 4 mills. $44, 44 cents, 4 mills. $4, 44 cents, 4 mills. 44 cents, 4 mills. 4 cents, 4 mills. 0.0 0 4 4 mills. It is customary in accounts to use only dollars, cents, and mills, so that eagles are expressed in dollars; and dimes in cents. In what ratio do the different denominations of Federal Money decrease? Are the rules for decimals applicable to this currency? Should Federal Money be treated as denominate numbers? In accounts, which denominations only are used? How then are eagles expressed? How are dimes expressed? Thus 5 eagles and six dollars is the same as 56 dollars. 4 dimes and 5 cents is the same as 45 cents. 3 dimes 3 cents and 3 mills is the same as 333 mills. 2 dimes and 2 mills is the same as 202 mills. 1 dollar is the same as 100 cents, which is 1000 mills. 2 dollars is the same as 200 cents, which is 2000 mills. 5 dollars is the same as 500 cents, which is 5000 mills. 7 dollars is the same as 700 cents, which is 7000 mills. |
