whole number has particular reference to the right hand figure, i. e., when all the orders of units are read together, their aggregate amount is so many units, so the aggregate amount of any number in Federal money takes the name of the DENOMINATION on the RIGHT. Thus, 2 cents and 1 mill may be written the same as a whole number, by setting down the 2 (two,) and placing 1 (one,) on its right; as, 21, i. e., 21 mills; also, 3 dimes, 2 cents, and 1 mill are, when written together, equal to 321 mills; 4 dollars, 3 dimes, 2 cents, and 1 mill, are equal to 4321 mills; and, lastly, 5 eagles, 4 dollars, 3 dimes, 2 cents, and 1 mill, are equal to 54321 mills. This very simple mode of expressing the relation of coins, is rendered still more simple by reducing the denominations to two, viz, dollars and cents, which are the only denominations of FEDERAL MONEY that are used, at the present time, for keeping accounts, or carrying on the operations of trade. Since I dime is equal to 10 cents, it follows, that 10 dimes, or 1 dollar, is equal to 10 times 10 cents, equal to 100 cents; and since 100 cents are equal to 1 dollar, it follows, that 1 cent will equal the dth part of a dollar, and hence, any other number of cents will equal that many hundredths part of a dollar. Therefore, any NUMBER of CENTS may be reduced to dollars by dividing IT by 100, and vice versa, any number of dollars may be reduced to cents by multiplying that number, by 100. Now, to divide a number by 100, it is only necessary to cut off Two of the right hand figures, which figures, so cut off, will show the REMAINDER, while the left hand figures will give the QUOTIENT; and to mul tiply by 100, we have only to affix Two ciphers to the RIGHT of the multiplicand. To separate dollars from cents, a point () is used, called the decimal point, the figures on the LEFT of the point, being DOLLARS, and those on the RIGHT of the point, are cENTS; hence, to reduce DOLLARS to cents, and CENTS to dollars, we have the following RULE. First, Affix Two ciphers to the right of the DOLLARS, and call the number thus formed, CENTS; and, Second, Cut off Two figures from the right of the CENTS, by a decimal point, the LEFT hand figures will be DOLLARS, and the RIGHT hand figures, CENTS. EXAMPLES. 1. In 245 dollars, how many cents? Ans. 24500 cts. 2. In 3 dollars, how many cents? How many cents in 7 dollars? 8 dollars? 12 dollars? 125 dollars? 3. How many cents are there in 1 dollar? 10 dollars? 100 dollars? 1000 dollars? 10000 dollars? 4. How many cents are there in 421 dollars? 763 dollars? 562 dollars? 649 dollars? $cts. 5. In 327 cents, how many dollars? Answer 3.27. 6. How many dollars are there, in 100 cents? in 112 cents? 671 cents? 567 cents? 585 cents? 7. How many dollars are there in 101 cents? in 1001 cents? 101010 cents? 2010 cents? 40302010 cents? 8. How many dollars are there in 600500403 cents? in 100 cents? in 1000 cents? in 10000 cents? We have already learned that RATIO does not exist between quantities which are not of the same denomination, hence, DENOMINATE NUMBERS, (so called, because they consist of different denominations,) are irrational, and cannot be compared by any process of reason, till they are reduced to the same denomination; thus, if 1 hundred weight of sugar cost 10 dollars, we cannot say that 2 pounds will cost twice 10 dollars, because hundreds weight and pounds, are not of the same denomination; but we can say, that 2 cwts. would cost twice 10 dollars, because the denominations are the same. We, therefore, see, that when a GIVEN and a REQUIRED quantity, are denominate, they must be reduced to the same name, or kind, before they can be made the subjects of Arithmetical calculation. On this principle, if 1 cwt. of sugar cost $10, it is plain, that the cost of 2 lbs. may be found, because 1 cwt. = 4 qrs., and 4 qrs. = 112 lbs., i. e., if 1 qr. 28 lbs., then it follows, that 4 qrs. will = 4 times 28 lbs. = to 112 lbs., and now we have the price of 112 lbs. given to 10 dollars, and the price of 2 lbs. required, and since both are pounds, it is plain, that the value of 2 lbs. may be found. The best mode of reducing a specified number of ONE denomination to an equivalent number of = ANOTHER denomination is, to find, first, the value of a unit of the former, when reduced to its equivalent value in the latter denomination, which value may be obtained at once from the proper Table, or by calculation, according to the following RULE. If the UNIT required, is of a HIGHER denomination than that to which it is to be reduced, then multiply successively, as MANY of the latter, as are necessary to make one of the next higher denomination, by the numbers which show how many of each intermediate denomination will make a unit of the next higher, till you arrive at THAT denomination, the value of whose UNIT is sought; the last product will be the But, ANSWER. If the required UNIT, is of a LOWER denomination than that to which IT is to be reduced, then divide a UNIT of the latter successively, by the numbers which show how many of each intermediate denomination are necessary to make ONE of the next higher, until you have arrived at that denomination in which the required UNIT is found, the last quotient will be the ANSWER. EXAMPLES. 1. How many mills are there in ONE dime? mills. Thus, 10× 10=100 mills. 2. What part of an Eagle is ONE dime? E. Thus, 1÷10÷10= toof ANSWER. 3. How many farthings are there in ONE pound? far. Thus, 4x 12 x 20=960 farthings. Answer. 4. What part of ONE pound is one penny? £ £ Thus, 1÷20÷12=1 of 2 of 1 to 10 Ans. 5. How many grains are there in ONE ounce troy weight? grs. Thus, 24×20=480 grains. Answer. 6. What part of a pound troy, is ONE grain? 7. How many ounces are there in 1 cwt. avoirdupois ? oz. Thus, 16 x 28 x 4=1792 ounces. 8. What part of a ton is ONE dram avoirdupois? T. Thus, 1÷20÷4÷28÷16÷16-1 of 1 of 1 Answer. of of Answer. 9. How many grains are there in ONE ounce, apothecaries' weight? grs. Thus, 20 × 3 × 3=480 grains. Answer. 10. What part of a pound is ONE grain? Thus, 1 ofofofof 1 to 70 Answer. 11. How many gills in ONE bushel, dry measure? gills. Thus, 4×2×8×4=256 gills. Answer. 12. What part of a peck is ONE gill? pk. pk. pk. Thus, 1÷8÷2÷4=1 of 1 of 1 of 1. Ans. 13. How many gills are there in ONE ton, liquid measure? gills. gills. Thus, 4×2×4 × 63 × 2 × 2=8064. 14. What part of a tierce is ONE pint, liquid measure? tier. tier. Thus, 1÷424÷2=1 of 1 of 2 of 1 Answer. 15. How many inches in ONE circle, long measure? inches. inches. Thus, 12 × 3 × 512 × 40 × 8 × 69 × 360=1585267200. Ans. 16. What part of a mile is ONE barley corn? mile. mile. Thus, of of of of of 1 of 1=1000. Ans. 17. In ONE rood, how many square inches? Thus, 144 × 9 × 30 × 40=1568160. 18. ONE square inch is what part of an acre? Thus, of of of of of 1760. Ans. 19. How many cubic inches in ONE ton of square timber? Thus, 1728 × 50=86400. 20. What part of a cubic yard is ONE cubic inch? 1 Thus, 172 of 1 cub. yard. Answer. of 1=56 of a cubic yard. Ans. 21. How many inches in ONE ell English? 22. What part of an Aune, or French ell, is ONE ell Hamburg? Aune. Thus, 24 to 1⁄2 of 3 of 1=11⁄2 of an Aune. Ans. 23. How many seconds are there in ONE sign? Thus, 60 × 60 × 30=108000 seconds. Ans. 34. What part of a revolution is ONE minute? revolu. Thus, of of 11⁄2 of 1=x1600 of a revolution. Ans. 25. In ONE year, how many minutes? Thus, 60 × 24 × 3651=525960. Ans. 26. ONE second is what part of a lunar month? Thus, lu. mo. lu. mo. ofofofofof 1=219200. Ans. 27. In 1 Eagle, how many mills? How many dimes? How many cents? Eagle is one dollar? One dime? 28. What part of an One cent? One mill? One mill is what part of a dollar? 29. In one penny, how many farthings? How many pence in one pound? How many farthings in one shilling? How many in one pound? 30. What part of a pound is one penny? One farthing? One shilling? One farthing is what part of a shilling? What part of a penny? 31. In 1 lb. Troy, how many ounces? how many dwts.? how many grs.? In 1 oz., how many grains? |