Find the decimal of 17 34 by inspection. ,8 of 16 Find the decimal of 12 9 by inspection. ,5 for the odd shilling. Answ. ,865 ,6 of 12* ,40 for the odd farthings. and excess above 37. Answ.,64 Find the decimals of the following compound parts of a pound sterling, by inspection. d. ADDITION OF DECIMALS. Place the numbers under each other according to the value of their places, keeping the decimal point in each row directly under the preceding. Find their sum as in whole numbers, and point off as many places for decimals, as are equal to the greatest number of decimal places in any of the given numbers. The work may be proved as in addition of whole numbers. Examples. Let 3,4+83,1+8,64+3,946+7,5+,8751+,0042+33,145+ 6,752 be added. 3,4 83,1 1. Add 3,5,1007+8,43+9,06+74,17 2. Add ,6489+6,489+64,89+648,9+6489 3. Add ,007493+7493+749,3 + 74,93+7,493+,7493+ ,07493. 4. 70083+7,0083+70,083+700,83 +7008,3 +70083+ ,070083+,0070083. 5. ,935846 + 93,5846 +9358,46+935846+935846+ ,00935846. 6. ,6,35+,035+,0035+,00035+,000035. 7. 7,5+8,43 +6,75+67,5+ 83,96 + 749,6 + 1757 +835,4 +67,413+84,963. 8. 7,005+70,05+700,5+7005 +9,7307 + 97,307+973,07 +9730,7. SUBTRACTION OF DECIMALS. Place the numbers according to their values, then subtract in whole numbers, and point on the decimals as in addition. The work may be proved as in whole numbers. Let the learner perform the preceding and all future operations in Decimals, by reducing the decimal to common fractions, with one common denominator, which will impress on his mind, the nature of decimal of fractions, more, than perhaps could be done by any other explanation. EXAMPLE. 5. From one million take 1004,1+10,041 +100,41 8. From 73,895,84+,873+647,5 take 84,7 +68,53+ 18,75+359,84+1,875 MULTIPLICATION OF DECIMALS. Place the factors, and multiply them as in whole numbers. Point off as many places for decimals in the product as there are decimals in both factors added together, and if there should not be as many figures in the product, supply the deficiency by prefixing ciphers. When pure decimals or mixed numbers are to be multiplied by 10, 100, 1000, &c. move the decimal point, as many places to the right as there are ciphers in the multiplier, annexing ciphers when necessary, and it is done. When one decimal is to be multiplied by another, and that it is not necessary to retain all the decimal places in the product; write the units place of the multiplier, under that figure of the multiplicand, whose place it would be desirable to retain, and set down the rest of the figures in an inverted order. Reject all the figures that are to the right of each multiplying figure, and place the products, so that their right-hand figures may be in a perpendicular line under each other, observing to increase the first figure of every product, with what would arise by the multiplication of the figures rejected, by carrying 1 from 5 to 15; 2 from 15 to 25; 3 from 25 to 35 &c. the sum will be the product required, sufficiently near for most purposes. 1. Multiply 64,1976 by 641967 retn. 3, 4 and 5 decl places. 2. Multiply 1,33333 by,5236 retn. 3, 4 and 5 decl places. 3. Multiply 39,3332 by ,07958 retn. 3, 4 and 5 decl places. 4. Multiply 698,23728 by ,7854 retn. 3, and 4 decl places. 5. Multiply 1378,5754 by 1,7321 retaining 4 decimal places. 6. Multiply 49912,34 by 3,1416 retaining 4 decimal places. 7. Multiply 796,042 by 12,5644 retaining 4 decimal places. 8. Multiply 406,253 by 62,8327 retn 3, 4 and 5 decl places. DIVIVISION OF DECIMALS. Proceed as in whole numbers, and from the right-hand point off as many places for decimals in the quotient as those in the dividend exceed those in the divisor. If the decimal places in the quotient are not as many as the rule requires, supply the deficiency by prefixing ciphers. If there should be a remainder, or the decimal places in the divisor exceed those in the dividend, ciphers may be affixed to the dividend, and the quotient carried on as far as is necessary. When the decimal places in the dividend and divisor are equal, the quotient will be a whole number, provided the divisor is a measure of the dividend; if there is a remainder, and that it is necessary to continue the division, annex to the whole number already found, one decimal place for every cipher annexed to the dividend. In general, four or five places at most, will be as far as may be necessary to continue the division for any practical purpose, if it should not sooner terminate, as the quotient will thereby be within part of the truth.. When the divisor is 10, 100, 1000, &c. division is instantly performed, by removing the decimal point as many places to the left, as the divisor hath ciphers, prefixing ciphers if necessary. |